Details

analyze7.0s (14.4%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4763	1069
1	4763	1069
0	5	5
1	5	5

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

Symmetry

(sort lambda1 lambda2)

(sort phi1 phi2)

Compiler

Compiled 66 to 47 computations (28.8% saved)

sample414.0ms (0.9%)

Algorithm

1×

intervals

Results

279.0ms	165×	body	1024	valid
57.0ms	51×	body	512	valid
22.0ms	6×	body	2048	valid
14.0ms	13×	body	256	valid
7.0ms	21×	body	128	valid

Compiler

Compiled 131 to 98 computations (25.2% saved)

simplify107.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4778	103
1	4778	103

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

23.3b

Counts

2 → 1

Compiler

Compiled 130 to 92 computations (29.2% saved)

localize36.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite134.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

23.0b

Rules

4×	`div-sub_binary64_1106` `sin-diff_binary64_1237` `pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`

Counts

4 → 32

Calls

4 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))

Compiler

Compiled 2328 to 1346 computations (42.2% saved)

series494.0ms (1%)

Error

22.5b

Counts

4 → 46

Calls

4 calls:

88.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
86.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
84.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
82.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 7924 to 5337 computations (32.6% saved)

simplify89.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4940	1330
1	4940	1330

prune309.0ms (0.6%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	63	15	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	64	15	79

Error

22.4b

Counts

79 → 15

Compiler

Compiled 6639 to 4013 computations (39.6% saved)

localize44.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite159.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Error

21.9b

Rules

4×	`div-sub_binary64_1106` `sin-diff_binary64_1237` `pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`

Counts

4 → 32

Calls

4 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))

Compiler

Compiled 2744 to 1730 computations (37% saved)

series534.0ms (1.1%)

Error

22.0b

Counts

4 → 43

Calls

4 calls:

96.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
95.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
94.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
79.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

Compiler

Compiled 8841 to 6291 computations (28.8% saved)

simplify133.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (117.0ms)

Iter	Nodes	Cost
0	4926	1225
1	4926	1225

prune430.0ms (0.9%)

Pruning

30 alts after pruning (30 fresh and 0 done)

	Pruned	Kept	Total
New	56	19	75
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	60	30	90

Error

21.8b

Counts

90 → 30

Compiler

Compiled 8658 to 5749 computations (33.6% saved)

localize59.0ms (0.1%)

Local error

Found 4 expressions with local error:

3.0b	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite178.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Error

12.3b

Rules

4×	`div-sub_binary64_1106` `sin-diff_binary64_1237` `pow1_binary64_1162` `add-log-exp_binary64_1140` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137` `add-cube-cbrt_binary64_1136` `add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`

Counts

4 → 32

Calls

4 calls:

5.0ms	(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))

Compiler

Compiled 3160 to 2114 computations (33.1% saved)

series644.0ms (1.3%)

Error

20.4b

Counts

4 → 47

Calls

4 calls:

107.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
107.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
106.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
97.0ms	(sin.f64 (/.f64 (-.f64 phi1 phi2) 2))

Compiler

Compiled 10904 to 8053 computations (26.1% saved)

simplify82.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4946	1371
1	4946	1371

prune532.0ms (1.1%)

Pruning

32 alts after pruning (32 fresh and 0 done)

	Pruned	Kept	Total
New	66	13	79
Fresh	10	19	29
Picked	1	0	1
Done	0	0	0
Total	77	32	109

Error

12.3b

Counts

109 → 32

Compiler

Compiled 10444 to 7269 computations (30.4% saved)

localize54.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.7b	(-.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))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))))))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
4.0b	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

rewrite335.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

12.1b

Rules

9×	`add-log-exp_binary64_1140`
8×	`add-sqr-sqrt_binary64_1123` `*-un-lft-identity_binary64_1101`
5×	`add-cube-cbrt_binary64_1136`
4×	`pow1_binary64_1162` `add-exp-log_binary64_1139` `add-cbrt-cube_binary64_1137`
3×	`div-sub_binary64_1106` `sin-diff_binary64_1237` `cancel-sign-sub-inv_binary64_1067`
2×	`diff-log_binary64_1193` `difference-of-squares_binary64_1070`
1×	`sum-log_binary64_1192` `flip3--_binary64_1105` `sub-neg_binary64_1094` `flip--_binary64_1076` `distribute-lft-out--_binary64_1053` `associate--r+_binary64_1037`

Counts

4 → 43

Calls

4 calls:

13.0ms	(-.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))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 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))

Compiler

Compiled 5551 to 3896 computations (29.8% saved)

series4.2s (8.6%)

Error

12.1b

Counts

4 → 56

Calls

4 calls:

3.3s	(-.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))) (-.f64 (.f64 (sin.f64 (/.f64 lambda1 2)) (cos.f64 (/.f64 lambda2 2))) (*.f64 (cos.f64 (/.f64 lambda1 2)) (sin.f64 (/.f64 lambda2 2)))))))
116.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
112.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))
112.0ms	(sin.f64 (/.f64 (-.f64 lambda1 lambda2) 2))

Compiler

Compiled 17102 to 12795 computations (25.2% saved)

simplify128.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5037	6758

prune775.0ms (1.6%)

Pruning

35 alts after pruning (35 fresh and 0 done)

	Pruned	Kept	Total
New	83	16	99
Fresh	12	19	31
Picked	1	0	1
Done	0	0	0
Total	96	35	131

Error

12.0b

Counts

131 → 35

Compiler

Compiled 12215 to 8549 computations (30% saved)

regimes8.9s (18.2%)

Accuracy

Total 0.6b remaining (4.5%)

Threshold costs 0.6b (4.5%)

Compiler

Compiled 160049 to 121649 computations (24% saved)

bsearch0.0ms (0%)

simplify67.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	569	187
1	569	187

Remove

(sort phi1 phi2)

(sort lambda1 lambda2)

Compiler

Compiled 468 to 372 computations (20.5% saved)

end0.0ms (0%)

sample22.9s (47%)

Algorithm

1×

intervals

Results

9.2s	5310×	body	1024	valid
1.4s	1226×	body	512	valid
1.3s	437×	body	2048	valid
270.0ms	384×	body	256	valid
198.0ms	643×	body	128	valid
2.0ms	1×	body	1024	invalid

Compiler

Compiled 13275 to 10101 computations (23.9% saved)

Details

analyze7.0s (14.4%)

sample414.0ms (0.9%)

simplify107.0ms (0.2%)

prune6.0ms (0%)

localize36.0ms (0.1%)

rewrite134.0ms (0.3%)

series494.0ms (1%)

simplify89.0ms (0.2%)

prune309.0ms (0.6%)

localize44.0ms (0.1%)

rewrite159.0ms (0.3%)

series534.0ms (1.1%)

simplify133.0ms (0.3%)

prune430.0ms (0.9%)

localize59.0ms (0.1%)

rewrite178.0ms (0.4%)

series644.0ms (1.3%)

simplify82.0ms (0.2%)

prune532.0ms (1.1%)

localize54.0ms (0.1%)

rewrite335.0ms (0.7%)

series4.2s (8.6%)

simplify128.0ms (0.3%)

prune775.0ms (1.6%)

regimes8.9s (18.2%)

bsearch0.0ms (0%)

simplify67.0ms (0.1%)

end0.0ms (0%)

sample22.9s (47%)

Profiling