Details

analyze8.2s (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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0.6%	99.2%	0.2%	13
1.8%	98%	0.2%	14

Compiler

Compiled 66 to 47 computations (28.8% saved)

sample558.0ms (1.1%)

Algorithm

1×

intervals

Results

370.0ms	168×	body	1024	valid
75.0ms	46×	body	512	valid
49.0ms	11×	body	2048	valid
9.0ms	21×	body	128	valid
9.0ms	10×	body	256	valid
4.0ms	1×	body	1024	invalid

Compiler

Compiled 131 to 98 computations (25.2% saved)

simplify262.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4778	103
1	4778	103

prune11.0ms (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

26.3b

Counts

2 → 1

Compiler

Compiled 130 to 92 computations (29.2% saved)

localize46.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(atan2.f64 (sqrt.f64 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))) (sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2)))))))
0.1b	(sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (sin.f64 (/.f64 (-.f64 phi1 phi2) 2)) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.1b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
4.1b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

rewrite35.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_1478` `sin-diff_binary64_1578` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `div-sub_binary64_1447` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`

Counts

4 → 32

Calls

8 calls:

8.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
8.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
7.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
6.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
0.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi2))

series353.0ms (0.7%)

Counts

4 → 38

Calls

4 calls:

95.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
95.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
88.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
75.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

Compiler

Compiled 4200 to 3052 computations (27.3% saved)

simplify86.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5178	1038

prune574.0ms (1.1%)

Pruning

22 alts after pruning (22 fresh and 0 done)

	Pruned	Kept	Total
New	48	22	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	22	71

Error

24.6b

Counts

71 → 22

Compiler

Compiled 6456 to 3957 computations (38.7% saved)

localize58.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(sqrt.f64 (-.f64 1 (+.f64 (pow.f64 (-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2)))) 2) (.f64 (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))) (sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))))))
0.1b	(-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.1b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

rewrite28.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_1478` `sin-diff_binary64_1578` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `div-sub_binary64_1447` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`

Counts

4 → 32

Calls

8 calls:

6.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
0.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi2))

series435.0ms (0.9%)

Counts

4 → 45

Calls

4 calls:

116.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
110.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
110.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
98.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

Compiler

Compiled 5408 to 4094 computations (24.3% saved)

simplify90.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4996	1289
1	4996	1289

prune599.0ms (1.2%)

Pruning

27 alts after pruning (27 fresh and 0 done)

	Pruned	Kept	Total
New	63	14	77
Fresh	8	13	21
Picked	1	0	1
Done	0	0	0
Total	72	27	99

Error

15.0b

Counts

99 → 27

Compiler

Compiled 8579 to 5663 computations (34% saved)

localize56.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))
0.1b	(-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite33.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_1478` `sin-diff_binary64_1578` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `div-sub_binary64_1447` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`

Counts

4 → 32

Calls

8 calls:

5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
0.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi2))

series518.0ms (1%)

Counts

4 → 46

Calls

4 calls:

145.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
136.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
119.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
118.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 6240 to 4808 computations (22.9% saved)

simplify109.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4940	1330
1	4940	1330

prune680.0ms (1.3%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	5	21	26
Picked	1	0	1
Done	0	0	0
Total	77	28	105

Error

14.9b

Counts

105 → 28

Compiler

Compiled 9893 to 6821 computations (31.1% saved)

localize67.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.1b	(-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))
0.1b	(-.f64 (.f64 (sin.f64 (/.f64 phi1 2)) (cos.f64 (/.f64 phi2 2))) (.f64 (cos.f64 (/.f64 phi1 2)) (sin.f64 (/.f64 phi2 2))))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
0.1b	(*.f64 (cos.f64 phi1) (cos.f64 phi2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
3.4b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite32.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-cbrt-cube_binary64_1478` `sin-diff_binary64_1578` `add-log-exp_binary64_1481` `add-exp-log_binary64_1480` `add-sqr-sqrt_binary64_1464` `pow1_binary64_1503` `div-sub_binary64_1447` `add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`

Counts

4 → 32

Calls

8 calls:

6.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
6.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
5.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
0.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi2))

series502.0ms (1%)

Counts

4 → 44

Calls

4 calls:

134.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
132.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
119.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
117.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7328 to 5512 computations (24.8% saved)

simplify83.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4986	1248
1	4986	1248

prune686.0ms (1.3%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	4	23	27
Picked	1	0	1
Done	0	0	0
Total	74	30	104

Error

14.9b

Counts

104 → 30

Compiler

Compiled 8652 to 5779 computations (33.2% saved)

simplify303.0ms (0.6%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (166.0ms)

Iter	Nodes	Cost
0	3136	8775
1	3136	8775

regimes3.0s (5.8%)

Accuracy

Total 0.6b remaining (4.4%)

Threshold costs 0.6b (4.4%)

Compiler

Compiled 44126 to 33096 computations (25% saved)

bsearch0.0ms (0%)

simplify8.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	141	145
1	141	145

end0.0ms (0%)

sample33.8s (66.1%)

Algorithm

1×

intervals

Results

12.3s	5290×	body	1024	valid
1.9s	1273×	body	512	valid
1.6s	422×	body	2048	valid
385.0ms	387×	body	256	valid
274.0ms	628×	body	128	valid
9.0ms	4×	body	1024	invalid

Compiler

Compiled 16781 to 12565 computations (25.1% saved)

Pareto

0.0963533236290374

Details

analyze8.2s (16%)

sample558.0ms (1.1%)

simplify262.0ms (0.5%)

prune11.0ms (0%)

localize46.0ms (0.1%)

rewrite35.0ms (0.1%)

series353.0ms (0.7%)

simplify86.0ms (0.2%)

prune574.0ms (1.1%)

localize58.0ms (0.1%)

rewrite28.0ms (0.1%)

series435.0ms (0.9%)

simplify90.0ms (0.2%)

prune599.0ms (1.2%)

localize56.0ms (0.1%)

rewrite33.0ms (0.1%)

series518.0ms (1%)

simplify109.0ms (0.2%)

prune680.0ms (1.3%)

localize67.0ms (0.1%)

rewrite32.0ms (0.1%)

series502.0ms (1%)

simplify83.0ms (0.2%)

prune686.0ms (1.3%)

simplify303.0ms (0.6%)

regimes3.0s (5.8%)

bsearch0.0ms (0%)

simplify8.0ms (0%)

end0.0ms (0%)

sample33.8s (66.1%)

Profiling