Details

analyze2.5s (17.2%)

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)

sample260.0ms (1.8%)

Algorithm

1×

intervals

Results

203.0ms	182×	body	1024	valid
20.0ms	34×	body	512	valid
17.0ms	6×	body	2048	valid
4.0ms	27×	body	128	valid
2.0ms	7×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify191.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

prune4.0ms (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: 13.2b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize31.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))
3.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_1127` `pow1_binary64_1166` `add-cbrt-cube_binary64_1141` `add-exp-log_binary64_1143`
9×	`*-un-lft-identity_binary64_1105` `add-cube-cbrt_binary64_1140`
6×	`associate-r_binary64_1045` `cancel-sign-sub-inv_binary64_1071`
4×	`add-log-exp_binary64_1144` `prod-exp_binary64_1154` `cos-sum_binary64_1239` `cbrt-unprod_binary64_1138` `associate-l_binary64_1046` `sin-sum_binary64_1238` `pow-prod-down_binary64_1176`
3×	`cos-diff_binary64_1242`
2×	`*-commutative_binary64_1036` `sin-cos-mult_binary64_1261` `sub-neg_binary64_1098`
1×	`sin-diff_binary64_1241` `unswap-sqr_binary64_1073` `associate-*l/_binary64_1048` `distribute-lft-in_binary64_1054` `distribute-rgt-in_binary64_1055`

Counts

4 → 64

Calls

4 calls:

8.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(sin.f64 (-.f64 lambda1 lambda2))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series395.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

210.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
119.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify68.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4859	1102
1	4859	1102

prune104.0ms (0.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	64	12	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	12	77

Merged error: 6.1b

Counts

77 → 12

Compiler

Compiled 2519 to 506 computations (79.9% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite36.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1127`
13×	`pow1_binary64_1166` `add-cbrt-cube_binary64_1141` `add-exp-log_binary64_1143`
10×	`*-un-lft-identity_binary64_1105` `add-cube-cbrt_binary64_1140`
9×	`associate-r_binary64_1045`
7×	`associate-l_binary64_1046`
5×	`prod-exp_binary64_1154` `cbrt-unprod_binary64_1138` `pow-prod-down_binary64_1176`
4×	`add-log-exp_binary64_1144` `cos-sum_binary64_1239`
3×	`-commutative_binary64_1036` `cancel-sign-sub-inv_binary64_1071` `associate-l/_binary64_1048` `cos-diff_binary64_1242`
2×	`sin-cos-mult_binary64_1261` `unswap-sqr_binary64_1073`
1×	`sub-neg_binary64_1098` `flip3--_binary64_1109` `flip--_binary64_1080` `distribute-lft-in_binary64_1054` `distribute-rgt-in_binary64_1055`

Counts

4 → 72

Calls

4 calls:

9.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))

series560.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

244.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
217.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
67.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify47.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5127	1472

prune113.0ms (0.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	82	2	84
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.1b

Counts

96 → 10

Compiler

Compiled 3392 to 557 computations (83.6% saved)

localize38.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_1166` `add-cbrt-cube_binary64_1141` `add-exp-log_binary64_1143`
18×	`prod-exp_binary64_1154` `cbrt-unprod_binary64_1138` `pow-prod-down_binary64_1176`
12×	`add-sqr-sqrt_binary64_1127`
8×	`-un-lft-identity_binary64_1105` `associate-r_binary64_1045` `associate-l*_binary64_1046` `add-cube-cbrt_binary64_1140`
4×	`-commutative_binary64_1036` `sin-cos-mult_binary64_1261` `add-log-exp_binary64_1144` `associate-l/_binary64_1048`
3×	`sin-mult_binary64_1260`
2×	`frac-times_binary64_1115` `cos-mult_binary64_1259` `unswap-sqr_binary64_1073` `associate-*r/_binary64_1047`
1×	`flip3--_binary64_1109` `flip--_binary64_1080`

Counts

4 → 89

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series774.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

256.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
242.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
206.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5153	1911

prune178.0ms (1.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	6	3	9
Picked	1	0	1
Done	0	0	0
Total	102	9	111

Merged error: 0.0b

Counts

111 → 9

Compiler

Compiled 5350 to 705 computations (86.8% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
0.7b	(cbrt.f64 (sin.f64 lambda2))
0.7b	(cbrt.f64 (sin.f64 lambda2))
0.7b	(cbrt.f64 (sin.f64 lambda2))

rewrite25.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1136`
23×	`add-sqr-sqrt_binary64_1127`
15×	`*-un-lft-identity_binary64_1105` `add-cube-cbrt_binary64_1140`
11×	`pow1_binary64_1166`
9×	`pow1/3_binary64_1187`
6×	`swap-sqr_binary64_1072` `associate-r_binary64_1045` `associate-l_binary64_1046` `add-exp-log_binary64_1143`
4×	`add-log-exp_binary64_1144` `add-cbrt-cube_binary64_1141` `unswap-sqr_binary64_1073`
2×	`pow-sqr_binary64_1078` `pow-prod-up_binary64_1175` `pow-prod-down_binary64_1176`
1×	`*-commutative_binary64_1036` `pow-plus_binary64_1168` `prod-exp_binary64_1154` `cbrt-unprod_binary64_1138` `pow2_binary64_1186`

Counts

4 → 73

Calls

4 calls:

8.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
2.0ms	(cbrt.f64 (sin.f64 lambda2))
2.0ms	(cbrt.f64 (sin.f64 lambda2))
2.0ms	(cbrt.f64 (sin.f64 lambda2))

series518.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
127.0ms	(cbrt.f64 (sin.f64 lambda2))
123.0ms	(cbrt.f64 (sin.f64 lambda2))
121.0ms	(cbrt.f64 (sin.f64 lambda2))

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4872	797
1	4872	797

prune128.0ms (0.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	85	9	94

Merged error: 0.0b

Counts

94 → 9

Compiler

Compiled 4757 to 687 computations (85.6% saved)

regimes177.0ms (1.2%)

Compiler: Compiled 2304 to 1270 computations (44.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	176	89
1	176	89

end0.0ms (0%)

sample8.0s (55.4%)

Algorithm

1×

intervals

Results

5.8s	5412×	body	1024	valid
743.0ms	1237×	body	512	valid
497.0ms	189×	body	2048	valid
137.0ms	801×	body	128	valid
136.0ms	361×	body	256	valid

Compiler

Compiled 518 to 282 computations (45.6% saved)

Details

analyze2.5s (17.2%)

sample260.0ms (1.8%)

simplify191.0ms (1.3%)

prune4.0ms (0%)

localize31.0ms (0.2%)

rewrite34.0ms (0.2%)

series395.0ms (2.7%)

simplify68.0ms (0.5%)

prune104.0ms (0.7%)

localize36.0ms (0.2%)

rewrite36.0ms (0.3%)

series560.0ms (3.9%)

simplify47.0ms (0.3%)

prune113.0ms (0.8%)

localize38.0ms (0.3%)

rewrite48.0ms (0.3%)

series774.0ms (5.3%)

simplify71.0ms (0.5%)

prune178.0ms (1.2%)

localize43.0ms (0.3%)

rewrite25.0ms (0.2%)

series518.0ms (3.6%)

simplify80.0ms (0.5%)

prune128.0ms (0.9%)

regimes177.0ms (1.2%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.0s (55.4%)

Profiling