Details

analyze2.6s (15.6%)

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)

sample273.0ms (1.7%)

Algorithm

1×

intervals

Results

201.0ms	178×	body	1024	valid
24.0ms	9×	body	2048	valid
19.0ms	31×	body	512	valid
11.0ms	16×	body	256	valid
4.0ms	22×	body	128	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify181.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	367	39
1	367	39

prune7.0ms (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: 14.6b

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 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.3b	(sin.f64 (-.f64 lambda1 lambda2))
4.5b	(cos.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 (sin.f64 (-.f64 lambda1 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	(sin.f64 (-.f64 lambda1 lambda2))

series400.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

212.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
124.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
33.0ms	(sin.f64 (-.f64 lambda1 lambda2))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify66.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4859	1102
1	4859	1102

prune536.0ms (3.2%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	59	17	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	17	77

Merged error: 7.4b

Counts

77 → 17

Compiler

Compiled 10261 to 5762 computations (43.8% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
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)))
4.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite35.0ms (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×	`associate-l/_binary64_2430` `-commutative_binary64_2418` `cancel-sign-sub-inv_binary64_2453` `cos-diff_binary64_2624`
2×	`unswap-sqr_binary64_2455`
1×	`distribute-rgt-in_binary64_2437` `flip--_binary64_2462` `sub-neg_binary64_2480` `distribute-lft-in_binary64_2436` `sin-cos-mult_binary64_2643` `flip3--_binary64_2491`

Counts

4 → 71

Calls

4 calls:

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

series578.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

270.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
210.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
69.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
29.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify48.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5240	1458

prune436.0ms (2.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	76	7	83
Fresh	9	7	16
Picked	1	0	1
Done	0	0	0
Total	86	14	100

Merged error: 0.1b

Counts

100 → 14

Compiler

Compiled 9300 to 4237 computations (54.4% saved)

localize36.0ms (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))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite50.0ms (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`
4×	`associate-l/_binary64_2430` `-commutative_binary64_2418` `sin-cos-mult_binary64_2643` `add-log-exp_binary64_2526`
3×	`sin-mult_binary64_2642`
2×	`unswap-sqr_binary64_2455` `frac-times_binary64_2497` `cos-mult_binary64_2641` `associate-*r/_binary64_2429`
1×	`flip--_binary64_2462` `flip3--_binary64_2491`

Counts

4 → 89

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

series792.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

255.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
248.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
221.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
67.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify69.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5153	1911

prune469.0ms (2.8%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	100	15	115

Merged error: 0.0b

Counts

115 → 15

Compiler

Compiled 11704 to 4492 computations (61.6% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite44.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64_2525` `add-cbrt-cube_binary64_2523` `pow1_binary64_2548`
16×	`add-sqr-sqrt_binary64_2509`
11×	`prod-exp_binary64_2536` `cbrt-unprod_binary64_2520` `pow-prod-down_binary64_2558`
10×	`-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×	`unswap-sqr_binary64_2455` `associate-*l/_binary64_2430` `sin-mult_binary64_2642`
2×	`sin-cos-mult_binary64_2643`
1×	`flip--_binary64_2462` `frac-times_binary64_2497` `associate-*r/_binary64_2429` `flip3--_binary64_2491`

Counts

4 → 82

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.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))
7.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series591.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
201.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
72.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
65.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify62.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5074	1602

prune196.0ms (1.2%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	94	15	109

Merged error: 0.0b

Counts

109 → 15

Compiler

Compiled 5982 to 1228 computations (79.5% saved)

regimes264.0ms (1.6%)

Compiler: Compiled 3399 to 1991 computations (41.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	148	73
1	148	73

end0.0ms (0%)

sample8.7s (52.5%)

Algorithm

1×

intervals

Results

6.1s	5351×	body	1024	valid
814.0ms	1235×	body	512	valid
570.0ms	211×	body	2048	valid
154.0ms	395×	body	256	valid
141.0ms	808×	body	128	valid

Compiler

Compiled 713 to 415 computations (41.8% saved)

Details

analyze2.6s (15.6%)

sample273.0ms (1.7%)

simplify181.0ms (1.1%)

prune7.0ms (0%)

localize26.0ms (0.2%)

rewrite32.0ms (0.2%)

series400.0ms (2.4%)

simplify66.0ms (0.4%)

prune536.0ms (3.2%)

localize35.0ms (0.2%)

rewrite35.0ms (0.2%)

series578.0ms (3.5%)

simplify48.0ms (0.3%)

prune436.0ms (2.6%)

localize36.0ms (0.2%)

rewrite50.0ms (0.3%)

series792.0ms (4.8%)

simplify69.0ms (0.4%)

prune469.0ms (2.8%)

localize36.0ms (0.2%)

rewrite44.0ms (0.3%)

series591.0ms (3.6%)

simplify62.0ms (0.4%)

prune196.0ms (1.2%)

regimes264.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.7s (52.5%)

Profiling