Details

analyze735.0ms (6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
25%	74.9%	0.1%	6
25%	74.9%	0.1%	7
25%	74.9%	0.1%	8
25%	74.9%	0.1%	9
25%	64%	11.1%	10
31.2%	54.6%	14.2%	11
39%	44.1%	16.9%	12
39%	41.5%	19.5%	13
42.9%	37%	20.1%	14

Compiler

Compiled 20 to 16 computations (20% saved)

sample87.0ms (0.7%)

Algorithm

1×

intervals

Results

20.0ms	65×	body	1024	invalid
18.0ms	60×	body	1024	valid
14.0ms	153×	body	128	valid
7.0ms	32×	body	512	valid
6.0ms	29×	body	512	invalid
2.0ms	23×	body	128	invalid
2.0ms	12×	body	256	invalid
1.0ms	10×	body	256	valid
0.0ms	1×	body	2048	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify99.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune6.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.4b

Counts

2 → 2

Compiler

Compiled 45 to 37 computations (17.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.2b	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

rewrite29.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
31×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
22×	`associate-r_binary64_359` `sqrt-prod_binary64_435`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
6×	`associate-/r*_binary64_363`
4×	`pow1_binary64_480`
3×	`unswap-sqr_binary64_387` `associate-l_binary64_360` `associate-/l*_binary64_364`
2×	`add-log-exp_binary64_458` `div-inv_binary64_416` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `pow-prod-down_binary64_490` `clear-num_binary64_418` `associate-r/_binary64_361` `-commutative_binary64_350` `frac-2neg_binary64_430` `flip-+_binary64_393`

Counts

2 → 83

Calls

4 calls:

13.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
7.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))
0.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
0.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

series613.0ms (5%)

Counts

2 → 30

Calls

2 calls:

421.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
192.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 785 to 753 computations (4.1% saved)

simplify68.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5339	2746

prune191.0ms (1.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	105	8	113
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	107	8	115

Error

Counts

115 → 8

Compiler

Compiled 2587 to 1055 computations (59.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
0.2b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.2b	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.4b	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
8×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`times-frac_binary64_425` `sqrt-prod_binary64_435` `associate-/r*_binary64_363`
4×	`associate-*l/_binary64_362` `pow1_binary64_480`
3×	`associate-r_binary64_359` `associate-l_binary64_360`
2×	`flip3-+_binary64_422` `add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `flip-+_binary64_393` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/l/_binary64_366`
1×	`pow-prod-down_binary64_490` `clear-num_binary64_418` `div-inv_binary64_416` `unswap-sqr_binary64_387` `-commutative_binary64_350` `frac-2neg_binary64_430` `associate-/l_binary64_364`

Counts

2 → 49

Calls

4 calls:

9.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
7.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))
0.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))

series705.0ms (5.8%)

Counts

2 → 36

Calls

2 calls:

434.0ms	(/.f64 (.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th)) (sqrt.f64 2))
271.0ms	(.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (cos.f64 th))

Compiler

Compiled 997 to 921 computations (7.6% saved)

simplify66.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4973	1803
1	4973	1803

prune99.0ms (0.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 1688 to 689 computations (59.2% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
0.3b	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.3b	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.4b	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

rewrite33.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

156×	`times-frac_binary64_425`
92×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-sqr-sqrt_binary64_441`
48×	`sqrt-prod_binary64_435`
25×	`associate-/r*_binary64_363`
9×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `associate-/l*_binary64_364`
6×	`div-inv_binary64_416`
4×	`div-exp_binary64_470` `cbrt-undiv_binary64_453`
2×	`clear-num_binary64_418` `add-log-exp_binary64_458` `frac-2neg_binary64_430` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`flip3-+_binary64_422` `associate-/r/_binary64_365` `flip-+_binary64_393`

Counts

2 → 147

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
4.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))
0.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))

series483.0ms (3.9%)

Counts

2 → 24

Calls

2 calls:

435.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (/.f64 (sqrt.f64 2) (cos.f64 th)))
48.0ms	(/.f64 (sqrt.f64 2) (cos.f64 th))

Compiler

Compiled 685 to 629 computations (8.2% saved)

simplify97.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4972	5346
1	4972	5346

prune195.0ms (1.6%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	171	8	179

Error

Counts

179 → 8

Compiler

Compiled 4267 to 1607 computations (62.3% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.2b	(.f64 (cos.f64 th) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))))
0.1b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))
0.2b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

rewrite96.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

149×	`add-sqr-sqrt_binary64_441`
146×	`times-frac_binary64_425`
127×	`sqrt-prod_binary64_435`
90×	`cbrt-prod_binary64_450`
87×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
58×	`associate-r_binary64_359`
27×	`add-exp-log_binary64_457`
21×	`unswap-sqr_binary64_387`
19×	`add-cbrt-cube_binary64_455`
10×	`associate-l_binary64_360`
9×	`associate-/r*_binary64_363`
8×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452` `pow1_binary64_480` `div-exp_binary64_470` `cbrt-undiv_binary64_453`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `div-inv_binary64_416` `flip-+_binary64_393`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `associate-/l/_binary64_366`
1×	`associate-l/_binary64_362` `pow-prod-down_binary64_490` `clear-num_binary64_418` `frac-times_binary64_429` `associate-r/_binary64_361` `*-commutative_binary64_350` `frac-2neg_binary64_430`

Counts

4 → 226

Calls

8 calls:

37.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
9.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
0.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (*.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2))))

series847.0ms (6.9%)

Counts

4 → 66

Calls

4 calls:

393.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
201.0ms	(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (.f64 (cbrt.f64 (sqrt.f64 2)) (cbrt.f64 (sqrt.f64 2)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2))))
127.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
125.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 3031 to 2653 computations (12.5% saved)

simplify134.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5068	9586

prune571.0ms (4.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	292	0	292
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	292	8	300

Error

Counts

300 → 8

Compiler

Compiled 11413 to 5435 computations (52.4% saved)

simplify33.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	378	2187
1	378	2187

regimes819.0ms (6.7%)

Compiler: Compiled 9864 to 7169 computations (27.3% saved)

bsearch0.0ms (0%)

regimes159.0ms (1.3%)

Compiler: Compiled 863 to 904 computations (-4.8% saved)

bsearch0.0ms (0%)

regimes387.0ms (3.2%)

Compiler: Compiled 739 to 822 computations (-11.2% saved)

bsearch254.0ms (2.1%)

Steps

Iters	Range		Point
8	9.909161599577049e+39	9.268963790430922e+42	1.0013825153403935e+40
11	114097.38159879587	8.706302023933451e+32	8.559570785050661e+32
8	0.6278813230483827	545.690321179667	14.067337249671915
8	1.5924856529064694e-38	5.103707833301825e-34	3.658565851425877e-37
8	1.0692517598010272e-91	3.9924612374639804e-87	1.4957781138824434e-90
10	-15042801.715910457	-2.8301028264389928e-08	-0.00013996848613896063

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes351.0ms (2.9%)

Compiler: Compiled 658 to 741 computations (-12.6% saved)

bsearch239.0ms (2%)

Steps

Iters	Range		Point
8	9.909161599577049e+39	9.268963790430922e+42	1.0013825153403935e+40
11	114097.38159879587	8.706302023933451e+32	8.559570785050661e+32
8	0.6278813230483827	545.690321179667	1.6161391151093947
8	1.5924856529064694e-38	5.103707833301825e-34	3.6712194853085634e-36
8	1.0692517598010272e-91	3.9924612374639804e-87	2.0024369545087612e-89
10	-15042801.715910457	-2.8301028264389928e-08	-2.8656778876668223e-08

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes258.0ms (2.1%)

Compiler: Compiled 414 to 476 computations (-15% saved)

bsearch249.0ms (2%)

Steps

Iters	Range		Point
8	9.909161599577049e+39	9.268963790430922e+42	1.0013825153403935e+40
11	114097.38159879587	8.706302023933451e+32	8.559570785050661e+32
8	0.6278813230483827	545.690321179667	0.6566216709852691
8	1.5924856529064694e-38	5.103707833301825e-34	3.21862941055769e-37
8	1.0692517598010272e-91	3.9924612374639804e-87	7.41520578192646e-89
10	-15042801.715910457	-2.8301028264389928e-08	-2.8656778876668223e-08

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes160.0ms (1.3%)

Compiler: Compiled 351 to 413 computations (-17.7% saved)

bsearch58.0ms (0.5%)

Steps

Iters	Range		Point
6	0.0016530866322637507	0.01370526432397266	0.013518404392208106
9	-0.006226319988244784	-3.696252479164817e-09	-0.005518748015215943

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes53.0ms (0.4%)

Compiler: Compiled 173 to 214 computations (-23.7% saved)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

Accuracy

Total 0.4b remaining (93.2%)

Threshold costs 0.4b (93.2%)

Compiler

Compiled 15 to 54 computations (-260% saved)

bsearch14.0ms (0.1%)

Compiler: Compiled 346 to 220 computations (36.4% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	481
1	120	481

end0.0ms (0%)

sample4.0s (32.3%)

Algorithm

1×

intervals

Results

517.0ms	1733×	body	1024	valid
477.0ms	1603×	body	1024	invalid
367.0ms	4952×	body	128	valid
192.0ms	839×	body	512	invalid
188.0ms	877×	body	512	valid
63.0ms	435×	body	256	valid
62.0ms	389×	body	256	invalid
52.0ms	633×	body	128	invalid
1.0ms	3×	body	2048	valid

Compiler

Compiled 1726 to 1231 computations (28.7% saved)

Pareto

0.12738473056754207

Details

analyze735.0ms (6%)

sample87.0ms (0.7%)

simplify99.0ms (0.8%)

prune6.0ms (0.1%)

localize10.0ms (0.1%)

rewrite29.0ms (0.2%)

series613.0ms (5%)

simplify68.0ms (0.6%)

prune191.0ms (1.6%)

localize10.0ms (0.1%)

rewrite23.0ms (0.2%)

series705.0ms (5.8%)

simplify66.0ms (0.5%)

prune99.0ms (0.8%)

localize10.0ms (0.1%)

rewrite33.0ms (0.3%)

series483.0ms (3.9%)

simplify97.0ms (0.8%)

prune195.0ms (1.6%)

localize16.0ms (0.1%)

rewrite96.0ms (0.8%)

series847.0ms (6.9%)

simplify134.0ms (1.1%)

prune571.0ms (4.7%)

simplify33.0ms (0.3%)

regimes819.0ms (6.7%)

bsearch0.0ms (0%)

regimes159.0ms (1.3%)

bsearch0.0ms (0%)

regimes387.0ms (3.2%)

bsearch254.0ms (2.1%)

regimes351.0ms (2.9%)

bsearch239.0ms (2%)

regimes258.0ms (2.1%)

bsearch249.0ms (2%)

regimes160.0ms (1.3%)

bsearch58.0ms (0.5%)

regimes53.0ms (0.4%)

bsearch0.0ms (0%)

regimes25.0ms (0.2%)

bsearch14.0ms (0.1%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample4.0s (32.3%)

Profiling