Details

analyze2.5s (17.8%)

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)

sample208.0ms (1.5%)

Algorithm

1×

intervals

Results

159.0ms	176×	body	1024	valid
21.0ms	41×	body	512	valid
7.0ms	4×	body	2048	valid
4.0ms	13×	body	256	valid
4.0ms	22×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify105.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	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

Error

13.5b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize19.0ms (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)))
3.3b	(sin.f64 (-.f64 lambda1 lambda2))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite251.0ms (1.8%)

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:

227.0ms	(*.f64 (sin.f64 phi1) (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	(sin.f64 (-.f64 lambda1 lambda2))

series187.0ms (1.3%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
43.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify79.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5077	1051

prune107.0ms (0.8%)

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

Error

5.8b

Counts

77 → 12

Compiler

Compiled 2528 to 556 computations (78% saved)

localize28.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.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)))
3.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite32.0ms (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×	`associate-l/_binary64_2408` `-commutative_binary64_2396` `cancel-sign-sub-inv_binary64_2431` `cos-diff_binary64_2602`
2×	`unswap-sqr_binary64_2433`
1×	`distribute-lft-in_binary64_2414` `flip--_binary64_2440` `sub-neg_binary64_2458` `sin-cos-mult_binary64_2621` `distribute-rgt-in_binary64_2415` `flip3--_binary64_2469`

Counts

4 → 71

Calls

4 calls:

7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
7.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series312.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

143.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
114.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
39.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5297	1458

prune123.0ms (0.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Error

0.1b

Counts

95 → 11

Compiler

Compiled 3471 to 596 computations (82.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite43.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
18×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
12×	`add-sqr-sqrt_binary64_2487`
8×	`-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `associate-r_binary64_2405` `associate-l*_binary64_2406`
4×	`associate-l/_binary64_2408` `add-log-exp_binary64_2504` `-commutative_binary64_2396` `sin-cos-mult_binary64_2621`
3×	`sin-mult_binary64_2620`
2×	`frac-times_binary64_2475` `associate-*r/_binary64_2407` `cos-mult_binary64_2619` `unswap-sqr_binary64_2433`
1×	`flip--_binary64_2440` `flip3--_binary64_2469`

Counts

4 → 89

Calls

4 calls:

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

series421.0ms (3%)

Counts

4 → 12

Calls

4 calls:

133.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
132.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
118.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
37.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify72.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5157	1911

prune164.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	100	12	112

Error

0.0b

Counts

112 → 12

Compiler

Compiled 5493 to 782 computations (85.8% saved)

localize29.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1)) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite45.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
18×	`prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
10×	`add-sqr-sqrt_binary64_2487` `associate-r_binary64_2405`
8×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500`
6×	`associate-l_binary64_2406`
4×	`associate-l/_binary64_2408` `add-log-exp_binary64_2504` `-commutative_binary64_2396`
3×	`sin-mult_binary64_2620`
2×	`cos-mult_binary64_2619` `sin-cos-mult_binary64_2621`
1×	`frac-times_binary64_2475` `associate-*r/_binary64_2407` `unswap-sqr_binary64_2433`

Counts

4 → 85

Calls

4 calls:

11.0ms	(.f64 (.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1)) (cos.f64 phi2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series366.0ms (2.6%)

Counts

4 → 12

Calls

4 calls:

130.0ms	(.f64 (.f64 (*.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1)) (cos.f64 phi2))
117.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
79.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4964	1548
1	4964	1548

prune114.0ms (0.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	97	12	109

Error

0.0b

Counts

109 → 12

Compiler

Compiled 4598 to 480 computations (89.6% saved)

regimes715.0ms (5.1%)

Accuracy

Total 0.1b remaining (71.2%)

Threshold costs 0.1b (71.2%)

Compiler

Compiled 10078 to 6263 computations (37.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	160	73
1	160	73

end0.0ms (0%)

sample7.9s (56.6%)

Algorithm

1×

intervals

Results

4.9s	5362×	body	1024	valid
717.0ms	1294×	body	512	valid
361.0ms	175×	body	2048	valid
149.0ms	402×	body	256	valid
146.0ms	767×	body	128	valid

Compiler

Compiled 1641 to 1015 computations (38.1% saved)

Details

analyze2.5s (17.8%)

sample208.0ms (1.5%)

simplify105.0ms (0.7%)

prune4.0ms (0%)

localize19.0ms (0.1%)

rewrite251.0ms (1.8%)

series187.0ms (1.3%)

simplify79.0ms (0.6%)

prune107.0ms (0.8%)

localize28.0ms (0.2%)

rewrite32.0ms (0.2%)

series312.0ms (2.2%)

simplify46.0ms (0.3%)

prune123.0ms (0.9%)

localize29.0ms (0.2%)

rewrite43.0ms (0.3%)

series421.0ms (3%)

simplify72.0ms (0.5%)

prune164.0ms (1.2%)

localize29.0ms (0.2%)

rewrite45.0ms (0.3%)

series366.0ms (2.6%)

simplify88.0ms (0.6%)

prune114.0ms (0.8%)

regimes715.0ms (5.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.9s (56.6%)

Profiling