Details

analyze1.1s (13.2%)

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
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample73.0ms (0.9%)

Algorithm

1×

intervals

Results

40.0ms	108×	body	1024	valid
11.0ms	50×	body	512	valid
5.0ms	75×	body	128	valid
3.0ms	3×	body	2048	valid
3.0ms	20×	body	256	valid

Compiler

Compiled 19 to 20 computations (-5.3% saved)

simplify177.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune2.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 16.3b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.0b	(cos.f64 (+.f64 a b))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
9×	`add-sqr-sqrt_binary64_435`
7×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
5×	`pow1_binary64_472`
3×	`times-frac_binary64_420` `associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356` `associate-/r*_binary64_360`
2×	`cbrt-undiv_binary64_445` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `div-inv_binary64_411` `-commutative_binary64_347` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `frac-2neg_binary64_425` `unswap-sqr_binary64_382` `associate-/l_binary64_361`

Counts

3 → 47

Calls

3 calls:

6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))
4.0ms	(*.f64 r (sin.f64 b))

series318.0ms (3.9%)

Counts

3 → 9

Calls

3 calls:

226.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
65.0ms	(*.f64 r (sin.f64 b))
28.0ms	(cos.f64 (+.f64 a b))

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4866	692
1	4866	692

prune51.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	6	57

Merged error: 0.2b

Counts

57 → 6

Compiler

Compiled 809 to 215 computations (73.4% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.3b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_435`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
10×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
8×	`pow1_binary64_472`
6×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356`
5×	`sin-mult_binary64_566`
4×	`associate-/r/_binary64_362` `cos-mult_binary64_565`
3×	`times-frac_binary64_420` `prod-exp_binary64_460` `cbrt-unprod_binary64_444` `associate-/r*_binary64_360`
2×	`flip3--_binary64_418` `*-commutative_binary64_347` `frac-sub_binary64_423` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `flip--_binary64_389` `unswap-sqr_binary64_382` `sub-div_binary64_421` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `div-inv_binary64_411` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-/l*_binary64_361`

Counts

4 → 75

Calls

4 calls:

10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
4.0ms	(*.f64 r (sin.f64 b))

series807.0ms (10%)

Counts

4 → 12

Calls

4 calls:

517.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))
152.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
73.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
65.0ms	(*.f64 r (sin.f64 b))

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6283	1553

prune101.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	78	9	87
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	83	10	93

Merged error: 0.0b

Counts

93 → 10

Compiler

Compiled 2084 to 433 computations (79.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
0.1b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_435`
22×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414`
20×	`associate-r_binary64_356`
19×	`times-frac_binary64_420`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r/_binary64_362` `pow1_binary64_472`
7×	`sin-mult_binary64_566`
6×	`cos-mult_binary64_565` `associate-l_binary64_357` `add-log-exp_binary64_450`
3×	`flip3--_binary64_418` `frac-sub_binary64_423` `prod-exp_binary64_460` `flip--_binary64_389` `unswap-sqr_binary64_382` `associate-/l_binary64_361` `cbrt-unprod_binary64_444` `sub-div_binary64_421` `associate-/r_binary64_360`
2×	`div-inv_binary64_411` `*-commutative_binary64_347` `cbrt-undiv_binary64_445` `pow-prod-down_binary64_482` `div-exp_binary64_462`
1×	`clear-num_binary64_413` `diff-log_binary64_503` `sub-neg_binary64_407` `frac-2neg_binary64_425` `associate-*r/_binary64_358`

Counts

4 → 99

Calls

4 calls:

13.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

series1.0s (12.5%)

Counts

4 → 12

Calls

4 calls:

491.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
287.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))
157.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
72.0ms	(*.f64 (sin.f64 b) (sin.f64 a))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6013	2846

prune115.0ms (1.4%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	110	11	121

Merged error: 0.0b

Counts

121 → 11

Compiler

Compiled 2994 to 587 computations (80.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 a) (cos.f64 b))
0.1b	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
0.2b	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
0.2b	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64_435`
28×	`*-un-lft-identity_binary64_414`
18×	`times-frac_binary64_420` `add-cube-cbrt_binary64_446`
13×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447`
8×	`associate-/r*_binary64_360`
6×	`pow1_binary64_472` `add-log-exp_binary64_450`
5×	`distribute-lft-out--_binary64_368` `difference-of-squares_binary64_383`
4×	`associate-/l*_binary64_361`
3×	`cbrt-undiv_binary64_445` `associate-l_binary64_357` `associate-r_binary64_356` `div-exp_binary64_462`
2×	`associate-/r/_binary64_362` `flip3--_binary64_418` `clear-num_binary64_413` `cos-mult_binary64_565` `div-inv_binary64_411` `prod-exp_binary64_460` `frac-2neg_binary64_425` `flip--_binary64_389` `cbrt-unprod_binary64_444`
1×	`diff-log_binary64_503` `*-commutative_binary64_347` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `unswap-sqr_binary64_382` `associate-/l/_binary64_363`

Counts

4 → 91

Calls

4 calls:

10.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
8.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
6.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
5.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

series851.0ms (10.5%)

Counts

4 → 12

Calls

4 calls:

454.0ms	(/.f64 r (-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a)))
180.0ms	(-.f64 (/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b)) (sin.f64 a))
150.0ms	(/.f64 (*.f64 (cos.f64 a) (cos.f64 b)) (sin.f64 b))
67.0ms	(*.f64 (cos.f64 a) (cos.f64 b))

simplify102.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4917	2329
1	4917	2329

prune87.0ms (1.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	102	12	114

Merged error: 0.0b

Counts

114 → 12

Compiler

Compiled 2100 to 373 computations (82.2% saved)

regimes88.0ms (1.1%)

Compiler: Compiled 951 to 522 computations (45.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms (0%)

sample2.8s (34.8%)

Algorithm

1×

intervals

Results

1.3s	3497×	body	1024	valid
333.0ms	1406×	body	512	valid
246.0ms	597×	body	256	valid
184.0ms	199×	body	2048	valid
181.0ms	2301×	body	128	valid

Compiler

Compiled 341 to 192 computations (43.7% saved)

Details

analyze1.1s (13.2%)

sample73.0ms (0.9%)

simplify177.0ms (2.2%)

prune2.0ms (0%)

localize10.0ms (0.1%)

rewrite18.0ms (0.2%)

series318.0ms (3.9%)

simplify79.0ms (1%)

prune51.0ms (0.6%)

localize16.0ms (0.2%)

rewrite32.0ms (0.4%)

series807.0ms (10%)

simplify74.0ms (0.9%)

prune101.0ms (1.3%)

localize16.0ms (0.2%)

rewrite46.0ms (0.6%)

series1.0s (12.5%)

simplify82.0ms (1%)

prune115.0ms (1.4%)

localize14.0ms (0.2%)

rewrite37.0ms (0.5%)

series851.0ms (10.5%)

simplify102.0ms (1.3%)

prune87.0ms (1.1%)

regimes88.0ms (1.1%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.8s (34.8%)

Profiling