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LHA VFNS SV is broken #215

Closed
felixhekhorn opened this issue Feb 16, 2023 · 4 comments · Fixed by #222
Closed

LHA VFNS SV is broken #215

felixhekhorn opened this issue Feb 16, 2023 · 4 comments · Fixed by #222
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@giacomomagni
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bug Something isn't working

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@felixhekhorn
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as the title says ...

  • f390a04 should be needed since fact_to_ren is gone (it is still in use inside the benchmark apparently)
  • FFNS is not affected - so ad seems not to be the culprit, which leaves ome
  • broken both at NLO and NNLO

(first detected inside #148 but then I found out it is already broken in master )

full benchmark output 
$ poe lha
Poe => python benchmarks/lha_paper_bench.py
 ──────────────────────────────────────── 
  Theories: 2 OCards: 1 PDFs: 1 ext: LHA  
 ──────────────────────────────────────── 
Computing for theory=0ab0ccc, ocard=4a8ce73 and pdf=ToyLH ...
Interpolation: number of points = 60, polynomial degree = 4, logarithmic = True
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.02e+01 - 3.06e+04 - inf], ref=2.0000000000000004 @ 3
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.02e+01 - 3.06e+04 - inf], ref=2.0000000000000004 @ 3
Strong Coupling: a_s(µ_R^2=2.000000)^(nf=3)=0.027852=0.350000/(4π)
Electromagnetic Coupling: a_em(µ_R^2=2.000000)^(nf=3)=0.000597=0.007496/(4π)
Prepare threshold operator
Evolution: skipping unity operator at 2.000000e+00
Matching: computing operators - 1/60 took: 555.408414 s
Matching: computing operators - 2/60 took: 3.618848 s
Matching: computing operators - 3/60 took: 3.581251 s
Matching: computing operators - 4/60 took: 3.267695 s
Matching: computing operators - 5/60 took: 3.284248 s
Matching: computing operators - 6/60 took: 3.023984 s
Matching: computing operators - 7/60 took: 3.093352 s
Matching: computing operators - 8/60 took: 2.781238 s
Matching: computing operators - 9/60 took: 2.904646 s
Matching: computing operators - 10/60 took: 2.869690 s
Matching: computing operators - 11/60 took: 2.613527 s
Matching: computing operators - 12/60 took: 2.504955 s
Matching: computing operators - 13/60 took: 2.597960 s
Matching: computing operators - 14/60 took: 2.453539 s
Matching: computing operators - 15/60 took: 2.399348 s
Matching: computing operators - 16/60 took: 2.418091 s
Matching: computing operators - 17/60 took: 2.353446 s
Matching: computing operators - 18/60 took: 2.266970 s
Matching: computing operators - 19/60 took: 2.294440 s
Matching: computing operators - 20/60 took: 2.386847 s
Matching: computing operators - 21/60 took: 1.998182 s
Matching: computing operators - 22/60 took: 1.889146 s
Matching: computing operators - 23/60 took: 2.012705 s
Matching: computing operators - 24/60 took: 1.956778 s
Matching: computing operators - 25/60 took: 1.710953 s
Matching: computing operators - 26/60 took: 1.620387 s
Matching: computing operators - 27/60 took: 1.634152 s
Matching: computing operators - 28/60 took: 1.439004 s
Matching: computing operators - 29/60 took: 1.417415 s
Matching: computing operators - 30/60 took: 1.205196 s
Matching: computing operators - 31/60 took: 1.110263 s
Matching: computing operators - 32/60 took: 1.104760 s
Matching: computing operators - 33/60 took: 0.902312 s
Matching: computing operators - 34/60 took: 0.852088 s
Matching: computing operators - 35/60 took: 0.787897 s
Matching: computing operators - 36/60 took: 0.451019 s
Matching: computing operators - 37/60 took: 0.387294 s
Matching: computing operators - 38/60 took: 0.359559 s
Matching: computing operators - 39/60 took: 0.318618 s
Matching: computing operators - 40/60 took: 0.294624 s
Matching: computing operators - 41/60 took: 0.278337 s
Matching: computing operators - 42/60 took: 0.254938 s
Matching: computing operators - 43/60 took: 0.254668 s
Matching: computing operators - 44/60 took: 0.237301 s
Matching: computing operators - 45/60 took: 0.222643 s
Matching: computing operators - 46/60 took: 0.221048 s
Matching: computing operators - 47/60 took: 0.197962 s
Matching: computing operators - 48/60 took: 0.193463 s
Matching: computing operators - 49/60 took: 0.193076 s
Matching: computing operators - 50/60 took: 0.175162 s
Matching: computing operators - 51/60 took: 0.163688 s
Matching: computing operators - 52/60 took: 0.148339 s
Matching: computing operators - 53/60 took: 0.142525 s
Matching: computing operators - 54/60 took: 0.130004 s
Matching: computing operators - 55/60 took: 0.120414 s
Matching: computing operators - 56/60 took: 0.111200 s
Matching: computing operators - 57/60 took: 0.104844 s
Matching: computing operators - 58/60 took: 0.100119 s
Matching: computing operators - 59/60 took: 0.091142 s
Matching: computing operators - 60/60 took: 0.071365 s
Matching: Total time 635.013781 s
Prepare threshold operator
Evolution: computing operators 2.000000e+00 -> 2.025000e+01, nf=4
Evolution: µ_R^2 distance: 1.000000e+00 -> 1.012500e+01
Scale Variation: (µ_F/µ_R)^2 = 2.000000e+00, mode: exponentiated
Evolution: a_s distance: 3.388408e-02 -> 1.930751e-02
Evolution: order: (2, 0), solution strategy: iterate-exact
Evolution: computing operators - 1/60 took: 51.560449 s
Evolution: computing operators - 2/60 took: 2.179604 s
Evolution: computing operators - 3/60 took: 2.334552 s
Evolution: computing operators - 4/60 took: 2.204881 s
Evolution: computing operators - 5/60 took: 2.124159 s
Evolution: computing operators - 6/60 took: 2.008763 s
Evolution: computing operators - 7/60 took: 1.959497 s
Evolution: computing operators - 8/60 took: 1.994453 s
Evolution: computing operators - 9/60 took: 1.978629 s
Evolution: computing operators - 10/60 took: 1.979148 s
Evolution: computing operators - 11/60 took: 1.875449 s
Evolution: computing operators - 12/60 took: 1.820837 s
Evolution: computing operators - 13/60 took: 1.747358 s
Evolution: computing operators - 14/60 took: 1.716158 s
Evolution: computing operators - 15/60 took: 1.659612 s
Evolution: computing operators - 16/60 took: 1.644497 s
Evolution: computing operators - 17/60 took: 1.594689 s
Evolution: computing operators - 18/60 took: 1.580426 s
Evolution: computing operators - 19/60 took: 1.520359 s
Evolution: computing operators - 20/60 took: 1.500948 s
Evolution: computing operators - 21/60 took: 1.485357 s
Evolution: computing operators - 22/60 took: 1.442026 s
Evolution: computing operators - 23/60 took: 1.401006 s
Evolution: computing operators - 24/60 took: 1.342475 s
Evolution: computing operators - 25/60 took: 1.316467 s
Evolution: computing operators - 26/60 took: 1.302603 s
Evolution: computing operators - 27/60 took: 1.230668 s
Evolution: computing operators - 28/60 took: 1.197779 s
Evolution: computing operators - 29/60 took: 1.155959 s
Evolution: computing operators - 30/60 took: 1.113205 s
Evolution: computing operators - 31/60 took: 1.102703 s
Evolution: computing operators - 32/60 took: 1.076845 s
Evolution: computing operators - 33/60 took: 1.023173 s
Evolution: computing operators - 34/60 took: 0.959251 s
Evolution: computing operators - 35/60 took: 0.922587 s
Evolution: computing operators - 36/60 took: 0.900117 s
Evolution: computing operators - 37/60 took: 0.864429 s
Evolution: computing operators - 38/60 took: 0.845778 s
Evolution: computing operators - 39/60 took: 0.812109 s
Evolution: computing operators - 40/60 took: 0.793377 s
Evolution: computing operators - 41/60 took: 0.726660 s
Evolution: computing operators - 42/60 took: 0.671862 s
Evolution: computing operators - 43/60 took: 0.643749 s
Evolution: computing operators - 44/60 took: 0.639750 s
Evolution: computing operators - 45/60 took: 0.601410 s
Evolution: computing operators - 46/60 took: 0.538288 s
Evolution: computing operators - 47/60 took: 0.531862 s
Evolution: computing operators - 48/60 took: 0.496186 s
Evolution: computing operators - 49/60 took: 0.471586 s
Evolution: computing operators - 50/60 took: 0.460267 s
Evolution: computing operators - 51/60 took: 0.458169 s
Evolution: computing operators - 52/60 took: 0.455725 s
Evolution: computing operators - 53/60 took: 0.444246 s
Evolution: computing operators - 54/60 took: 0.434378 s
Evolution: computing operators - 55/60 took: 0.426662 s
Evolution: computing operators - 56/60 took: 0.416938 s
Evolution: computing operators - 57/60 took: 0.410878 s
Evolution: computing operators - 58/60 took: 0.417360 s
Evolution: computing operators - 59/60 took: 0.402494 s
Evolution: computing operators - 60/60 took: 0.269390 s
Evolution: Total time 119.217876 s
Matching: computing operators - 1/60 took: 3.631363 s
Matching: computing operators - 2/60 took: 3.480852 s
Matching: computing operators - 3/60 took: 3.417121 s
Matching: computing operators - 4/60 took: 3.299129 s
Matching: computing operators - 5/60 took: 3.186405 s
Matching: computing operators - 6/60 took: 3.025969 s
Matching: computing operators - 7/60 took: 3.194254 s
Matching: computing operators - 8/60 took: 2.804753 s
Matching: computing operators - 9/60 took: 2.981696 s
Matching: computing operators - 10/60 took: 3.025283 s
Matching: computing operators - 11/60 took: 2.837599 s
Matching: computing operators - 12/60 took: 2.587667 s
Matching: computing operators - 13/60 took: 2.728609 s
Matching: computing operators - 14/60 took: 2.576950 s
Matching: computing operators - 15/60 took: 2.564460 s
Matching: computing operators - 16/60 took: 2.328114 s
Matching: computing operators - 17/60 took: 2.483604 s
Matching: computing operators - 18/60 took: 2.277520 s
Matching: computing operators - 19/60 took: 2.155863 s
Matching: computing operators - 20/60 took: 2.182983 s
Matching: computing operators - 21/60 took: 1.977293 s
Matching: computing operators - 22/60 took: 1.781261 s
Matching: computing operators - 23/60 took: 2.005851 s
Matching: computing operators - 24/60 took: 1.882504 s
Matching: computing operators - 25/60 took: 1.713041 s
Matching: computing operators - 26/60 took: 1.652733 s
Matching: computing operators - 27/60 took: 1.631904 s
Matching: computing operators - 28/60 took: 1.455224 s
Matching: computing operators - 29/60 took: 1.441447 s
Matching: computing operators - 30/60 took: 1.238496 s
Matching: computing operators - 31/60 took: 1.150049 s
Matching: computing operators - 32/60 took: 1.139607 s
Matching: computing operators - 33/60 took: 0.937206 s
Matching: computing operators - 34/60 took: 0.906531 s
Matching: computing operators - 35/60 took: 0.813351 s
Matching: computing operators - 36/60 took: 0.492194 s
Matching: computing operators - 37/60 took: 0.409425 s
Matching: computing operators - 38/60 took: 0.383995 s
Matching: computing operators - 39/60 took: 0.393396 s
Matching: computing operators - 40/60 took: 0.328087 s
Matching: computing operators - 41/60 took: 0.309399 s
Matching: computing operators - 42/60 took: 0.274201 s
Matching: computing operators - 43/60 took: 0.278593 s
Matching: computing operators - 44/60 took: 0.247324 s
Matching: computing operators - 45/60 took: 0.263437 s
Matching: computing operators - 46/60 took: 0.228659 s
Matching: computing operators - 47/60 took: 0.220621 s
Matching: computing operators - 48/60 took: 0.215470 s
Matching: computing operators - 49/60 took: 0.199842 s
Matching: computing operators - 50/60 took: 0.190171 s
Matching: computing operators - 51/60 took: 0.180763 s
Matching: computing operators - 52/60 took: 0.171516 s
Matching: computing operators - 53/60 took: 0.166607 s
Matching: computing operators - 54/60 took: 0.150954 s
Matching: computing operators - 55/60 took: 0.139186 s
Matching: computing operators - 56/60 took: 0.131514 s
Matching: computing operators - 57/60 took: 0.124693 s
Matching: computing operators - 58/60 took: 0.119720 s
Matching: computing operators - 59/60 took: 0.110880 s
Matching: computing operators - 60/60 took: 0.091998 s
Matching: Total time 84.348563 s
Evolution: computing operators 2.025000e+01 -> 1.000000e+04, nf=5
Evolution: µ_R^2 distance: 1.012500e+01 -> 5.000000e+03
Scale Variation: (µ_F/µ_R)^2 = 2.000000e+00, mode: exponentiated
Evolution: a_s distance: 1.890791e-02 -> 9.651589e-03
Evolution: order: (2, 0), solution strategy: iterate-exact
Evolution: computing operators - 1/60 took: 2.167329 s
Evolution: computing operators - 2/60 took: 2.224420 s
Evolution: computing operators - 3/60 took: 2.134760 s
Evolution: computing operators - 4/60 took: 2.047787 s
Evolution: computing operators - 5/60 took: 1.972052 s
Evolution: computing operators - 6/60 took: 1.977161 s
Evolution: computing operators - 7/60 took: 1.967400 s
Evolution: computing operators - 8/60 took: 1.931480 s
Evolution: computing operators - 9/60 took: 1.967899 s
Evolution: computing operators - 10/60 took: 1.905548 s
Evolution: computing operators - 11/60 took: 1.849138 s
Evolution: computing operators - 12/60 took: 1.853768 s
Evolution: computing operators - 13/60 took: 1.955068 s
Evolution: computing operators - 14/60 took: 1.872453 s
Evolution: computing operators - 15/60 took: 1.801568 s
Evolution: computing operators - 16/60 took: 1.660310 s
Evolution: computing operators - 17/60 took: 1.708119 s
Evolution: computing operators - 18/60 took: 1.610310 s
Evolution: computing operators - 19/60 took: 1.599756 s
Evolution: computing operators - 20/60 took: 1.523260 s
Evolution: computing operators - 21/60 took: 1.492825 s
Evolution: computing operators - 22/60 took: 1.448668 s
Evolution: computing operators - 23/60 took: 1.391444 s
Evolution: computing operators - 24/60 took: 1.415114 s
Evolution: computing operators - 25/60 took: 1.402185 s
Evolution: computing operators - 26/60 took: 1.301326 s
Evolution: computing operators - 27/60 took: 1.273688 s
Evolution: computing operators - 28/60 took: 1.210672 s
Evolution: computing operators - 29/60 took: 1.150379 s
Evolution: computing operators - 30/60 took: 1.148426 s
Evolution: computing operators - 31/60 took: 1.184241 s
Evolution: computing operators - 32/60 took: 1.244703 s
Evolution: computing operators - 33/60 took: 1.101626 s
Evolution: computing operators - 34/60 took: 1.029721 s
Evolution: computing operators - 35/60 took: 0.961160 s
Evolution: computing operators - 36/60 took: 1.000691 s
Evolution: computing operators - 37/60 took: 0.908032 s
Evolution: computing operators - 38/60 took: 0.872508 s
Evolution: computing operators - 39/60 took: 0.830739 s
Evolution: computing operators - 40/60 took: 0.791626 s
Evolution: computing operators - 41/60 took: 0.818513 s
Evolution: computing operators - 42/60 took: 0.820803 s
Evolution: computing operators - 43/60 took: 0.776083 s
Evolution: computing operators - 44/60 took: 0.668451 s
Evolution: computing operators - 45/60 took: 0.636101 s
Evolution: computing operators - 46/60 took: 0.594499 s
Evolution: computing operators - 47/60 took: 0.563873 s
Evolution: computing operators - 48/60 took: 0.566465 s
Evolution: computing operators - 49/60 took: 0.551779 s
Evolution: computing operators - 50/60 took: 0.563631 s
Evolution: computing operators - 51/60 took: 0.531590 s
Evolution: computing operators - 52/60 took: 0.549988 s
Evolution: computing operators - 53/60 took: 0.628506 s
Evolution: computing operators - 54/60 took: 0.524256 s
Evolution: computing operators - 55/60 took: 0.490398 s
Evolution: computing operators - 56/60 took: 0.508757 s
Evolution: computing operators - 57/60 took: 0.544718 s
Evolution: computing operators - 58/60 took: 0.483292 s
Evolution: computing operators - 59/60 took: 0.506089 s
Evolution: computing operators - 60/60 took: 0.343099 s
Evolution: Total time 72.585549 s
Compute external result
Interpolation: number of points = 60, polynomial degree = 4, logarithmic = True

Log added, hash=65837f9ecd469a702501d256633d7777fc9ef0aba150b1fcc8c1e63db46b1097


 ─── 
  S  
 ─── 
               x       Q2         eko     eko_error         LHA  percent_error
0   1.000000e-07  10000.0  339.616039  1.239605e-03  359.827205      -5.616909
1   1.000000e-06  10000.0  169.430184  6.482979e-04  178.523012      -5.093365
2   1.000000e-05  10000.0   79.759077  3.289767e-04   83.482841      -4.460514
3   1.000000e-04  10000.0   34.762130  1.423588e-04   36.108687      -3.729178
4   1.000000e-03  10000.0   13.636680  6.151189e-05   14.027097      -2.783308
5   1.000000e-02  10000.0    4.659968  1.587070e-05    4.728020      -1.439336
6   1.000000e-01  10000.0    1.416514  1.553992e-05    1.409249       0.515530
7   3.000000e-01  10000.0    0.522160  1.896478e-06    0.513659       1.655152
8   5.000000e-01  10000.0    0.152633  2.820459e-07    0.148882       2.518924
9   7.000000e-01  10000.0    0.022617  1.020571e-08    0.021839       3.562039
10  9.000000e-01  10000.0    0.000354  2.957331e-10    0.000337       5.017067

 ─── 
  g  
 ─── 
               x       Q2          eko     eko_error          LHA  percent_error
0   1.000000e-07  10000.0  1072.401361  4.027594e-03  1123.900000      -4.582137
1   1.000000e-06  10000.0   506.257851  1.871397e-03   527.630000      -4.050594
2   1.000000e-05  10000.0   222.213814  9.234989e-04   230.060000      -3.410495
3   1.000000e-04  10000.0    88.164189  3.473092e-04    90.599000      -2.687459
4   1.000000e-03  10000.0    30.040593  1.360428e-04    30.589000      -1.792823
5   1.000000e-02  10000.0     7.751329  3.924583e-05     7.799600      -0.618890
6   1.000000e-01  10000.0     0.858417  4.379506e-06     0.848010       1.227240
7   3.000000e-01  10000.0     0.079773  1.621094e-07     0.077817       2.513264
8   5.000000e-01  10000.0     0.007737  1.658740e-08     0.007494       3.241634
9   7.000000e-01  10000.0     0.000376  1.355488e-09     0.000362       3.842141
10  9.000000e-01  10000.0     0.000001  2.155473e-11     0.000001      13.856706

 ─── 
  V  
 ─── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000197  4.268296e-10  0.000205      -4.168268
1   1.000000e-06  10000.0  0.000975  2.711200e-09  0.001012      -3.642784
2   1.000000e-05  10000.0  0.004692  1.799233e-08  0.004841      -3.070418
3   1.000000e-04  10000.0  0.021744  9.760618e-08  0.022287      -2.438539
4   1.000000e-03  10000.0  0.095038  3.161530e-07  0.096697      -1.716119
5   1.000000e-02  10000.0  0.364573  8.660442e-07  0.367610      -0.826018
6   1.000000e-01  10000.0  0.818579  2.169208e-07  0.814570       0.492161
7   3.000000e-01  10000.0  0.473697  1.025871e-08  0.466310       1.584103
8   5.000000e-01  10000.0  0.149513  1.099244e-07  0.145924       2.459507
9   7.000000e-01  10000.0  0.022540  4.471274e-12  0.021778       3.496242
10  9.000000e-01  10000.0  0.000353  2.217445e-13  0.000337       4.907302

 ──── 
  V3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000051  1.085810e-10  0.000054      -4.265762
1   1.000000e-06  10000.0  0.000256  6.931954e-10  0.000266      -3.747153
2   1.000000e-05  10000.0  0.001241  4.621166e-09  0.001282      -3.182931
3   1.000000e-04  10000.0  0.005800  2.514158e-08  0.005953      -2.564825
4   1.000000e-03  10000.0  0.025732  8.292392e-08  0.026219      -1.858419
5   1.000000e-02  10000.0  0.102829  2.380853e-07  0.103870      -1.001958
6   1.000000e-01  10000.0  0.278812  8.414734e-08  0.278030       0.281314
7   3.000000e-01  10000.0  0.217385  6.671633e-09  0.214390       1.397210
8   5.000000e-01  10000.0  0.087845  6.713150e-08  0.085856       2.316833
9   7.000000e-01  10000.0  0.016536  3.757110e-12  0.015994       3.390223
10  9.000000e-01  10000.0  0.000318  1.819498e-13  0.000304       4.507533

 ──── 
  T3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000040  9.299750e-11  0.000042      -3.940156
1   1.000000e-06  10000.0  0.000208  8.034600e-10  0.000216      -3.491020
2   1.000000e-05  10000.0  0.001040  2.616852e-09  0.001072      -2.998760
3   1.000000e-04  10000.0  0.005003  1.875519e-08  0.005129      -2.456939
4   1.000000e-03  10000.0  0.022687  5.839362e-08  0.023108      -1.821185
5   1.000000e-02  10000.0  0.091973  3.400876e-07  0.092922      -1.021993
6   1.000000e-01  10000.0  0.259090  1.562518e-07  0.258464       0.242082
7   3.000000e-01  10000.0  0.211491  3.686092e-07  0.208615       1.378806
8   5.000000e-01  10000.0  0.087110  5.160678e-08  0.085143       2.310524
9   7.000000e-01  10000.0  0.016510  3.799707e-12  0.015969       3.389132
10  9.000000e-01  10000.0  0.000318  2.476709e-13  0.000304       4.505793

 ──── 
  T8  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  2.147487  2.080959e-06  2.144205       0.153080
1   1.000000e-06  10000.0  1.706038  8.398341e-06  1.704012       0.118934
2   1.000000e-05  10000.0  1.358086  5.432880e-06  1.356841       0.091772
3   1.000000e-04  10000.0  1.091848  6.239790e-06  1.090687       0.106387
4   1.000000e-03  10000.0  0.922909  2.745610e-06  0.922497       0.044614
5   1.000000e-02  10000.0  0.926738  3.818796e-06  0.926990      -0.027223
6   1.000000e-01  10000.0  0.978600  4.452068e-07  0.972460       0.631369
7   3.000000e-01  10000.0  0.490575  8.424698e-07  0.482799       1.610435
8   5.000000e-01  10000.0  0.150705  8.490821e-08  0.147079       2.465464
9   7.000000e-01  10000.0  0.022567  4.551369e-12  0.021804       3.496465
10  9.000000e-01  10000.0  0.000353  3.026426e-13  0.000337       4.908595

 ───── 
  T15  
 ───── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  4.294705  4.347855e-06  4.286205       0.198315
1   1.000000e-06  10000.0  3.411180  1.685664e-05  3.405012       0.181165
2   1.000000e-05  10000.0  2.711832  1.121274e-05  2.706841       0.184384
3   1.000000e-04  10000.0  2.162894  1.716257e-05  2.159887       0.139198
4   1.000000e-03  10000.0  1.752438  5.308784e-06  1.750197       0.128068
5   1.000000e-02  10000.0  1.490106  6.553041e-06  1.487630       0.166442
6   1.000000e-01  10000.0  1.138688  4.534517e-06  1.130425       0.730941
7   3.000000e-01  10000.0  0.507453  9.312748e-07  0.499290       1.634979
8   5.000000e-01  10000.0  0.151898  9.600901e-08  0.148234       2.471356
9   7.000000e-01  10000.0  0.022594  5.642662e-10  0.021831       3.496704
10  9.000000e-01  10000.0  0.000353  3.831735e-11  0.000337       4.911163

 ───── 
  T24  
 ───── 
               x       Q2        eko     eko_error        LHA  percent_error
0   1.000000e-07  10000.0  37.232652  7.885109e-05  38.702205      -3.797079
1   1.000000e-06  10000.0  23.448295  1.015568e-04  24.293012      -3.477200
2   1.000000e-05  10000.0  14.254363  3.639292e-05  14.702841      -3.050281
3   1.000000e-04  10000.0   8.278408  6.031195e-05   8.492687      -2.523105
4   1.000000e-03  10000.0   4.558022  1.183903e-05   4.640597      -1.779405
5   1.000000e-02  10000.0   2.430410  9.957328e-06   2.448670      -0.745723
6   1.000000e-01  10000.0   1.239434  1.359922e-05   1.231629       0.633703
7   3.000000e-01  10000.0   0.512802  7.057244e-07   0.504505       1.644698
8   5.000000e-01  10000.0   0.152117  1.824578e-07   0.148421       2.490151
9   7.000000e-01  10000.0   0.022599  5.002883e-09   0.021830       3.520200
10  9.000000e-01  10000.0   0.000353  1.979745e-10   0.000337       4.950166
Computing for theory=90736c5, ocard=4a8ce73 and pdf=ToyLH ...
Interpolation: number of points = 60, polynomial degree = 4, logarithmic = True
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.02e+01 - 3.06e+04 - inf], ref=2.0000000000000004 @ 3
ThresholdsAtlas [0.00e+00 - 2.00e+00 - 2.02e+01 - 3.06e+04 - inf], ref=2.0000000000000004 @ 3
Strong Coupling: a_s(µ_R^2=2.000000)^(nf=3)=0.027852=0.350000/(4π)
Electromagnetic Coupling: a_em(µ_R^2=2.000000)^(nf=3)=0.000597=0.007496/(4π)
Prepare threshold operator
Evolution: skipping unity operator at 2.000000e+00
Matching: computing operators - 1/60 took: 3.331426 s
Matching: computing operators - 2/60 took: 3.432851 s
Matching: computing operators - 3/60 took: 3.287515 s
Matching: computing operators - 4/60 took: 3.217003 s
Matching: computing operators - 5/60 took: 3.214532 s
Matching: computing operators - 6/60 took: 3.105048 s
Matching: computing operators - 7/60 took: 3.152589 s
Matching: computing operators - 8/60 took: 2.858591 s
Matching: computing operators - 9/60 took: 3.210632 s
Matching: computing operators - 10/60 took: 3.085438 s
Matching: computing operators - 11/60 took: 2.611853 s
Matching: computing operators - 12/60 took: 2.487008 s
Matching: computing operators - 13/60 took: 2.586112 s
Matching: computing operators - 14/60 took: 2.432982 s
Matching: computing operators - 15/60 took: 2.305304 s
Matching: computing operators - 16/60 took: 2.284363 s
Matching: computing operators - 17/60 took: 2.281705 s
Matching: computing operators - 18/60 took: 2.218050 s
Matching: computing operators - 19/60 took: 2.128602 s
Matching: computing operators - 20/60 took: 2.149831 s
Matching: computing operators - 21/60 took: 1.947688 s
Matching: computing operators - 22/60 took: 1.769713 s
Matching: computing operators - 23/60 took: 1.987362 s
Matching: computing operators - 24/60 took: 1.854813 s
Matching: computing operators - 25/60 took: 1.685908 s
Matching: computing operators - 26/60 took: 1.632272 s
Matching: computing operators - 27/60 took: 1.633979 s
Matching: computing operators - 28/60 took: 1.453767 s
Matching: computing operators - 29/60 took: 1.485702 s
Matching: computing operators - 30/60 took: 1.244184 s
Matching: computing operators - 31/60 took: 1.146432 s
Matching: computing operators - 32/60 took: 1.124042 s
Matching: computing operators - 33/60 took: 0.908788 s
Matching: computing operators - 34/60 took: 0.825760 s
Matching: computing operators - 35/60 took: 0.772697 s
Matching: computing operators - 36/60 took: 0.452518 s
Matching: computing operators - 37/60 took: 0.377101 s
Matching: computing operators - 38/60 took: 0.353730 s
Matching: computing operators - 39/60 took: 0.351406 s
Matching: computing operators - 40/60 took: 0.288837 s
Matching: computing operators - 41/60 took: 0.271986 s
Matching: computing operators - 42/60 took: 0.255850 s
Matching: computing operators - 43/60 took: 0.250059 s
Matching: computing operators - 44/60 took: 0.227913 s
Matching: computing operators - 45/60 took: 0.212297 s
Matching: computing operators - 46/60 took: 0.210752 s
Matching: computing operators - 47/60 took: 0.197446 s
Matching: computing operators - 48/60 took: 0.192812 s
Matching: computing operators - 49/60 took: 0.181856 s
Matching: computing operators - 50/60 took: 0.168479 s
Matching: computing operators - 51/60 took: 0.161004 s
Matching: computing operators - 52/60 took: 0.153237 s
Matching: computing operators - 53/60 took: 0.143510 s
Matching: computing operators - 54/60 took: 0.136210 s
Matching: computing operators - 55/60 took: 0.130078 s
Matching: computing operators - 56/60 took: 0.116985 s
Matching: computing operators - 57/60 took: 0.105785 s
Matching: computing operators - 58/60 took: 0.101142 s
Matching: computing operators - 59/60 took: 0.091621 s
Matching: computing operators - 60/60 took: 0.070682 s
Matching: Total time 82.084972 s
Prepare threshold operator
Evolution: computing operators 2.000000e+00 -> 2.025000e+01, nf=4
Evolution: µ_R^2 distance: 4.000000e+00 -> 4.050000e+01
Scale Variation: (µ_F/µ_R)^2 = 5.000000e-01, mode: exponentiated
Evolution: a_s distance: 2.372871e-02 -> 1.569648e-02
Evolution: order: (2, 0), solution strategy: iterate-exact
Evolution: computing operators - 1/60 took: 2.096513 s
Evolution: computing operators - 2/60 took: 2.130743 s
Evolution: computing operators - 3/60 took: 2.098799 s
Evolution: computing operators - 4/60 took: 2.022234 s
Evolution: computing operators - 5/60 took: 1.953830 s
Evolution: computing operators - 6/60 took: 1.887063 s
Evolution: computing operators - 7/60 took: 1.861079 s
Evolution: computing operators - 8/60 took: 1.864365 s
Evolution: computing operators - 9/60 took: 1.843399 s
Evolution: computing operators - 10/60 took: 1.806417 s
Evolution: computing operators - 11/60 took: 1.765366 s
Evolution: computing operators - 12/60 took: 1.701859 s
Evolution: computing operators - 13/60 took: 1.691138 s
Evolution: computing operators - 14/60 took: 1.678225 s
Evolution: computing operators - 15/60 took: 1.636433 s
Evolution: computing operators - 16/60 took: 1.617965 s
Evolution: computing operators - 17/60 took: 1.560943 s
Evolution: computing operators - 18/60 took: 1.546103 s
Evolution: computing operators - 19/60 took: 1.476948 s
Evolution: computing operators - 20/60 took: 1.443598 s
Evolution: computing operators - 21/60 took: 1.447291 s
Evolution: computing operators - 22/60 took: 1.394931 s
Evolution: computing operators - 23/60 took: 1.379689 s
Evolution: computing operators - 24/60 took: 1.357470 s
Evolution: computing operators - 25/60 took: 1.339666 s
Evolution: computing operators - 26/60 took: 1.249745 s
Evolution: computing operators - 27/60 took: 1.234522 s
Evolution: computing operators - 28/60 took: 1.186841 s
Evolution: computing operators - 29/60 took: 1.130033 s
Evolution: computing operators - 30/60 took: 1.076064 s
Evolution: computing operators - 31/60 took: 1.061099 s
Evolution: computing operators - 32/60 took: 1.037659 s
Evolution: computing operators - 33/60 took: 0.987660 s
Evolution: computing operators - 34/60 took: 0.996772 s
Evolution: computing operators - 35/60 took: 0.925777 s
Evolution: computing operators - 36/60 took: 0.991808 s
Evolution: computing operators - 37/60 took: 0.850001 s
Evolution: computing operators - 38/60 took: 0.881498 s
Evolution: computing operators - 39/60 took: 0.812736 s
Evolution: computing operators - 40/60 took: 0.764275 s
Evolution: computing operators - 41/60 took: 0.694798 s
Evolution: computing operators - 42/60 took: 0.681099 s
Evolution: computing operators - 43/60 took: 0.654798 s
Evolution: computing operators - 44/60 took: 0.637272 s
Evolution: computing operators - 45/60 took: 0.604531 s
Evolution: computing operators - 46/60 took: 0.551461 s
Evolution: computing operators - 47/60 took: 0.527767 s
Evolution: computing operators - 48/60 took: 0.487279 s
Evolution: computing operators - 49/60 took: 0.479449 s
Evolution: computing operators - 50/60 took: 0.468180 s
Evolution: computing operators - 51/60 took: 0.464279 s
Evolution: computing operators - 52/60 took: 0.448137 s
Evolution: computing operators - 53/60 took: 0.455092 s
Evolution: computing operators - 54/60 took: 0.431473 s
Evolution: computing operators - 55/60 took: 0.421850 s
Evolution: computing operators - 56/60 took: 0.414452 s
Evolution: computing operators - 57/60 took: 0.412875 s
Evolution: computing operators - 58/60 took: 0.405940 s
Evolution: computing operators - 59/60 took: 0.390171 s
Evolution: computing operators - 60/60 took: 0.269454 s
Evolution: Total time 67.712942 s
Matching: computing operators - 1/60 took: 3.333006 s
Matching: computing operators - 2/60 took: 3.394646 s
Matching: computing operators - 3/60 took: 3.286249 s
Matching: computing operators - 4/60 took: 3.222516 s
Matching: computing operators - 5/60 took: 3.119671 s
Matching: computing operators - 6/60 took: 2.957262 s
Matching: computing operators - 7/60 took: 3.107674 s
Matching: computing operators - 8/60 took: 2.759738 s
Matching: computing operators - 9/60 took: 2.878886 s
Matching: computing operators - 10/60 took: 3.016507 s
Matching: computing operators - 11/60 took: 3.326236 s
Matching: computing operators - 12/60 took: 3.118026 s
Matching: computing operators - 13/60 took: 2.874500 s
Matching: computing operators - 14/60 took: 2.623077 s
Matching: computing operators - 15/60 took: 2.423636 s
Matching: computing operators - 16/60 took: 2.260780 s
Matching: computing operators - 17/60 took: 2.292312 s
Matching: computing operators - 18/60 took: 2.282697 s
Matching: computing operators - 19/60 took: 2.143466 s
Matching: computing operators - 20/60 took: 2.132647 s
Matching: computing operators - 21/60 took: 1.931621 s
Matching: computing operators - 22/60 took: 1.743106 s
Matching: computing operators - 23/60 took: 1.969127 s
Matching: computing operators - 24/60 took: 1.945254 s
Matching: computing operators - 25/60 took: 1.690306 s
Matching: computing operators - 26/60 took: 1.676323 s
Matching: computing operators - 27/60 took: 1.682164 s
Matching: computing operators - 28/60 took: 1.540759 s
Matching: computing operators - 29/60 took: 1.464339 s
Matching: computing operators - 30/60 took: 1.308656 s
Matching: computing operators - 31/60 took: 1.202729 s
Matching: computing operators - 32/60 took: 1.177519 s
Matching: computing operators - 33/60 took: 0.917762 s
Matching: computing operators - 34/60 took: 0.879446 s
Matching: computing operators - 35/60 took: 0.929591 s
Matching: computing operators - 36/60 took: 0.608155 s
Matching: computing operators - 37/60 took: 0.478509 s
Matching: computing operators - 38/60 took: 0.488014 s
Matching: computing operators - 39/60 took: 0.333766 s
Matching: computing operators - 40/60 took: 0.369406 s
Matching: computing operators - 41/60 took: 0.356404 s
Matching: computing operators - 42/60 took: 0.316653 s
Matching: computing operators - 43/60 took: 0.263485 s
Matching: computing operators - 44/60 took: 0.273630 s
Matching: computing operators - 45/60 took: 0.245231 s
Matching: computing operators - 46/60 took: 0.226021 s
Matching: computing operators - 47/60 took: 0.220719 s
Matching: computing operators - 48/60 took: 0.208527 s
Matching: computing operators - 49/60 took: 0.247688 s
Matching: computing operators - 50/60 took: 0.217117 s
Matching: computing operators - 51/60 took: 0.180971 s
Matching: computing operators - 52/60 took: 0.172589 s
Matching: computing operators - 53/60 took: 0.216841 s
Matching: computing operators - 54/60 took: 0.204410 s
Matching: computing operators - 55/60 took: 0.159314 s
Matching: computing operators - 56/60 took: 0.145457 s
Matching: computing operators - 57/60 took: 0.200509 s
Matching: computing operators - 58/60 took: 0.132451 s
Matching: computing operators - 59/60 took: 0.113425 s
Matching: computing operators - 60/60 took: 0.088693 s
Matching: Total time 85.109137 s
Evolution: computing operators 2.025000e+01 -> 1.000000e+04, nf=5
Evolution: µ_R^2 distance: 4.050000e+01 -> 2.000000e+04
Scale Variation: (µ_F/µ_R)^2 = 5.000000e-01, mode: exponentiated
Evolution: a_s distance: 1.596208e-02 -> 8.849299e-03
Evolution: order: (2, 0), solution strategy: iterate-exact
Evolution: computing operators - 1/60 took: 2.177823 s
Evolution: computing operators - 2/60 took: 2.249421 s
Evolution: computing operators - 3/60 took: 2.349141 s
Evolution: computing operators - 4/60 took: 2.158218 s
Evolution: computing operators - 5/60 took: 2.112945 s
Evolution: computing operators - 6/60 took: 2.174839 s
Evolution: computing operators - 7/60 took: 2.600044 s
Evolution: computing operators - 8/60 took: 2.131433 s
Evolution: computing operators - 9/60 took: 1.987483 s
Evolution: computing operators - 10/60 took: 1.853179 s
Evolution: computing operators - 11/60 took: 1.771399 s
Evolution: computing operators - 12/60 took: 1.763482 s
Evolution: computing operators - 13/60 took: 1.826957 s
Evolution: computing operators - 14/60 took: 1.914649 s
Evolution: computing operators - 15/60 took: 1.713636 s
Evolution: computing operators - 16/60 took: 1.756470 s
Evolution: computing operators - 17/60 took: 1.637066 s
Evolution: computing operators - 18/60 took: 1.713112 s
Evolution: computing operators - 19/60 took: 1.728186 s
Evolution: computing operators - 20/60 took: 1.676126 s
Evolution: computing operators - 21/60 took: 1.457400 s
Evolution: computing operators - 22/60 took: 1.421261 s
Evolution: computing operators - 23/60 took: 1.506364 s
Evolution: computing operators - 24/60 took: 1.541233 s
Evolution: computing operators - 25/60 took: 1.477953 s
Evolution: computing operators - 26/60 took: 1.322380 s
Evolution: computing operators - 27/60 took: 1.380420 s
Evolution: computing operators - 28/60 took: 1.602617 s
Evolution: computing operators - 29/60 took: 1.493167 s
Evolution: computing operators - 30/60 took: 1.347479 s
Evolution: computing operators - 31/60 took: 1.291373 s
Evolution: computing operators - 32/60 took: 1.184719 s
Evolution: computing operators - 33/60 took: 1.051668 s
Evolution: computing operators - 34/60 took: 1.055099 s
Evolution: computing operators - 35/60 took: 1.065021 s
Evolution: computing operators - 36/60 took: 1.016656 s
Evolution: computing operators - 37/60 took: 0.898650 s
Evolution: computing operators - 38/60 took: 0.865734 s
Evolution: computing operators - 39/60 took: 0.853877 s
Evolution: computing operators - 40/60 took: 0.861251 s
Evolution: computing operators - 41/60 took: 0.782613 s
Evolution: computing operators - 42/60 took: 0.741204 s
Evolution: computing operators - 43/60 took: 0.810561 s
Evolution: computing operators - 44/60 took: 0.696554 s
Evolution: computing operators - 45/60 took: 0.677523 s
Evolution: computing operators - 46/60 took: 0.680492 s
Evolution: computing operators - 47/60 took: 0.662123 s
Evolution: computing operators - 48/60 took: 0.779549 s
Evolution: computing operators - 49/60 took: 0.545481 s
Evolution: computing operators - 50/60 took: 0.648714 s
Evolution: computing operators - 51/60 took: 0.515092 s
Evolution: computing operators - 52/60 took: 0.611033 s
Evolution: computing operators - 53/60 took: 0.599624 s
Evolution: computing operators - 54/60 took: 0.694689 s
Evolution: computing operators - 55/60 took: 0.672289 s
Evolution: computing operators - 56/60 took: 0.519996 s
Evolution: computing operators - 57/60 took: 0.568528 s
Evolution: computing operators - 58/60 took: 0.534987 s
Evolution: computing operators - 59/60 took: 0.584085 s
Evolution: computing operators - 60/60 took: 0.326024 s
Evolution: Total time 76.668671 s
Compute external result
Interpolation: number of points = 60, polynomial degree = 4, logarithmic = True

Log added, hash=d0769aef499a95cbea03811e1d961d634e8f346612e57bd244eb54e2cb2f0a42


 ─── 
  S  
 ─── 
               x       Q2         eko     eko_error         LHA  percent_error
0   1.000000e-07  10000.0  312.044160  1.107843e-03  297.053151       5.046575
1   1.000000e-06  10000.0  154.713065  6.395683e-04  148.107784       4.459780
2   1.000000e-05  10000.0   72.505641  3.244119e-04   69.824957       3.839148
3   1.000000e-04  10000.0   31.590995  1.336940e-04   30.641836       3.097591
4   1.000000e-03  10000.0   12.516624  4.947302e-05   12.245546       2.213685
5   1.000000e-02  10000.0    4.425625  1.342489e-05    4.378700       1.071675
6   1.000000e-01  10000.0    1.437828  1.838015e-05    1.442850      -0.348086
7   3.000000e-01  10000.0    0.543782  2.283578e-06    0.550372      -1.197308
8   5.000000e-01  10000.0    0.161145  2.926554e-07    0.164177      -1.846498
9   7.000000e-01  10000.0    0.024293  1.014540e-08    0.024944      -2.609326
10  9.000000e-01  10000.0    0.000393  2.876272e-10    0.000411      -4.405974

 ─── 
  g  
 ─── 
               x       Q2          eko     eko_error          LHA  percent_error
0   1.000000e-07  10000.0  1100.136556  3.931691e-03  1056.800000       4.100734
1   1.000000e-06  10000.0   515.029654  1.964350e-03   497.440000       3.536035
2   1.000000e-05  10000.0   224.253785  9.524027e-04   217.830000       2.948990
3   1.000000e-04  10000.0    88.321674  3.936838e-04    86.372000       2.257299
4   1.000000e-03  10000.0    29.918354  1.410324e-04    29.488000       1.459422
5   1.000000e-02  10000.0     7.705606  3.344886e-05     7.671300       0.447202
6   1.000000e-01  10000.0     0.862234  4.457682e-06     0.870750      -0.978050
7   3.000000e-01  10000.0     0.081052  1.517406e-07     0.082697      -1.988814
8   5.000000e-01  10000.0     0.007907  1.730920e-08     0.008113      -2.535134
9   7.000000e-01  10000.0     0.000386  1.530419e-09     0.000398      -3.042919
10  9.000000e-01  10000.0     0.000001  2.490974e-11     0.000001       3.409923

 ─── 
  V  
 ─── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000156  3.670100e-10  0.000151       3.016527
1   1.000000e-06  10000.0  0.000805  2.036102e-09  0.000784       2.659082
2   1.000000e-05  10000.0  0.004047  1.040493e-08  0.003957       2.269338
3   1.000000e-04  10000.0  0.019589  9.257927e-08  0.019236       1.833727
4   1.000000e-03  10000.0  0.089313  2.785586e-07  0.088146       1.323504
5   1.000000e-02  10000.0  0.356647  4.455632e-07  0.354260       0.673901
6   1.000000e-01  10000.0  0.832742  1.698108e-07  0.835510      -0.331252
7   3.000000e-01  10000.0  0.492205  1.132689e-08  0.498110      -1.185385
8   5.000000e-01  10000.0  0.157709  1.345843e-07  0.160701      -1.862025
9   7.000000e-01  10000.0  0.024209  4.758516e-12  0.024866      -2.640784
10  9.000000e-01  10000.0  0.000393  2.480265e-13  0.000411      -4.467276

 ──── 
  V3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000040  9.315394e-11  0.000039       3.083125
1   1.000000e-06  10000.0  0.000210  5.151789e-10  0.000204       2.731611
2   1.000000e-05  10000.0  0.001062  2.644091e-09  0.001037       2.348590
3   1.000000e-04  10000.0  0.005184  2.367948e-08  0.005086       1.927549
4   1.000000e-03  10000.0  0.024005  7.218808e-08  0.023668       1.424342
5   1.000000e-02  10000.0  0.099940  1.245169e-07  0.099140       0.806598
6   1.000000e-01  10000.0  0.282327  6.925061e-08  0.282790      -0.163643
7   3.000000e-01  10000.0  0.225144  7.371230e-09  0.227510      -1.039810
8   5.000000e-01  10000.0  0.092431  7.715771e-08  0.094079      -1.752045
9   7.000000e-01  10000.0  0.017731  4.009552e-12  0.018202      -2.588072
10  9.000000e-01  10000.0  0.000354  2.032824e-13  0.000372      -4.742146

 ──── 
  T3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000033  1.009930e-10  0.000032       2.875551
1   1.000000e-06  10000.0  0.000176  6.102270e-10  0.000172       2.572983
2   1.000000e-05  10000.0  0.000912  3.831176e-09  0.000892       2.238769
3   1.000000e-04  10000.0  0.004537  1.931597e-08  0.004454       1.866353
4   1.000000e-03  10000.0  0.021287  4.580470e-08  0.020993       1.404687
5   1.000000e-02  10000.0  0.089410  2.493369e-07  0.088679       0.823898
6   1.000000e-01  10000.0  0.262142  5.796073e-08  0.262488      -0.131796
7   3.000000e-01  10000.0  0.218969  7.293533e-09  0.221237      -1.025061
8   5.000000e-01  10000.0  0.091647  2.233809e-07  0.093277      -1.747328
9   7.000000e-01  10000.0  0.017703  3.989076e-12  0.018173      -2.587030
10  9.000000e-01  10000.0  0.000354  2.592030e-13  0.000372      -4.743762

 ──── 
  T8  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  2.160404  9.177004e-06  2.162151      -0.080822
1   1.000000e-06  10000.0  1.716219  5.588541e-06  1.719784      -0.207297
2   1.000000e-05  10000.0  1.365883  1.046805e-05  1.367957      -0.151678
3   1.000000e-04  10000.0  1.097101  6.777036e-06  1.098436      -0.121577
4   1.000000e-03  10000.0  0.924913  2.492798e-06  0.925346      -0.046789
5   1.000000e-02  10000.0  0.928084  2.835875e-06  0.927820       0.028445
6   1.000000e-01  10000.0  0.998315  1.561685e-07  1.002770      -0.444297
7   3.000000e-01  10000.0  0.509978  1.132081e-08  0.516205      -1.206317
8   5.000000e-01  10000.0  0.158984  3.877852e-07  0.162008      -1.866925
9   7.000000e-01  10000.0  0.024239  4.740454e-12  0.024896      -2.642180
10  9.000000e-01  10000.0  0.000393  3.168916e-13  0.000411      -4.465943

 ───── 
  T15  
 ───── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  4.320567  1.953240e-05  4.325151      -0.105978
1   1.000000e-06  10000.0  3.431671  1.122988e-05  3.435784      -0.119732
2   1.000000e-05  10000.0  2.727940  2.124767e-05  2.732957      -0.183586
3   1.000000e-04  10000.0  2.175224  1.835016e-05  2.178136      -0.133707
4   1.000000e-03  10000.0  1.761611  4.848123e-06  1.763846      -0.126715
5   1.000000e-02  10000.0  1.500332  4.927679e-06  1.502200      -0.124328
6   1.000000e-01  10000.0  1.163933  4.436100e-06  1.170086      -0.525829
7   3.000000e-01  10000.0  0.527751  7.733785e-08  0.534301      -1.225878
8   5.000000e-01  10000.0  0.160259  4.020762e-07  0.163316      -1.871712
9   7.000000e-01  10000.0  0.024268  6.080991e-10  0.024927      -2.643562
10  9.000000e-01  10000.0  0.000393  4.094394e-11  0.000411      -4.463502

 ───── 
  T24  
 ───── 
               x       Q2        eko     eko_error        LHA  percent_error
0   1.000000e-07  10000.0  28.257080  5.348182e-05  27.473151       2.853437
1   1.000000e-06  10000.0  18.042933  8.198706e-05  17.607784       2.471345
2   1.000000e-05  10000.0  11.214224  6.892161e-05  10.984957       2.087096
3   1.000000e-04  10000.0   6.750453  5.413001e-05   6.643336       1.612402
4   1.000000e-03  10000.0   3.936399  6.961525e-06   3.895046       1.061682
5   1.000000e-02  10000.0   2.280433  7.749738e-06   2.271400       0.397684
6   1.000000e-01  10000.0   1.259581  1.443409e-05   1.265390      -0.459040
7   3.000000e-01  10000.0   0.533859  8.881062e-07   0.540437      -1.217267
8   5.000000e-01  10000.0   0.160581  5.102968e-07   0.163635      -1.865891
9   7.000000e-01  10000.0   0.024275  4.832204e-09   0.024932      -2.635579
10  9.000000e-01  10000.0   0.000393  1.908849e-10   0.000411      -4.447360
@felixhekhorn felixhekhorn added the bug Something isn't working label Feb 16, 2023
@felixhekhorn felixhekhorn mentioned this issue Feb 16, 2023
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@giacomomagni
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giacomomagni commented Feb 16, 2023 •
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Sv are unrelated to the matching conditions if I'm not mistaken.
So the error might have been introduced in one of major refactoring...
Why do we actually need to have fact_to_ren_scale_ratio around? shouldn't we use only XIF everywhere?
Why both in apfel_bench.py and lha_paper_bench.py do we vary XIR, which should have no effect?

EDIT: most likely XIR have an effect in apfel right?

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giacomomagni commented Feb 17, 2023 •
edited
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Just to confirm that if I run the benchmark in eko=0.10 and the bug is not present.

NLO benchmark output 
 ─── 
  S  
 ─── 
               x       Q2         eko     eko_error         LHA  percent_error
0   1.000000e-07  10000.0  359.535786  1.334030e-03  359.827205      -0.080989
1   1.000000e-06  10000.0  178.351308  7.035550e-04  178.523012      -0.096180
2   1.000000e-05  10000.0   83.417404  3.622460e-04   83.482841      -0.078384
3   1.000000e-04  10000.0   36.079294  1.483124e-04   36.108687      -0.081403
4   1.000000e-03  10000.0   14.017127  6.218054e-05   14.027097      -0.071078
5   1.000000e-02  10000.0    4.725499  1.671181e-05    4.728020      -0.053312
6   1.000000e-01  10000.0    1.409335  1.454889e-05    1.409249       0.006073
7   3.000000e-01  10000.0    0.513807  1.881750e-06    0.513659       0.028957
8   5.000000e-01  10000.0    0.148950  2.801101e-07    0.148882       0.045465
9   7.000000e-01  10000.0    0.021854  1.002127e-08    0.021839       0.070159
10  9.000000e-01  10000.0    0.000336  2.857411e-10    0.000337      -0.346766

 ─── 
  g  
 ─── 
               x       Q2          eko     eko_error          LHA  percent_error
0   1.000000e-07  10000.0  1122.254980  4.256444e-03  1123.900000      -0.146367
1   1.000000e-06  10000.0   526.819801  1.974976e-03   527.630000      -0.153554
2   1.000000e-05  10000.0   229.777954  9.077189e-04   230.060000      -0.122597
3   1.000000e-04  10000.0    90.497875  3.713683e-04    90.599000      -0.111618
4   1.000000e-03  10000.0    30.562857  1.335833e-04    30.589000      -0.085466
5   1.000000e-02  10000.0     7.795009  4.013714e-05     7.799600      -0.058859
6   1.000000e-01  10000.0     0.848238  4.252394e-06     0.848010       0.026944
7   3.000000e-01  10000.0     0.077862  1.667655e-07     0.077817       0.057801
8   5.000000e-01  10000.0     0.007500  1.539652e-08     0.007494       0.077618
9   7.000000e-01  10000.0     0.000362  1.308163e-09     0.000362       0.039419
10  9.000000e-01  10000.0     0.000001  2.256985e-11     0.000001       8.531692

 ─── 
  V  
 ─── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000205  6.850073e-10  0.000205      -0.001085
1   1.000000e-06  10000.0  0.001012  2.936174e-09  0.001012       0.000161
2   1.000000e-05  10000.0  0.004841  2.021656e-08  0.004841       0.000655
3   1.000000e-04  10000.0  0.022287  1.034723e-07  0.022287      -0.000606
4   1.000000e-03  10000.0  0.096697  3.493366e-07  0.096697      -0.000280
5   1.000000e-02  10000.0  0.367609  9.017016e-07  0.367610      -0.000278
6   1.000000e-01  10000.0  0.814569  2.224878e-07  0.814570      -0.000122
7   3.000000e-01  10000.0  0.466311  2.658142e-08  0.466310       0.000293
8   5.000000e-01  10000.0  0.145924  5.237766e-08  0.145924      -0.000160
9   7.000000e-01  10000.0  0.021780  4.415226e-12  0.021778       0.006064
10  9.000000e-01  10000.0  0.000335  2.283651e-13  0.000337      -0.456558

 ──── 
  V3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000054  1.751656e-10  0.000054      -0.003258
1   1.000000e-06  10000.0  0.000266  7.513141e-10  0.000266      -0.001689
2   1.000000e-05  10000.0  0.001282  5.179922e-09  0.001282      -0.000409
3   1.000000e-04  10000.0  0.005952  2.666019e-08  0.005953      -0.003892
4   1.000000e-03  10000.0  0.026219  9.165810e-08  0.026219      -0.001591
5   1.000000e-02  10000.0  0.103868  2.480386e-07  0.103870      -0.002374
6   1.000000e-01  10000.0  0.278031  8.644555e-08  0.278030       0.000209
7   3.000000e-01  10000.0  0.214390  1.640675e-08  0.214390       0.000011
8   5.000000e-01  10000.0  0.085855  3.340684e-08  0.085856      -0.000928
9   7.000000e-01  10000.0  0.015992  3.711473e-12  0.015994      -0.009425
10  9.000000e-01  10000.0  0.000302  1.873087e-13  0.000304      -0.826880

 ──── 
  T3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000042  1.017339e-10  0.000042      -0.004273
1   1.000000e-06  10000.0  0.000216  8.214703e-10  0.000216      -0.002313
2   1.000000e-05  10000.0  0.001073  3.000294e-09  0.001072       0.000173
3   1.000000e-04  10000.0  0.005129  1.948836e-08  0.005129      -0.004570
4   1.000000e-03  10000.0  0.023107  7.032813e-08  0.023108      -0.001669
5   1.000000e-02  10000.0  0.092920  3.106203e-07  0.092922      -0.002707
6   1.000000e-01  10000.0  0.258465  2.240917e-07  0.258464       0.000258
7   3.000000e-01  10000.0  0.208615  4.468356e-07  0.208615       0.000027
8   5.000000e-01  10000.0  0.085142  2.439965e-07  0.085143      -0.001085
9   7.000000e-01  10000.0  0.015967  3.758015e-12  0.015969      -0.009290
10  9.000000e-01  10000.0  0.000302  2.572694e-13  0.000304      -0.828421

 ──── 
  T8  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  2.143652  2.272023e-06  2.144205      -0.025812
1   1.000000e-06  10000.0  1.703012  9.196203e-06  1.704012      -0.058676
2   1.000000e-05  10000.0  1.355759  6.149240e-06  1.356841      -0.079785
3   1.000000e-04  10000.0  1.090271  5.850343e-06  1.090687      -0.038166
4   1.000000e-03  10000.0  0.922399  3.038294e-06  0.922497      -0.010593
5   1.000000e-02  10000.0  0.926934  3.435865e-06  0.926990      -0.006070
6   1.000000e-01  10000.0  0.972459  6.856298e-07  0.972460      -0.000131
7   3.000000e-01  10000.0  0.482801  1.101705e-06  0.482799       0.000357
8   5.000000e-01  10000.0  0.147079  4.472236e-07  0.147079      -0.000277
9   7.000000e-01  10000.0  0.021806  4.497794e-12  0.021804       0.005342
10  9.000000e-01  10000.0  0.000335  3.144625e-13  0.000337      -0.455486

 ───── 
  T15  
 ───── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  4.287026  4.686080e-06  4.286205       0.019163
1   1.000000e-06  10000.0  3.405097  1.845444e-05  3.405012       0.002500
2   1.000000e-05  10000.0  2.707046  1.265344e-05  2.706841       0.007571
3   1.000000e-04  10000.0  2.159240  1.634408e-05  2.159887      -0.029972
4   1.000000e-03  10000.0  1.749825  5.846094e-06  1.750197      -0.021233
5   1.000000e-02  10000.0  1.487500  5.932475e-06  1.487630      -0.008724
6   1.000000e-01  10000.0  1.130417  4.710390e-06  1.130425      -0.000720
7   3.000000e-01  10000.0  0.499292  1.209446e-06  0.499290       0.000374
8   5.000000e-01  10000.0  0.148234  4.621238e-07  0.148234      -0.000367
9   7.000000e-01  10000.0  0.021832  5.441454e-10  0.021831       0.004636
10  9.000000e-01  10000.0  0.000335  3.712493e-11  0.000337      -0.453177

 ───── 
  T24  
 ───── 
               x       Q2        eko     eko_error        LHA  percent_error
0   1.000000e-07  10000.0  38.707418  8.289281e-05  38.702205       0.013468
1   1.000000e-06  10000.0  24.289308  1.141806e-04  24.293012      -0.015247
2   1.000000e-05  10000.0  14.700857  3.972513e-05  14.702841      -0.013493
3   1.000000e-04  10000.0   8.489811  6.464708e-05   8.492687      -0.033870
4   1.000000e-03  10000.0   4.639048  1.189701e-05   4.640597      -0.033384
5   1.000000e-02  10000.0   2.447959  8.933026e-06   2.448670      -0.029046
6   1.000000e-01  10000.0   1.231633  1.295222e-05   1.231629       0.000323
7   3.000000e-01  10000.0   0.504556  6.934904e-07   0.504505       0.010235
8   5.000000e-01  10000.0   0.148444  1.288850e-07   0.148421       0.015681
9   7.000000e-01  10000.0   0.021836  4.909050e-09   0.021830       0.027596
10  9.000000e-01  10000.0   0.000335  1.929134e-10   0.000337      -0.413943

─── 
  S  
 ─── 
               x       Q2         eko     eko_error         LHA  percent_error
0   1.000000e-07  10000.0  296.911425  1.006657e-03  297.053151      -0.047711
1   1.000000e-06  10000.0  148.008744  5.989809e-04  148.107784      -0.066871
2   1.000000e-05  10000.0   69.787679  3.080504e-04   69.824957      -0.053389
3   1.000000e-04  10000.0   30.623164  1.306890e-04   30.641836      -0.060936
4   1.000000e-03  10000.0   12.238804  4.567245e-05   12.245546      -0.055059
5   1.000000e-02  10000.0    4.376832  1.295306e-05    4.378700      -0.042663
6   1.000000e-01  10000.0    1.442870  1.927378e-05    1.442850       0.001394
7   3.000000e-01  10000.0    0.550449  2.279895e-06    0.550372       0.014135
8   5.000000e-01  10000.0    0.164217  2.933315e-07    0.164177       0.024820
9   7.000000e-01  10000.0    0.024953  1.032874e-08    0.024944       0.036198
10  9.000000e-01  10000.0    0.000410  2.969108e-10    0.000411      -0.387752

 ─── 
  g  
 ─── 
               x       Q2          eko     eko_error          LHA  percent_error
0   1.000000e-07  10000.0  1055.895843  3.856417e-03  1056.800000      -0.085556
1   1.000000e-06  10000.0   496.949513  1.877183e-03   497.440000      -0.098602
2   1.000000e-05  10000.0   217.663188  9.013173e-04   217.830000      -0.076579
3   1.000000e-04  10000.0    86.305438  3.682880e-04    86.372000      -0.077064
4   1.000000e-03  10000.0    29.469515  1.352134e-04    29.488000      -0.062687
5   1.000000e-02  10000.0     7.667344  3.288296e-05     7.671300      -0.051571
6   1.000000e-01  10000.0     0.870858  4.532781e-06     0.870750       0.012413
7   3.000000e-01  10000.0     0.082720  1.554055e-07     0.082697       0.027950
8   5.000000e-01  10000.0     0.008116  1.734076e-08     0.008113       0.037604
9   7.000000e-01  10000.0     0.000398  1.565571e-09     0.000398      -0.010125
10  9.000000e-01  10000.0     0.000001  2.712240e-11     0.000001       7.498215

 ─── 
  V  
 ─── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000151  3.595620e-10  0.000151       0.000081
1   1.000000e-06  10000.0  0.000784  1.853577e-09  0.000784       0.000047
2   1.000000e-05  10000.0  0.003957  9.893538e-09  0.003957       0.001407
3   1.000000e-04  10000.0  0.019237  8.863640e-08  0.019236       0.002341
4   1.000000e-03  10000.0  0.088146  2.734695e-07  0.088146      -0.000059
5   1.000000e-02  10000.0  0.354255  4.360339e-07  0.354260      -0.001532
6   1.000000e-01  10000.0  0.835505  1.692202e-07  0.835510      -0.000613
7   3.000000e-01  10000.0  0.498107  1.179014e-08  0.498110      -0.000601
8   5.000000e-01  10000.0  0.160703  5.484800e-07  0.160701       0.001453
9   7.000000e-01  10000.0  0.024867  4.906651e-12  0.024866       0.003829
10  9.000000e-01  10000.0  0.000410  2.404291e-13  0.000411      -0.449326

 ──── 
  V3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000039  9.119152e-11  0.000039       0.000643
1   1.000000e-06  10000.0  0.000204  4.690128e-10  0.000204       0.001320
2   1.000000e-05  10000.0  0.001037  2.513102e-09  0.001037       0.002798
3   1.000000e-04  10000.0  0.005086  2.266904e-08  0.005086       0.008945
4   1.000000e-03  10000.0  0.023668  7.086485e-08  0.023668      -0.001763
5   1.000000e-02  10000.0  0.099139  1.218869e-07  0.099140      -0.000725
6   1.000000e-01  10000.0  0.282788  6.935647e-08  0.282790      -0.000771
7   3.000000e-01  10000.0  0.227503  7.664962e-09  0.227510      -0.003065
8   5.000000e-01  10000.0  0.094080  3.125422e-07  0.094079       0.000879
9   7.000000e-01  10000.0  0.018200  4.139954e-12  0.018202      -0.012287
10  9.000000e-01  10000.0  0.000369  1.971334e-13  0.000372      -0.744290

 ──── 
  T3  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  0.000032  9.889811e-11  0.000032       0.000557
1   1.000000e-06  10000.0  0.000172  5.223862e-10  0.000172       0.001614
2   1.000000e-05  10000.0  0.000892  3.731286e-09  0.000892       0.003137
3   1.000000e-04  10000.0  0.004454  1.867326e-08  0.004454       0.010301
4   1.000000e-03  10000.0  0.020992  4.703239e-08  0.020993      -0.002490
5   1.000000e-02  10000.0  0.088678  2.553788e-07  0.088679      -0.000853
6   1.000000e-01  10000.0  0.262486  5.908650e-08  0.262488      -0.000675
7   3.000000e-01  10000.0  0.221230  7.600921e-09  0.221237      -0.003123
8   5.000000e-01  10000.0  0.093278  1.575367e-07  0.093277       0.000743
9   7.000000e-01  10000.0  0.018171  4.124318e-12  0.018173      -0.012189
10  9.000000e-01  10000.0  0.000369  2.505033e-13  0.000372      -0.746055

 ──── 
  T8  
 ──── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  2.163191  8.168386e-06  2.162151       0.048094
1   1.000000e-06  10000.0  1.718421  4.385442e-06  1.719784      -0.079290
2   1.000000e-05  10000.0  1.367582  9.983821e-06  1.367957      -0.027445
3   1.000000e-04  10000.0  1.098263  6.477850e-06  1.098436      -0.015767
4   1.000000e-03  10000.0  0.925279  2.493628e-06  0.925346      -0.007281
5   1.000000e-02  10000.0  0.927761  2.929654e-06  0.927820      -0.006341
6   1.000000e-01  10000.0  1.002763  1.584652e-07  1.002770      -0.000674
7   3.000000e-01  10000.0  0.516203  1.181831e-08  0.516205      -0.000486
8   5.000000e-01  10000.0  0.162011  2.625038e-07  0.162008       0.001329
9   7.000000e-01  10000.0  0.024897  4.894922e-12  0.024896       0.003160
10  9.000000e-01  10000.0  0.000410  3.061661e-13  0.000411      -0.447824

 ───── 
  T15  
 ───── 
               x       Q2       eko     eko_error       LHA  percent_error
0   1.000000e-07  10000.0  4.326146  1.733508e-05  4.325151       0.023011
1   1.000000e-06  10000.0  3.436092  8.822634e-06  3.435784       0.008942
2   1.000000e-05  10000.0  2.731421  2.027262e-05  2.732957      -0.056228
3   1.000000e-04  10000.0  2.177881  1.777999e-05  2.178136      -0.011702
4   1.000000e-03  10000.0  1.763479  4.842966e-06  1.763846      -0.020815
5   1.000000e-02  10000.0  1.502062  5.081419e-06  1.502200      -0.009178
6   1.000000e-01  10000.0  1.170067  4.517119e-06  1.170086      -0.001601
7   3.000000e-01  10000.0  0.534299  7.871627e-08  0.534301      -0.000428
8   5.000000e-01  10000.0  0.163318  2.757828e-07  0.163316       0.001241
9   7.000000e-01  10000.0  0.024928  6.257342e-10  0.024927       0.002504
10  9.000000e-01  10000.0  0.000410  4.194788e-11  0.000411      -0.445188

 ───── 
  T24  
 ───── 
               x       Q2        eko     eko_error        LHA  percent_error
0   1.000000e-07  10000.0  27.475845  5.326440e-05  27.473151       0.009805
1   1.000000e-06  10000.0  17.603038  6.834294e-05  17.607784      -0.026958
2   1.000000e-05  10000.0  10.983181  6.366674e-05  10.984957      -0.016169
3   1.000000e-04  10000.0   6.641553  5.207211e-05   6.643336      -0.026844
4   1.000000e-03  10000.0   3.894162  6.500600e-06   3.895046      -0.022703
5   1.000000e-02  10000.0   2.270934  7.509126e-06   2.271400      -0.020507
6   1.000000e-01  10000.0   1.265374  1.471305e-05   1.265390      -0.001246
7   3.000000e-01  10000.0   0.540453  8.918512e-07   0.540437       0.002989
8   5.000000e-01  10000.0   0.163646  3.845568e-07   0.163635       0.006881
9   7.000000e-01  10000.0   0.024935  4.935708e-09   0.024932       0.010538
10  9.000000e-01  10000.0   0.000410  1.955599e-10   0.000411      -0.428961

@giacomomagni giacomomagni mentioned this issue Feb 21, 2023
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@felixhekhorn
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So the error might have been introduced in one of major refactoring...

this conjecture seems to be true

@alecandido how to bisect/proceed further? between the two commits there is quasi one gigantic commit (since you rewrote history 🙃 ) and I don't know where I can step in ...

to add my own conjecture: I'm guessing this is related to linear vs. squared scales ... (which was part of #172)

@alecandido
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to add my own conjecture: I'm guessing this is related to linear vs. squared scales ... (which was part of #172)

I know here everything was not so clear, and that conversion might be confusing. Exactly for this reason yesterday I introduced (in #217) the following:

eko/src/eko/io/types.py

Lines 14 to 18 in fb6dc24

Scale = float
LinearScale = Scale
SquaredScale = Scale

At the moment, I'm using aliases to be able to add explicit marks, but without breaking compatibility.
In the future, I really hope to transition to the NewType, such that the editors will help themselves preventing this kind of errors.

This was referenced Feb 24, 2023
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@felixhekhorn felixhekhorn mentioned this issue Mar 7, 2023
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@felixhekhorn felixhekhorn mentioned this issue Mar 22, 2023
Merged
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