Details

analyze701.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	1.5%	98.5%	0
0%	1.5%	98.5%	1
0%	1.5%	98.5%	2
0%	1.5%	98.5%	3
0.4%	1.1%	98.5%	4
0.6%	1%	98.5%	5
0.6%	1%	98.5%	6
0.7%	0.9%	98.5%	7
1%	0.5%	98.5%	8
1%	0.5%	98.5%	9
1%	0.5%	98.5%	10
1.3%	0.3%	98.5%	11
1.3%	0.3%	98.5%	12
1.3%	0.3%	98.5%	13
1.4%	0.1%	98.5%	14

Compiler

Compiled 38 to 30 computations (21.1% saved)

sample52.0ms (0.4%)

Algorithm

1×

intervals

Results

21.0ms	224×	body	128	valid
8.0ms	256×	pre	128	true
7.0ms	32×	body	256	valid

Compiler

Compiled 63 to 53 computations (15.9% saved)

simplify201.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5026	36

prune5.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 0.4b

Counts

2 → 1

Compiler

Compiled 46 to 36 computations (21.7% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
0.1b	(sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))))
0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
0.4b	(.f32 (.f32 uy 2) PI.f32)

rewrite58.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`sqrt-div_binary32_93`
14×	`pow1_binary32_135`
13×	`add-log-exp_binary32_113`
12×	`associate-*r/_binary32_21`
11×	`add-cbrt-cube_binary32_110` `add-exp-log_binary32_112`
9×	`*-un-lft-identity_binary32_77` `add-sqr-sqrt_binary32_98`
8×	`frac-times_binary32_87`
7×	`associate-r_binary32_19` `flip3-+_binary32_80` `add-cube-cbrt_binary32_109` `flip-+_binary32_51`
6×	`flip3--_binary32_81` `flip--_binary32_52`
5×	`sum-log_binary32_165` `pow-prod-down_binary32_145`
4×	`associate-l/_binary32_22` `prod-exp_binary32_123` `associate-l*_binary32_20` `cbrt-unprod_binary32_107`
2×	`sqrt-pow1_binary32_94` `*-commutative_binary32_10` `sqrt-prod_binary32_92`
1×	`distribute-lft-out_binary32_30` `unswap-sqr_binary32_45` `pow1/2_binary32_154` `associate-+r-_binary32_13` `+-commutative_binary32_9` `associate-+l-_binary32_14` `associate-+r+_binary32_11` `diff-log_binary32_166`

Counts

4 → 80

Calls

4 calls:

18.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
12.0ms	(sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))))
10.0ms	(+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))
8.0ms	(.f32 (.f32 uy 2) PI.f32)

series648.0ms (5.5%)

Counts

4 → 12

Calls

4 calls:

427.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (.f32 ux maxCos))))))
160.0ms	(sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))))
34.0ms	(.f32 (.f32 uy 2) PI.f32)
27.0ms	(+.f32 1 (+.f32 (-.f32 1 ux) (*.f32 ux maxCos)))

simplify77.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4997	2301
1	4997	2301

prune154.0ms (1.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	8	93

Merged error: 0.0b

Counts

93 → 8

Compiler

Compiled 3165 to 1627 computations (48.6% saved)

localize39.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f32 (-.f32 ux (*.f32 ux maxCos)))
0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))
0.4b	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos)))))
0.4b	(.f32 (.f32 uy 2) PI.f32)

rewrite50.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`sqrt-div_binary32_93`
22×	`add-sqr-sqrt_binary32_98`
19×	`pow1_binary32_135`
16×	`add-cbrt-cube_binary32_110` `add-exp-log_binary32_112`
15×	`sqrt-prod_binary32_92`
13×	`flip3--_binary32_81` `*-un-lft-identity_binary32_77` `flip--_binary32_52`
12×	`associate-r_binary32_19` `associate-*r/_binary32_21`
11×	`add-cube-cbrt_binary32_109`
10×	`associate-l_binary32_20`
9×	`pow-prod-down_binary32_145`
8×	`frac-times_binary32_87`
7×	`prod-exp_binary32_123` `cbrt-unprod_binary32_107`
4×	`add-log-exp_binary32_113` `associate-*l/_binary32_22` `unswap-sqr_binary32_45`
3×	`pow1/2_binary32_154` `sqrt-pow1_binary32_94` `*-commutative_binary32_10`
1×	`rem-sqrt-square_binary32_90` `sqrt-unprod_binary32_96` `difference-of-squares_binary32_46` `distribute-lft-out--_binary32_31`

Counts

4 → 99

Calls

4 calls:

16.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))
14.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos)))))
5.0ms	(.f32 (.f32 uy 2) PI.f32)
3.0ms	(sqrt.f32 (-.f32 ux (*.f32 ux maxCos)))

series796.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos))))))
204.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos)))))
50.0ms	(sqrt.f32 (-.f32 ux (*.f32 ux maxCos)))
35.0ms	(.f32 (.f32 uy 2) PI.f32)

simplify67.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5950	2972

prune156.0ms (1.3%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	108	3	111
Fresh	4	3	7
Picked	0	1	1
Done	0	0	0
Total	112	7	119

Merged error: 0.0b

Counts

119 → 7

Compiler

Compiled 3724 to 1689 computations (54.6% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))))
0.4b	(.f32 (.f32 uy 2) PI.f32)
0.4b	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))
0.4b	(.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))

rewrite119.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

198×	`sqrt-div_binary32_93`
60×	`flip3--_binary32_81` `frac-times_binary32_87` `flip--_binary32_52`
44×	`associate-*r/_binary32_21`
38×	`sqrt-prod_binary32_92`
30×	`associate-*l/_binary32_22` `pow1_binary32_135` `add-sqr-sqrt_binary32_98`
26×	`associate-r_binary32_19`
25×	`add-cbrt-cube_binary32_110` `add-exp-log_binary32_112`
19×	`pow-prod-down_binary32_145`
18×	`*-un-lft-identity_binary32_77`
14×	`add-cube-cbrt_binary32_109`
13×	`prod-exp_binary32_123` `cbrt-unprod_binary32_107`
11×	`associate-l_binary32_20`
6×	`unswap-sqr_binary32_45`
5×	`pow1/2_binary32_154` `sqrt-pow1_binary32_94`
4×	`add-log-exp_binary32_113` `*-commutative_binary32_10`
3×	`sqrt-unprod_binary32_96`
2×	`difference-of-squares_binary32_46` `distribute-lft-out--_binary32_31`

Counts

4 → 165

Calls

4 calls:

31.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))))
27.0ms	(.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))
16.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))
5.0ms	(.f32 (.f32 uy 2) PI.f32)

series1.0s (8.6%)

Counts

4 → 12

Calls

4 calls:

515.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))))
251.0ms	(.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))
204.0ms	(.f32 (.f32 (sqrt.f32 (-.f32 ux (.f32 ux maxCos))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (.f32 ux maxCos)))))) (sqrt.f32 (sqrt.f32 (-.f32 2 (-.f32 ux (*.f32 ux maxCos))))))
32.0ms	(.f32 (.f32 uy 2) PI.f32)

simplify122.0ms (1%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4956	6981
1	4956	6981

prune354.0ms (3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	176	8	184

Merged error: 0b

Counts

184 → 8

Compiler

Compiled 8369 to 3853 computations (54% saved)

localize68.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.1b	(.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))
0.1b	(pow.f32 (+.f32 (*.f32 ux maxCos) (-.f32 1 ux)) 3)
0.3b	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (/.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3)))) (sqrt.f32 (+.f32 1 (.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))))))
0.4b	(.f32 (.f32 uy 2) PI.f32)

rewrite82.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`associate-r_binary32_19` `add-sqr-sqrt_binary32_98`
26×	`add-cube-cbrt_binary32_109` `*-un-lft-identity_binary32_77` `times-frac_binary32_83`
19×	`sqrt-prod_binary32_92`
17×	`add-cbrt-cube_binary32_110` `add-exp-log_binary32_112`
14×	`pow1_binary32_135`
7×	`associate-l_binary32_20`
6×	`prod-exp_binary32_123` `cbrt-unprod_binary32_107`
5×	`flip3-+_binary32_80` `flip-+_binary32_51` `pow-prod-down_binary32_145`
4×	`add-log-exp_binary32_113` `unswap-sqr_binary32_45` `frac-times_binary32_87`
3×	`flip3--_binary32_81` `pow-unpow_binary32_151` `associate-r/_binary32_21` `unpow-prod-down_binary32_153` `cube-prod_binary32_102` `-commutative_binary32_10` `flip--_binary32_52`
2×	`associate-*l/_binary32_22` `associate-/r/_binary32_25` `sub-neg_binary32_70` `sqrt-div_binary32_93` `cube-div_binary32_103`
1×	`cube-mult_binary32_104` `pow-pow_binary32_146` `unpow3_binary32_140` `distribute-rgt-in_binary32_29` `cbrt-undiv_binary32_108` `pow-exp_binary32_142` `distribute-lft-in_binary32_28` `rem-cube-cbrt_binary32_99` `sqr-pow_binary32_49` `div-exp_binary32_125` `pow-to-exp_binary32_143` `div-inv_binary32_74`

Counts

4 → 121

Calls

4 calls:

31.0ms	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (/.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3)))) (sqrt.f32 (+.f32 1 (.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))))))
15.0ms	(.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))
9.0ms	(pow.f32 (+.f32 (*.f32 ux maxCos) (-.f32 1 ux)) 3)
5.0ms	(.f32 (.f32 uy 2) PI.f32)

series4.5s (38.3%)

Counts

4 → 12

Calls

4 calls:

4.3s	(.f32 (sin.f32 (.f32 (.f32 uy 2) PI.f32)) (/.f32 (sqrt.f32 (.f32 (-.f32 ux (.f32 ux maxCos)) (+.f32 1 (pow.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) 3)))) (sqrt.f32 (+.f32 1 (.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))))))
52.0ms	(pow.f32 (+.f32 (*.f32 ux maxCos) (-.f32 1 ux)) 3)
51.0ms	(.f32 (+.f32 (.f32 ux maxCos) (-.f32 1 ux)) (-.f32 (*.f32 ux maxCos) ux))
34.0ms	(.f32 (.f32 uy 2) PI.f32)

simplify93.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5068	5139

prune331.0ms (2.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	133	8	141

Merged error: 0b

Counts

141 → 8

Compiler

Compiled 7465 to 3978 computations (46.7% saved)

regimes154.0ms (1.3%)

Compiler: Compiled 2050 to 1312 computations (36% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	112	35
1	112	35

end0.0ms (0%)

sample1.8s (15.3%)

Algorithm

1×

intervals

Results

694.0ms	6983×	body	128	valid
252.0ms	8000×	pre	128	true
214.0ms	1017×	body	256	valid

Compiler

Compiled 396 to 258 computations (34.8% saved)

Details

analyze701.0ms (6%)

sample52.0ms (0.4%)

simplify201.0ms (1.7%)

prune5.0ms (0%)

localize45.0ms (0.4%)

rewrite58.0ms (0.5%)

series648.0ms (5.5%)

simplify77.0ms (0.7%)

prune154.0ms (1.3%)

localize39.0ms (0.3%)

rewrite50.0ms (0.4%)

series796.0ms (6.8%)

simplify67.0ms (0.6%)

prune156.0ms (1.3%)

localize46.0ms (0.4%)

rewrite119.0ms (1%)

series1.0s (8.6%)

simplify122.0ms (1%)

prune354.0ms (3%)

localize68.0ms (0.6%)

rewrite82.0ms (0.7%)

series4.5s (38.3%)

simplify93.0ms (0.8%)

prune331.0ms (2.8%)

regimes154.0ms (1.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.8s (15.3%)

Profiling