Details

analyze3.6s (16.1%)

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample288.0ms (1.3%)

Algorithm

1×

intervals

Results

187.0ms	133×	body	1024	valid
49.0ms	61×	body	512	valid
12.0ms	4×	body	2048	valid
10.0ms	20×	body	256	valid
9.0ms	38×	body	128	valid

Compiler

Compiled 41 to 33 computations (19.5% saved)

simplify328.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	211	32
1	211	32

prune6.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.5b

Counts

2 → 1

Compiler

Compiled 40 to 28 computations (30% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))
3.9b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite34.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-log-exp_binary64_450`
4×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-sqr-sqrt_binary64_435`
3×	`cos-diff_binary64_548`
2×	`associate-+r+_binary64_348` `sub-neg_binary64_407`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `sin-diff_binary64_547` `+-commutative_binary64_346` `cos-sum_binary64_545` `flip-+_binary64_388` `sin-sum_binary64_544` `sum-log_binary64_502`

Counts

4 → 38

Calls

4 calls:

9.0ms	(sin.f64 (-.f64 lambda1 lambda2))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
8.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series653.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

410.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
133.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
59.0ms	(sin.f64 (-.f64 lambda1 lambda2))
51.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify207.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (177.0ms)

Iter	Nodes	Cost
0	4805	950
1	4805	950

prune172.0ms (0.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	36	14	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	14	51

Merged error: 0.4b

Counts

51 → 14

Compiler

Compiled 1749 to 491 computations (71.9% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.7b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_435`
6×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447` `add-log-exp_binary64_450`
3×	`cos-diff_binary64_548` `associate-l_binary64_357` `associate-r_binary64_356`
2×	`associate-+r+_binary64_348`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `*-commutative_binary64_347` `+-commutative_binary64_346` `prod-exp_binary64_460` `cos-sum_binary64_545` `pow-prod-down_binary64_482` `sub-neg_binary64_407` `flip-+_binary64_388` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `sum-log_binary64_502`

Counts

4 → 47

Calls

4 calls:

10.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
9.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
9.0ms	(cos.f64 (-.f64 lambda1 lambda2))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))

series791.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

427.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
172.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2)))))
137.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
55.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify149.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4921	1188
1	4921	1188

prune170.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	1	59
Fresh	1	12	13
Picked	1	0	1
Done	0	0	0
Total	60	13	73

Merged error: 0.1b

Counts

73 → 13

Compiler

Compiled 2383 to 537 computations (77.5% saved)

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.4b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite46.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_435`
8×	`pow1_binary64_472` `add-cube-cbrt_binary64_446` `add-exp-log_binary64_449` `*-un-lft-identity_binary64_414` `add-cbrt-cube_binary64_447`
6×	`associate-l_binary64_357` `add-log-exp_binary64_450` `associate-r_binary64_356`
2×	`*-commutative_binary64_347` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `associate-+r+_binary64_348` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `distribute-rgt-in_binary64_366` `+-commutative_binary64_346` `flip-+_binary64_388` `sum-log_binary64_502` `sin-mult_binary64_566`

Counts

4 → 57

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
9.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
1.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series1.3s (5.7%)

Counts

4 → 12

Calls

4 calls:

838.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
203.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
129.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
122.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))

simplify146.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4978	1626
1	4978	1626

prune190.0ms (0.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	68	1	69
Fresh	0	12	12
Picked	1	0	1
Done	0	0	0
Total	69	13	82

Merged error: 0.1b

Counts

82 → 13

Compiler

Compiled 3221 to 602 computations (81.3% saved)

localize66.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.3b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.4b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
0.6b	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64_435`
9×	`add-cube-cbrt_binary64_446` `*-un-lft-identity_binary64_414` `add-log-exp_binary64_450`
7×	`pow1_binary64_472`
6×	`add-exp-log_binary64_449` `add-cbrt-cube_binary64_447` `exp-prod_binary64_463`
4×	`log-pow_binary64_500` `log-prod_binary64_497`
3×	`associate-l_binary64_357` `associate-r_binary64_356`
2×	`exp-sum_binary64_457` `rem-exp-log_binary64_451` `associate-+r+_binary64_348` `sum-log_binary64_502`
1×	`distribute-lft-in_binary64_365` `flip3-+_binary64_417` `rem-log-exp_binary64_452` `distribute-rgt-in_binary64_366` `*-commutative_binary64_347` `+-commutative_binary64_346` `prod-exp_binary64_460` `pow-prod-down_binary64_482` `flip-+_binary64_388` `unswap-sqr_binary64_382` `cbrt-unprod_binary64_444` `sin-mult_binary64_566`

Counts

4 → 61

Calls

4 calls:

11.0ms	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
10.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
9.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series3.3s (14.8%)

Counts

4 → 12

Calls

4 calls:

1.3s	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))
1.2s	(exp.f64 (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
806.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
121.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify127.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5031	1890

prune172.0ms (0.8%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	70	3	73
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	71	15	86

Merged error: 0.1b

Counts

86 → 15

Compiler

Compiled 3140 to 409 computations (87% saved)

regimes473.0ms (2.1%)

Compiler: Compiled 3502 to 1786 computations (49% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	59	60
1	59	60

end0.0ms (0%)

sample10.0s (44.4%)

Algorithm

1×

intervals

Results

6.3s	4443×	body	1024	valid
1.4s	1787×	body	512	valid
359.0ms	719×	body	256	valid
349.0ms	107×	body	2048	valid
216.0ms	944×	body	128	valid

Compiler

Compiled 638 to 331 computations (48.1% saved)

Details

analyze3.6s (16.1%)

sample288.0ms (1.3%)

simplify328.0ms (1.5%)

prune6.0ms (0%)

localize41.0ms (0.2%)

rewrite34.0ms (0.1%)

series653.0ms (2.9%)

simplify207.0ms (0.9%)

prune172.0ms (0.8%)

localize63.0ms (0.3%)

rewrite40.0ms (0.2%)

series791.0ms (3.5%)

simplify149.0ms (0.7%)

prune170.0ms (0.8%)

localize60.0ms (0.3%)

rewrite46.0ms (0.2%)

series1.3s (5.7%)

simplify146.0ms (0.6%)

prune190.0ms (0.8%)

localize66.0ms (0.3%)

rewrite62.0ms (0.3%)

series3.3s (14.8%)

simplify127.0ms (0.6%)

prune172.0ms (0.8%)

regimes473.0ms (2.1%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample10.0s (44.4%)

Profiling