Details

analyze739.0ms (6.4%)

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)

sample73.0ms (0.6%)

Algorithm

1×

intervals

Results

14.0ms	46×	body	1024	valid
14.0ms	46×	body	1024	invalid
12.0ms	168×	body	128	valid
7.0ms	32×	body	512	valid
4.0ms	19×	body	512	invalid
2.0ms	31×	body	128	invalid
2.0ms	13×	body	256	invalid
1.0ms	10×	body	256	valid

Compiler

Compiled 39 to 34 computations (12.8% saved)

simplify101.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	106	20
1	106	20

prune4.0ms (0%)

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)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(.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))

rewrite130.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

39×	`add-sqr-sqrt_binary64_441`
38×	`times-frac_binary64_425`
31×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
22×	`sqrt-prod_binary64_435` `associate-r_binary64_359`
9×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
6×	`associate-/r*_binary64_363`
4×	`pow1_binary64_480`
3×	`associate-/l_binary64_364` `unswap-sqr_binary64_387` `associate-l*_binary64_360`
2×	`div-exp_binary64_470` `add-log-exp_binary64_458` `cbrt-undiv_binary64_453` `div-inv_binary64_416` `associate-/l/_binary64_366` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
1×	`frac-2neg_binary64_430` `clear-num_binary64_418` `flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `associate-r/_binary64_361` `-commutative_binary64_350`

Counts

2 → 83

Calls

2 calls:

12.0ms	(.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))

Compiler

Compiled 2118 to 796 computations (62.4% saved)

series596.0ms (5.1%)

Error

0.3b

Counts

2 → 30

Calls

2 calls:

398.0ms	(.f64 (cos.f64 th) (/.f64 (+.f64 (.f64 a1 a1) (*.f64 a2 a2)) (sqrt.f64 2)))
162.0ms	(/.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)) (sqrt.f64 2))

Compiler

Compiled 1334 to 1170 computations (12.3% saved)

simplify70.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5339	2746

prune130.0ms (1.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	107	6	113
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	108	7	115

Error

Counts

115 → 7

Compiler

Compiled 2544 to 1036 computations (59.3% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
0.4b	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
6.4b	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
6.4b	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

rewrite238.0ms (2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

84×	`sqrt-prod_binary64_435`
72×	`times-frac_binary64_425`
61×	`add-sqr-sqrt_binary64_441`
59×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
40×	`associate-r_binary64_359`
18×	`add-exp-log_binary64_457` `add-cbrt-cube_binary64_455`
11×	`pow1_binary64_480`
10×	`sqrt-div_binary64_436`
6×	`associate-/l_binary64_364` `associate-/r_binary64_363` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
5×	`flip3-+_binary64_422` `flip-+_binary64_393` `associate-*r/_binary64_361`
4×	`add-log-exp_binary64_458`
3×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `pow-prod-down_binary64_490`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-inv_binary64_416` `associate-/l/_binary64_366` `frac-times_binary64_429` `associate-*l/_binary64_362`
1×	`sqrt-undiv_binary64_440` `frac-2neg_binary64_430` `clear-num_binary64_418` `associate-l_binary64_360` `*-commutative_binary64_350`

Counts

4 → 157

Calls

4 calls:

20.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
4.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
4.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 5839 to 1470 computations (74.8% saved)

series781.0ms (6.7%)

Error

Counts

4 → 54

Calls

4 calls:

407.0ms	(.f64 (.f64 (cos.f64 th) (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))) (/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2)))
147.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (sqrt.f64 2))
85.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))
83.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 3293 to 2408 computations (26.9% saved)

simplify118.0ms (1%)

Algorithm

1×	egg-herbie

Counts

211 → 211

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4966	5413
1	4966	5413

prune215.0ms (1.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	211	7	218

Error

Counts

218 → 7

Compiler

Compiled 6256 to 1908 computations (69.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

rewrite69.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Error

Rules

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

Counts

2 → 49

Calls

2 calls:

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

Compiler

Compiled 1103 to 358 computations (67.5% saved)

series666.0ms (5.7%)

Error

Counts

2 → 36

Calls

2 calls:

374.0ms	(/.f64 (.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th)) (sqrt.f64 2))
250.0ms	(.f64 (+.f64 (.f64 a2 a2) (*.f64 a1 a1)) (cos.f64 th))

Compiler

Compiled 1732 to 1472 computations (15% saved)

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4973	1803
1	4973	1803

prune75.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	85	7	92

Error

Counts

92 → 7

Compiler

Compiled 1636 to 671 computations (59% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite475.0ms (4.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`times-frac_binary64_425`
102×	`sqrt-prod_binary64_435`
86×	`add-sqr-sqrt_binary64_441`
84×	`add-cube-cbrt_binary64_454` `*-un-lft-identity_binary64_419`
78×	`cbrt-prod_binary64_450`
58×	`associate-r_binary64_359`
38×	`add-exp-log_binary64_457`
29×	`add-cbrt-cube_binary64_455`
16×	`prod-exp_binary64_468` `cbrt-unprod_binary64_452`
11×	`pow1_binary64_480`
9×	`div-exp_binary64_470` `cbrt-undiv_binary64_453` `associate-/r*_binary64_363`
6×	`sqrt-div_binary64_436` `associate-/l*_binary64_364`
4×	`add-log-exp_binary64_458`
3×	`flip3-+_binary64_422` `flip-+_binary64_393` `pow-prod-down_binary64_490` `associate-*r/_binary64_361`
2×	`pow1/2_binary64_499` `sqrt-pow1_binary64_437` `rem-sqrt-square_binary64_432` `div-inv_binary64_416` `associate-/l/_binary64_366`
1×	`frac-times_binary64_429` `associate-l/_binary64_362` `associate-l_binary64_360` `-commutative_binary64_350` `frac-2neg_binary64_430` `clear-num_binary64_418`

Counts

4 → 201

Calls

4 calls:

29.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
8.0ms	(/.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 a2 a2) (.f64 a1 a1)))

Compiler

Compiled 9640 to 4180 computations (56.6% saved)

series1.1s (9.7%)

Error

Counts

4 → 54

Calls

4 calls:

394.0ms	(.f64 (.f64 (cos.f64 th) (/.f64 (sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1))) (.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))))
295.0ms	(sqrt.f64 (+.f64 (.f64 a2 a2) (.f64 a1 a1)))
268.0ms	(/.f64 (sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2))) (cbrt.f64 (sqrt.f64 2)))
88.0ms	(sqrt.f64 (+.f64 (.f64 a1 a1) (.f64 a2 a2)))

Compiler

Compiled 4313 to 3453 computations (19.9% saved)

simplify126.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

255 → 255

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5016	8176

prune429.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	255	0	255
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	255	7	262

Error

Counts

262 → 7

Compiler

Compiled 9599 to 4411 computations (54% saved)

regimes1.2s (10.6%)

Accuracy

Total 0.3b remaining (95.2%)

Threshold costs 0.3b (95.2%)

Compiler

Compiled 16231 to 11729 computations (27.7% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	34
1	17	34

end0.0ms (0%)

sample4.1s (35.4%)

Algorithm

1×

intervals

Results

570.0ms	1842×	body	1024	valid
482.0ms	1522×	body	1024	invalid
368.0ms	4795×	body	128	valid
209.0ms	911×	body	512	valid
161.0ms	726×	body	512	invalid
67.0ms	447×	body	256	valid
58.0ms	393×	body	256	invalid
55.0ms	669×	body	128	invalid
2.0ms	5×	body	2048	valid

Compiler

Compiled 2053 to 1479 computations (28% saved)

Details

analyze739.0ms (6.4%)

sample73.0ms (0.6%)

simplify101.0ms (0.9%)

prune4.0ms (0%)

localize9.0ms (0.1%)

rewrite130.0ms (1.1%)

series596.0ms (5.1%)

simplify70.0ms (0.6%)

prune130.0ms (1.1%)

localize14.0ms (0.1%)

rewrite238.0ms (2%)

series781.0ms (6.7%)

simplify118.0ms (1%)

prune215.0ms (1.8%)

localize10.0ms (0.1%)

rewrite69.0ms (0.6%)

series666.0ms (5.7%)

simplify64.0ms (0.6%)

prune75.0ms (0.6%)

localize19.0ms (0.2%)

rewrite475.0ms (4.1%)

series1.1s (9.7%)

simplify126.0ms (1.1%)

prune429.0ms (3.7%)

regimes1.2s (10.6%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample4.1s (35.4%)

Profiling