Fixes for order and missing terms in trigonometric integrals

[arnabnandikgp]

References to other Issues or PRs

Fixes #26207
Fixes #26257

Brief description of what is fixed or changed

Other comments

Release Notes

• functions
  • Fixes for order and missing terms in trigonometric integrals in error functions

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• functions
  • Fixes for order and missing terms in trigonometric integrals in error functions (#26290 by @arnabnandikgp)

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#### References to other Issues or PRs
Fixes #26207
Fixes #26257
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* functions
  * Fixes for order and missing terms in trigonometric integrals in error functions

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Update

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[github-actions]

Benchmark results from GitHub Actions

Lower numbers are good, higher numbers are bad. A ratio less than 1
means a speed up and greater than 1 means a slowdown. Green lines
beginning with + are slowdowns (the PR is slower then master or
master is slower than the previous release). Red lines beginning
with - are speedups.

Significantly changed benchmark results (PR vs master)

Significantly changed benchmark results (master vs previous release)

| Change   | Before [a00718ba]    | After [cb29c92f]    |   Ratio | Benchmark (Parameter)                                                |
|----------|----------------------|---------------------|---------|----------------------------------------------------------------------|
| -        | 71.1±2ms             | 44.7±0.2ms          |    0.63 | integrate.TimeIntegrationRisch02.time_doit(10)                       |
| -        | 68.6±1ms             | 43.7±0.3ms          |    0.64 | integrate.TimeIntegrationRisch02.time_doit_risch(10)                 |
| +        | 18.6±0.3μs           | 30.1±0.3μs          |    1.62 | integrate.TimeIntegrationRisch03.time_doit(1)                        |
| -        | 5.40±0.04ms          | 2.87±0.02ms         |    0.53 | logic.LogicSuite.time_load_file                                      |
| -        | 73.0±0.7ms           | 28.8±0.2ms          |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'dense')                           |
| -        | 25.8±0.2ms           | 17.0±0.05ms         |    0.66 | polys.TimeGCD_GaussInt.time_op(1, 'expr')                            |
| -        | 74.2±0.3ms           | 28.8±0.07ms         |    0.39 | polys.TimeGCD_GaussInt.time_op(1, 'sparse')                          |
| -        | 255±0.6ms            | 123±0.8ms           |    0.48 | polys.TimeGCD_GaussInt.time_op(2, 'dense')                           |
| -        | 259±1ms              | 125±0.6ms           |    0.48 | polys.TimeGCD_GaussInt.time_op(2, 'sparse')                          |
| -        | 660±3ms              | 370±2ms             |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'dense')                           |
| -        | 657±2ms              | 370±2ms             |    0.56 | polys.TimeGCD_GaussInt.time_op(3, 'sparse')                          |
| -        | 501±4μs              | 285±2μs             |    0.57 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(1, 'dense')            |
| -        | 1.78±0.01ms          | 1.04±0.01ms         |    0.59 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(2, 'dense')            |
| -        | 5.75±0.1ms           | 3.06±0.01ms         |    0.53 | polys.TimeGCD_LinearDenseQuadraticGCD.time_op(3, 'dense')            |
| -        | 451±3μs              | 228±2μs             |    0.5  | polys.TimeGCD_QuadraticNonMonicGCD.time_op(1, 'dense')               |
| -        | 1.47±0.01ms          | 675±3μs             |    0.46 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(2, 'dense')               |
| -        | 4.95±0.04ms          | 1.64±0.01ms         |    0.33 | polys.TimeGCD_QuadraticNonMonicGCD.time_op(3, 'dense')               |
| -        | 380±3μs              | 204±2μs             |    0.54 | polys.TimeGCD_SparseGCDHighDegree.time_op(1, 'dense')                |
| -        | 2.43±0.02ms          | 1.21±0.02ms         |    0.5  | polys.TimeGCD_SparseGCDHighDegree.time_op(3, 'dense')                |
| -        | 10.0±0.1ms           | 4.31±0.01ms         |    0.43 | polys.TimeGCD_SparseGCDHighDegree.time_op(5, 'dense')                |
| -        | 363±1μs              | 167±1μs             |    0.46 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(1, 'dense')            |
| -        | 2.54±0.03ms          | 884±6μs             |    0.35 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(3, 'dense')            |
| -        | 9.65±0.03ms          | 2.62±0.01ms         |    0.27 | polys.TimeGCD_SparseNonMonicQuadratic.time_op(5, 'dense')            |
| -        | 1.02±0.01ms          | 429±2μs             |    0.42 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'dense')           |
| -        | 1.75±0.01ms          | 499±2μs             |    0.29 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(3, 'sparse')          |
| -        | 5.91±0.06ms          | 1.78±0.01ms         |    0.3  | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'dense')           |
| -        | 8.49±0.2ms           | 1.47±0.01ms         |    0.17 | polys.TimePREM_LinearDenseQuadraticGCD.time_op(5, 'sparse')          |
| -        | 288±0.9μs            | 64.2±0.5μs          |    0.22 | polys.TimePREM_QuadraticNonMonicGCD.time_op(1, 'sparse')             |
| -        | 3.42±0.03ms          | 401±3μs             |    0.12 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'dense')              |
| -        | 3.99±0.03ms          | 280±2μs             |    0.07 | polys.TimePREM_QuadraticNonMonicGCD.time_op(3, 'sparse')             |
| -        | 7.06±0.1ms           | 1.27±0ms            |    0.18 | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'dense')              |
| -        | 8.67±0.1ms           | 843±2μs             |    0.1  | polys.TimePREM_QuadraticNonMonicGCD.time_op(5, 'sparse')             |
| -        | 5.01±0.02ms          | 2.98±0ms            |    0.6  | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(2, 'sparse') |
| -        | 12.2±0.2ms           | 6.61±0.02ms         |    0.54 | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'dense')  |
| -        | 22.4±0.2ms           | 9.06±0.03ms         |    0.4  | polys.TimeSUBRESULTANTS_LinearDenseQuadraticGCD.time_op(3, 'sparse') |
| -        | 5.26±0.02ms          | 869±1μs             |    0.17 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(1, 'sparse')    |
| -        | 12.6±0.06ms          | 7.05±0.03ms         |    0.56 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(2, 'sparse')    |
| -        | 102±1ms              | 25.8±0.1ms          |    0.25 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'dense')     |
| -        | 167±0.9ms            | 54.2±0.08ms         |    0.32 | polys.TimeSUBRESULTANTS_QuadraticNonMonicGCD.time_op(3, 'sparse')    |
| -        | 175±0.7μs            | 109±0.3μs           |    0.63 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'dense')      |
| -        | 364±2μs              | 221±1μs             |    0.61 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(1, 'sparse')     |
| -        | 4.39±0.02ms          | 845±6μs             |    0.19 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'dense')      |
| -        | 5.28±0.02ms          | 384±1μs             |    0.07 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(3, 'sparse')     |
| -        | 20.3±0.3ms           | 2.79±0.01ms         |    0.14 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'dense')      |
| -        | 22.8±0.3ms           | 625±2μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseGCDHighDegree.time_op(5, 'sparse')     |
| -        | 487±6μs              | 136±0.5μs           |    0.28 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(1, 'sparse') |
| -        | 4.75±0.06ms          | 608±1μs             |    0.13 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'dense')  |
| -        | 5.39±0.07ms          | 139±1μs             |    0.03 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(3, 'sparse') |
| -        | 13.4±0.3ms           | 1.27±0.01ms         |    0.09 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'dense')  |
| -        | 14.0±0.2ms           | 141±0.9μs           |    0.01 | polys.TimeSUBRESULTANTS_SparseNonMonicQuadratic.time_op(5, 'sparse') |
| -        | 136±2μs              | 74.3±0.4μs          |    0.55 | solve.TimeMatrixOperations.time_rref(3, 0)                           |
| -        | 255±3μs              | 87.2±0.2μs          |    0.34 | solve.TimeMatrixOperations.time_rref(4, 0)                           |
| -        | 24.2±0.2ms           | 10.1±0.05ms         |    0.42 | solve.TimeSolveLinSys189x49.time_solve_lin_sys                       |
| -        | 29.6±0.3ms           | 15.5±0.06ms         |    0.53 | solve.TimeSparseSystem.time_linsolve_Aaug(20)                        |
| -        | 56.5±0.1ms           | 24.7±0.1ms          |    0.44 | solve.TimeSparseSystem.time_linsolve_Aaug(30)                        |
| -        | 29.2±0.3ms           | 15.2±0.08ms         |    0.52 | solve.TimeSparseSystem.time_linsolve_Ab(20)                          |
| -        | 55.9±0.7ms           | 24.5±0.08ms         |    0.44 | solve.TimeSparseSystem.time_linsolve_Ab(30)                          |

Full benchmark results can be found as artifacts in GitHub Actions
(click on checks at the top of the PR).

[anutosh491]

Few tests fail but I don't think they are arising from the changes made here. Looks good.

[arnabnandikgp]

I think the failing numpy job is passing now, we can restart the tests if needed before merging.

[oscarbenjamin]

think the failing numpy job is passing now, we can restart the tests if needed before merging.

It doesn't matter if the numpy nightly job fails. The PR can still be merged anyway and there is no need to restart the tests.