Details

analyze2.7s (16%)

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)

sample264.0ms (1.6%)

Algorithm

1×

intervals

Results

212.0ms	175×	body	1024	valid
27.0ms	41×	body	512	valid
7.0ms	16×	body	256	valid
4.0ms	24×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify184.0ms (1.1%)

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: 12.6b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))
3.2b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548` `add-sqr-sqrt_binary64_2509`
9×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522`
6×	`cancel-sign-sub-inv_binary64_2453` `associate-r_binary64_2427`
4×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `sin-sum_binary64_2620` `pow-prod-down_binary64_2558` `add-log-exp_binary64_2526` `cos-sum_binary64_2621` `associate-l_binary64_2428`
3×	`cos-diff_binary64_2624`
2×	`sub-neg_binary64_2480` `*-commutative_binary64_2418` `sin-cos-mult_binary64_2643`
1×	`unswap-sqr_binary64_2455` `distribute-rgt-in_binary64_2437` `associate-*l/_binary64_2430` `distribute-lft-in_binary64_2436` `sin-diff_binary64_2623`

Counts

4 → 64

Calls

4 calls:

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

series347.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

214.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
69.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
35.0ms	(sin.f64 (-.f64 lambda1 lambda2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify90.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4876	1051
1	4876	1051

prune286.0ms (1.7%)

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: 7.3b

Counts

77 → 12

Compiler

Compiled 5854 to 2833 computations (51.6% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
3.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2509`
13×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
10×	`*-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522`
9×	`associate-r_binary64_2427`
7×	`associate-l_binary64_2428`
5×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558`
4×	`add-log-exp_binary64_2526` `cos-sum_binary64_2621`
3×	`*-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `cos-diff_binary64_2624`
2×	`unswap-sqr_binary64_2455` `sin-cos-mult_binary64_2643`
1×	`distribute-rgt-in_binary64_2437` `associate-*l/_binary64_2430` `sub-neg_binary64_2480` `distribute-lft-in_binary64_2436`

Counts

4 → 70

Calls

4 calls:

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 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series386.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

211.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
79.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
66.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5088	1103

prune212.0ms (1.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 0.1b

Counts

94 → 11

Compiler

Compiled 5029 to 1747 computations (65.3% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
18×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558`
12×	`add-sqr-sqrt_binary64_2509`
8×	`-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `associate-l_binary64_2428` `associate-r*_binary64_2427`
5×	`sin-cos-mult_binary64_2643`
4×	`*-commutative_binary64_2418` `add-log-exp_binary64_2526`
3×	`sin-mult_binary64_2642`
2×	`unswap-sqr_binary64_2455` `associate-l/_binary64_2430` `frac-times_binary64_2497` `cos-mult_binary64_2641` `associate-r/_binary64_2429`

Counts

4 → 88

Calls

4 calls:

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

series593.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

235.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
218.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
67.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify77.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4960	1556
1	4960	1556

prune441.0ms (2.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 0.1b

Counts

111 → 13

Compiler

Compiled 10854 to 4131 computations (61.9% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
18×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558`
10×	`add-sqr-sqrt_binary64_2509`
8×	`-un-lft-identity_binary64_2487` `add-cube-cbrt_binary64_2522` `associate-l_binary64_2428` `associate-r*_binary64_2427`
4×	`*-commutative_binary64_2418` `add-log-exp_binary64_2526`
3×	`sin-mult_binary64_2642` `associate-*r/_binary64_2429`
2×	`associate-*l/_binary64_2430` `sin-cos-mult_binary64_2643` `cos-mult_binary64_2641`
1×	`unswap-sqr_binary64_2455` `frac-times_binary64_2497`

Counts

4 → 85

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (cos.f64 phi2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
7.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series653.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 lambda1) (cos.f64 lambda2))) (cos.f64 phi2))
218.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
129.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 lambda1) (cos.f64 lambda2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify76.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5111	1551

prune123.0ms (0.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	97	13	110

Merged error: 0.1b

Counts

110 → 13

Compiler

Compiled 4600 to 483 computations (89.5% saved)

regimes577.0ms (3.5%)

Compiler: Compiled 7446 to 4592 computations (38.3% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	63
1	136	63

end0.0ms (0%)

sample9.4s (56%)

Algorithm

1×

intervals

Results

6.5s	5424×	body	1024	valid
845.0ms	1270×	body	512	valid
473.0ms	168×	body	2048	valid
150.0ms	784×	body	128	valid
140.0ms	354×	body	256	valid

Compiler

Compiled 1237 to 759 computations (38.6% saved)

Details

analyze2.7s (16%)

sample264.0ms (1.6%)

simplify184.0ms (1.1%)

prune4.0ms (0%)

localize26.0ms (0.2%)

rewrite32.0ms (0.2%)

series347.0ms (2.1%)

simplify90.0ms (0.5%)

prune286.0ms (1.7%)

localize33.0ms (0.2%)

rewrite32.0ms (0.2%)

series386.0ms (2.3%)

simplify81.0ms (0.5%)

prune212.0ms (1.3%)

localize38.0ms (0.2%)

rewrite44.0ms (0.3%)

series593.0ms (3.5%)

simplify77.0ms (0.5%)

prune441.0ms (2.6%)

localize38.0ms (0.2%)

rewrite46.0ms (0.3%)

series653.0ms (3.9%)

simplify76.0ms (0.5%)

prune123.0ms (0.7%)

regimes577.0ms (3.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample9.4s (56%)

Profiling