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many-sample q-calibration gradient of a sphere form-factor objective
AD speed-up on the same differentiation workload (against finite differences) Speed-up: 213.9×
High-dimensional demo
many-sample q-calibration gradient of a sphere form-factor objective
Supplied demo scenario wording.
FD components requested 1 – 256 · AD components 4096
View demo measurements
| Measure | Value |
|---|---|
| AD median (s) | 0.00012770900502800941 |
| FD median (s) | 0.0273165829712525 |
| FD / AD | 213.89707769832964 |
| Max scaled error | 6.666098872898374e-8 |
| AD components | 4096 |
| FD components requested | 256 |
| AD parameters | 256 |
| Repeats | 11 |
| FD components requested | AD median (s) | FD median (s) | FD / AD | Max scaled error | AD components |
|---|---|---|---|---|---|
| 1 | 4096 | 0.00013004103675484657 | 0.00010954204481095076 | 0.84236520674208 | 3.740863720760835e-9 |
| 2 | 4096 | 0.0001287920167669654 | 0.00021291698794811964 | 1.653184671635113 | 3.740863720760835e-9 |
| 4 | 4096 | 0.00012804195284843445 | 0.00042345805559307337 | 3.3071821084635302 | 6.5369025160303545e-9 |
| 8 | 4096 | 0.00012600002810359 | 0.0008421669481322169 | 6.683863176917988 | 6.5369025160303545e-9 |
| 16 | 4096 | 0.00012850004713982344 | 0.0016925830859690905 | 13.171847977046712 | 1.0082172120136424e-8 |
| 32 | 4096 | 0.00012400001287460327 | 0.0033822909463196993 | 27.276537057621823 | 1.5836297450472214e-8 |
| 64 | 4096 | 0.00012716592755168676 | 0.006873624981380999 | 54.05241100126608 | 1.719973772434935e-8 |
| 128 | 4096 | 0.00012883299496024847 | 0.013706208090297878 | 106.38740560620313 | 3.002174390600675e-8 |
| 256 | 4096 | 0.00012770900502800941 | 0.0273165829712525 | 213.89707769832964 | 6.666098872898374e-8 |
One-direction performance audit
View audit measurements
| Demo scenario | Problem size | Repeats | AD median (s) | FD median (s) | FD / AD | Relative error | Supplied verdict |
|---|---|---|---|---|---|---|---|
| sphere_directmodel_one_parameter | 1000_q_points | — | 0.00021779 | 0.000123958 | 0.5691602 | — | modest AD slowdown |
FD/AD > 1 means automatic differentiation is faster; FD/AD < 1 means the finite-difference comparison is faster. One direction only, measured inside the package's own case.