Details

analyze4.8s (19.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
7.8%	92%	0.2%	9
7.8%	92%	0.2%	10
10.1%	89.7%	0.2%	11
10.1%	89.7%	0.2%	12
13.9%	85.9%	0.2%	13
13.9%	85.9%	0.2%	14

Compiler

Compiled 25 to 18 computations (28% saved)

sample373.0ms (1.5%)

Algorithm

1×

intervals

Results

264.0ms	158×	body	1024	valid
48.0ms	39×	body	512	valid
16.0ms	5×	body	2048	valid
12.0ms	37×	body	128	valid
11.0ms	17×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify189.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune6.0ms (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: 9.9b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.7b	(sin.f64 (-.f64 lambda1 lambda2))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite50.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64_2503` `add-sqr-sqrt_binary64_2487` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
9×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
6×	`cancel-sign-sub-inv_binary64_2431` `associate-r_binary64_2405`
4×	`add-log-exp_binary64_2504` `cos-sum_binary64_2599` `prod-exp_binary64_2514` `sin-sum_binary64_2598` `pow-prod-down_binary64_2536` `associate-l_binary64_2406` `cbrt-unprod_binary64_2498`
3×	`cos-diff_binary64_2602`
2×	`*-commutative_binary64_2396` `sub-neg_binary64_2458` `sin-cos-mult_binary64_2621`
1×	`associate-*l/_binary64_2408` `sin-diff_binary64_2601` `distribute-lft-in_binary64_2414` `unswap-sqr_binary64_2433` `distribute-rgt-in_binary64_2415`

Counts

4 → 64

Calls

4 calls:

14.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
8.0ms	(cos.f64 (-.f64 lambda1 lambda2))
8.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series349.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

209.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
76.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify145.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5077	1051

prune197.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 4.6b

Counts

77 → 10

Compiler

Compiled 2508 to 518 computations (79.3% saved)

localize49.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite62.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2487`
13×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
10×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
9×	`associate-r_binary64_2405`
7×	`associate-l_binary64_2406`
5×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
4×	`add-log-exp_binary64_2504` `cos-sum_binary64_2599`
3×	`*-commutative_binary64_2396` `cancel-sign-sub-inv_binary64_2431` `cos-diff_binary64_2602`
2×	`unswap-sqr_binary64_2433` `sin-cos-mult_binary64_2621`
1×	`associate-*l/_binary64_2408` `distribute-lft-in_binary64_2414` `sub-neg_binary64_2458` `distribute-rgt-in_binary64_2415`

Counts

4 → 70

Calls

4 calls:

15.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
9.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series351.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

180.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
74.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
69.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
27.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify221.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (189.0ms)

Iter	Nodes	Cost
0	4830	1103
1	4830	1103

prune210.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	3	82
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 0.0b

Counts

92 → 10

Compiler

Compiled 3266 to 580 computations (82.2% saved)

localize68.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.1b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite69.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_2487`
15×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
12×	`associate-r_binary64_2405`
11×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
10×	`associate-l_binary64_2406`
6×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
5×	`sin-cos-mult_binary64_2621`
4×	`add-log-exp_binary64_2504` `*-commutative_binary64_2396`
3×	`sin-mult_binary64_2620` `frac-times_binary64_2475` `associate-*r/_binary64_2407` `unswap-sqr_binary64_2433`
2×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `cos-mult_binary64_2619` `frac-add_binary64_2473`
1×	`associate-*l/_binary64_2408` `distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`

Counts

4 → 83

Calls

4 calls:

22.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
8.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
8.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

series525.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
62.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
60.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
59.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify128.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5026	1744

prune268.0ms (1.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	90	5	95
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	95	10	105

Merged error: 0.0b

Counts

105 → 10

Compiler

Compiled 4607 to 734 computations (84.1% saved)

localize69.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(cbrt.f64 (cos.f64 lambda2))
0.2b	(cbrt.f64 (cos.f64 lambda2))
0.2b	(cbrt.f64 (cos.f64 lambda2))

rewrite48.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526` `cbrt-prod_binary64_2496`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-sqr-sqrt_binary64_2487`
4×	`add-log-exp_binary64_2504` `sin-cos-mult_binary64_2621`
3×	`frac-times_binary64_2475` `associate-r/_binary64_2407` `pow1/3_binary64_2547` `prod-exp_binary64_2514` `associate-r*_binary64_2405` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
2×	`flip3-+_binary64_2468` `sin-mult_binary64_2620` `flip-+_binary64_2439` `cos-mult_binary64_2619` `frac-add_binary64_2473`
1×	`associate-l/_binary64_2408` `distribute-lft-in_binary64_2414` `-commutative_binary64_2396` `distribute-rgt-in_binary64_2415` `associate-l_binary64_2406`

Counts

4 → 60

Calls

4 calls:

22.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
3.0ms	(cbrt.f64 (cos.f64 lambda2))
3.0ms	(cbrt.f64 (cos.f64 lambda2))
3.0ms	(cbrt.f64 (cos.f64 lambda2))

series768.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

392.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
133.0ms	(cbrt.f64 (cos.f64 lambda2))
132.0ms	(cbrt.f64 (cos.f64 lambda2))
111.0ms	(cbrt.f64 (cos.f64 lambda2))

simplify201.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (164.0ms)

Iter	Nodes	Cost
0	4949	1398
1	4949	1398

prune190.0ms (0.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	72	10	82

Merged error: 0.0b

Counts

82 → 10

Compiler

Compiled 3831 to 427 computations (88.9% saved)

regimes976.0ms (3.9%)

Compiler: Compiled 6931 to 4496 computations (35.1% saved)

bsearch0.0ms (0%)

simplify10.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	128	67
1	128	67

end0.0ms (0%)

sample14.6s (58.6%)

Algorithm

1×

intervals

Results

9.6s	5296×	body	1024	valid
1.4s	1324×	body	512	valid
699.0ms	186×	body	2048	valid
289.0ms	414×	body	256	valid
250.0ms	780×	body	128	valid

Compiler

Compiled 1135 to 736 computations (35.2% saved)

Details

analyze4.8s (19.1%)

sample373.0ms (1.5%)

simplify189.0ms (0.8%)

prune6.0ms (0%)

localize36.0ms (0.1%)

rewrite50.0ms (0.2%)

series349.0ms (1.4%)

simplify145.0ms (0.6%)

prune197.0ms (0.8%)

localize49.0ms (0.2%)

rewrite62.0ms (0.2%)

series351.0ms (1.4%)

simplify221.0ms (0.9%)

prune210.0ms (0.8%)

localize68.0ms (0.3%)

rewrite69.0ms (0.3%)

series525.0ms (2.1%)

simplify128.0ms (0.5%)

prune268.0ms (1.1%)

localize69.0ms (0.3%)

rewrite48.0ms (0.2%)

series768.0ms (3.1%)

simplify201.0ms (0.8%)

prune190.0ms (0.8%)

regimes976.0ms (3.9%)

bsearch0.0ms (0%)

simplify10.0ms (0%)

end0.0ms (0%)

sample14.6s (58.6%)

Profiling