Details

analyze3.8s (18.5%)

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)

sample318.0ms (1.5%)

Algorithm

1×

intervals

Results

250.0ms	181×	body	1024	valid
31.0ms	38×	body	512	valid
8.0ms	3×	body	2048	valid
5.0ms	24×	body	128	valid
5.0ms	10×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify167.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

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

Error

12.7b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize40.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))
2.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite55.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_441` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
9×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
6×	`associate-r_binary64_359` `cancel-sign-sub-inv_binary64_385`
4×	`pow-prod-down_binary64_490` `cos-sum_binary64_553` `add-log-exp_binary64_458` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `sin-sum_binary64_552` `associate-l_binary64_360`
3×	`cos-diff_binary64_556`
2×	`sub-neg_binary64_412` `*-commutative_binary64_350`
1×	`associate-*l/_binary64_362` `sin-cos-mult_binary64_575` `sin-diff_binary64_555` `distribute-rgt-in_binary64_369` `unswap-sqr_binary64_387` `distribute-lft-in_binary64_368`

Counts

4 → 63

Calls

4 calls:

16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
15.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
10.0ms	(sin.f64 (-.f64 lambda1 lambda2))
8.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series221.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

134.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
41.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
26.0ms	(cos.f64 (-.f64 lambda1 lambda2))
20.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify126.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (108.0ms)

Iter	Nodes	Cost
0	4860	1037
1	4860	1037

prune129.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	64	11	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	11	76

Error

7.3b

Counts

76 → 11

Compiler

Compiled 2475 to 517 computations (79.1% saved)

localize48.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.2b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_441`
13×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
9×	`associate-r_binary64_359`
7×	`associate-l_binary64_360`
5×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
4×	`cos-sum_binary64_553` `add-log-exp_binary64_458`
3×	`associate-l/_binary64_362` `-commutative_binary64_350` `cancel-sign-sub-inv_binary64_385` `cos-diff_binary64_556`
2×	`unswap-sqr_binary64_387`
1×	`sin-cos-mult_binary64_575` `sub-neg_binary64_412` `distribute-rgt-in_binary64_369` `flip3--_binary64_423` `distribute-lft-in_binary64_368` `flip--_binary64_394`

Counts

4 → 71

Calls

4 calls:

11.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
8.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series522.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
201.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
79.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
25.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify71.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5316	1458

prune136.0ms (0.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	86	8	94

Error

0.1b

Counts

94 → 8

Compiler

Compiled 3333 to 507 computations (84.8% saved)

localize51.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite68.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
18×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
12×	`add-sqr-sqrt_binary64_441`
8×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `associate-l*_binary64_360`
4×	`sin-cos-mult_binary64_575` `add-log-exp_binary64_458` `*-commutative_binary64_350`
3×	`sin-mult_binary64_574`
2×	`associate-l/_binary64_362` `unswap-sqr_binary64_387` `frac-times_binary64_429` `associate-r/_binary64_361` `cos-mult_binary64_573`

Counts

4 → 87

Calls

4 calls:

19.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
18.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series466.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
121.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
65.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
63.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify104.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4933	1542
1	4933	1542

prune239.0ms (1.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Error

0.0b

Counts

107 → 12

Compiler

Compiled 5229 to 763 computations (85.4% saved)

localize490.0ms (2.4%)

Local error

Found 4 expressions with local error:

0.2b	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
0.3b	(.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)))
26.4b	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
24×	`pow-prod-down_binary64_490` `prod-exp_binary64_468` `cbrt-unprod_binary64_452`
8×	`sin-cos-mult_binary64_575` `cbrt-prod_binary64_450`
6×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `sin-mult_binary64_574` `add-sqr-sqrt_binary64_441` `cube-div_binary64_448`
5×	`rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `pow-pow_binary64_491`
4×	`associate-l/_binary64_362` `add-log-exp_binary64_458` `frac-times_binary64_429` `associate-r/_binary64_361`
3×	`cbrt-div_binary64_451` `pow-unpow_binary64_496`
2×	`unpow-prod-down_binary64_498` `unpow3_binary64_485` `cube-mult_binary64_449` `associate-r_binary64_359` `sqr-pow_binary64_391` `cos-mult_binary64_573` `-commutative_binary64_350` `cube-prod_binary64_447` `associate-l*_binary64_360`
1×	`pow1/3_binary64_501` `rem-cbrt-cube_binary64_443` `pow-to-exp_binary64_488`

Counts

4 → 104

Calls

4 calls:

10.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
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)))
4.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))

series1.1s (5.1%)

Counts

4 → 12

Calls

4 calls:

470.0ms	(pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3)
212.0ms	(cbrt.f64 (pow.f64 (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2))) 3))
196.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
173.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify117.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5749	2323

prune199.0ms (1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Error

0.0b

Counts

128 → 11

Compiler

Compiled 5989 to 890 computations (85.1% saved)

regimes986.0ms (4.8%)

Accuracy

Total 0.1b remaining (72.1%)

Threshold costs 0.1b (72.1%)

Compiler

Compiled 9448 to 5858 computations (38% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	131	78
1	131	78

end0.0ms (0%)

sample11.1s (53.9%)

Algorithm

1×

intervals

Results

6.9s	5360×	body	1024	valid
1.1s	1317×	body	512	valid
531.0ms	199×	body	2048	valid
197.0ms	374×	body	256	valid
175.0ms	750×	body	128	valid

Compiler

Compiled 1558 to 959 computations (38.4% saved)

Details

analyze3.8s (18.5%)

sample318.0ms (1.5%)

simplify167.0ms (0.8%)

prune6.0ms (0%)

localize40.0ms (0.2%)

rewrite55.0ms (0.3%)

series221.0ms (1.1%)

simplify126.0ms (0.6%)

prune129.0ms (0.6%)

localize48.0ms (0.2%)

rewrite40.0ms (0.2%)

series522.0ms (2.5%)

simplify71.0ms (0.3%)

prune136.0ms (0.7%)

localize51.0ms (0.2%)

rewrite68.0ms (0.3%)

series466.0ms (2.3%)

simplify104.0ms (0.5%)

prune239.0ms (1.2%)

localize490.0ms (2.4%)

rewrite49.0ms (0.2%)

series1.1s (5.1%)

simplify117.0ms (0.6%)

prune199.0ms (1%)

regimes986.0ms (4.8%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample11.1s (53.9%)

Profiling