Details

analyze2.6s (16.5%)

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)

sample258.0ms (1.6%)

Algorithm

1×

intervals

Results

195.0ms	173×	body	1024	valid
30.0ms	50×	body	512	valid
11.0ms	4×	body	2048	valid
4.0ms	10×	body	256	valid
3.0ms	19×	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 (16.0ms)

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: 15.3b

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))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.4b	(cos.f64 (-.f64 lambda1 lambda2))
5.4b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite34.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64_1860` `add-sqr-sqrt_binary64_1821` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
9×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
6×	`cancel-sign-sub-inv_binary64_1765` `associate-r_binary64_1739`
4×	`add-log-exp_binary64_1838` `prod-exp_binary64_1848` `cos-sum_binary64_1933` `associate-l_binary64_1740` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870` `sin-sum_binary64_1932`
3×	`cos-diff_binary64_1936`
2×	`sub-neg_binary64_1792` `*-commutative_binary64_1730` `sin-cos-mult_binary64_1955`
1×	`distribute-rgt-in_binary64_1749` `distribute-lft-in_binary64_1748` `unswap-sqr_binary64_1767` `sin-diff_binary64_1935` `associate-*l/_binary64_1742`

Counts

4 → 64

Calls

4 calls:

9.0ms	(.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))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series353.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
70.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
36.0ms	(sin.f64 (-.f64 lambda1 lambda2))
35.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify88.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4876	1051
1	4876	1051

prune370.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 8.1b

Counts

77 → 11

Compiler

Compiled 7245 to 3679 computations (49.2% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.4b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_1821`
13×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
10×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
9×	`associate-r_binary64_1739`
7×	`associate-l_binary64_1740`
5×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
4×	`add-log-exp_binary64_1838` `cos-sum_binary64_1933`
3×	`cos-diff_binary64_1936` `-commutative_binary64_1730` `cancel-sign-sub-inv_binary64_1765` `associate-l/_binary64_1742`
2×	`unswap-sqr_binary64_1767` `sin-cos-mult_binary64_1955`
1×	`distribute-rgt-in_binary64_1749` `sub-neg_binary64_1792` `distribute-lft-in_binary64_1748` `flip--_binary64_1774` `flip3--_binary64_1803`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
9.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
6.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

series573.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

263.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
212.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
67.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify46.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5082	1472

prune355.0ms (2.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	84	11	95

Merged error: 0.1b

Counts

95 → 11

Compiler

Compiled 8197 to 3389 computations (58.7% 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 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.2b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_1860` `add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
18×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
12×	`add-sqr-sqrt_binary64_1821`
8×	`add-cube-cbrt_binary64_1834` `associate-l_binary64_1740` `-un-lft-identity_binary64_1799` `associate-r*_binary64_1739`
5×	`sin-cos-mult_binary64_1955`
4×	`add-log-exp_binary64_1838` `*-commutative_binary64_1730`
3×	`sin-mult_binary64_1954`
2×	`unswap-sqr_binary64_1767` `associate-r/_binary64_1741` `cos-mult_binary64_1953` `frac-times_binary64_1809` `associate-l/_binary64_1742`

Counts

4 → 88

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

series609.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

250.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
221.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
70.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
68.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))

simplify73.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4960	1556
1	4960	1556

prune471.0ms (3%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	95	5	100
Fresh	1	9	10
Picked	1	0	1
Done	0	0	0
Total	97	14	111

Merged error: 0.0b

Counts

111 → 14

Compiler

Compiled 12084 to 4513 computations (62.7% saved)

localize39.0ms (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)))
3.5b	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`pow1_binary64_1860`
20×	`add-cbrt-cube_binary64_1835` `add-exp-log_binary64_1837`
13×	`add-sqr-sqrt_binary64_1821`
10×	`prod-exp_binary64_1848` `cbrt-unprod_binary64_1832` `pow-prod-down_binary64_1870`
9×	`add-cube-cbrt_binary64_1834` `*-un-lft-identity_binary64_1799`
7×	`associate-l_binary64_1740` `associate-r_binary64_1739`
5×	`add-log-exp_binary64_1838`
3×	`log-prod_binary64_1885` `*-commutative_binary64_1730` `log-pow_binary64_1888` `sin-cos-mult_binary64_1955`
2×	`unswap-sqr_binary64_1767` `cos-mult_binary64_1953`
1×	`exp-to-pow_binary64_1861` `associate-r/_binary64_1741` `sin-mult_binary64_1954` `exp-prod_binary64_1851` `rem-log-exp_binary64_1840` `frac-times_binary64_1809` `associate-l/_binary64_1742`

Counts

4 → 77

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
7.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
6.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
3.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series539.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
162.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
68.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
67.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify64.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5019	1196

prune151.0ms (1%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	88	1	89
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	89	14	103

Merged error: 0.0b

Counts

103 → 14

Compiler

Compiled 5113 to 902 computations (82.4% saved)

regimes255.0ms (1.6%)

Compiler: Compiled 3457 to 1937 computations (44% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	77
1	140	77

end0.0ms (0%)

sample8.5s (53.8%)

Algorithm

1×

intervals

Results

6.0s	5369×	body	1024	valid
829.0ms	1279×	body	512	valid
494.0ms	185×	body	2048	valid
159.0ms	405×	body	256	valid
136.0ms	762×	body	128	valid

Compiler

Compiled 739 to 414 computations (44% saved)

Details

analyze2.6s (16.5%)

sample258.0ms (1.6%)

simplify181.0ms (1.1%)

prune4.0ms (0%)

localize26.0ms (0.2%)

rewrite34.0ms (0.2%)

series353.0ms (2.2%)

simplify88.0ms (0.6%)

prune370.0ms (2.3%)

localize37.0ms (0.2%)

rewrite40.0ms (0.3%)

series573.0ms (3.6%)

simplify46.0ms (0.3%)

prune355.0ms (2.2%)

localize38.0ms (0.2%)

rewrite49.0ms (0.3%)

series609.0ms (3.9%)

simplify73.0ms (0.5%)

prune471.0ms (3%)

localize39.0ms (0.2%)

rewrite38.0ms (0.2%)

series539.0ms (3.4%)

simplify64.0ms (0.4%)

prune151.0ms (1%)

regimes255.0ms (1.6%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.5s (53.8%)

Profiling