Details

analyze2.6s (17.3%)

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)

sample298.0ms (2%)

Algorithm

1×

intervals

Results

217.0ms	151×	body	1280	valid
56.0ms	69×	body	640	valid
6.0ms	11×	body	320	valid
3.0ms	19×	body	80	valid
2.0ms	6×	body	160	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	386	39
1	386	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

Merged error: 12.8b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize30.0ms (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)))
2.6b	(sin.f64 (-.f64 lambda1 lambda2))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 57

Calls

4 calls:

8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series44.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify118.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4811	929
1	4811	929

prune96.0ms (0.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 7.7b

Counts

70 → 12

Compiler

Compiled 2311 to 541 computations (76.6% saved)

localize35.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.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)))
2.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
9×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cos-diff_binary64` `associate-l/_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64`

Counts

4 → 68

Calls

4 calls:

8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series73.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

34.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
26.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify55.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5099	1404

prune90.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	7	4	11
Picked	1	0	1
Done	0	0	0
Total	81	11	92

Merged error: 0.1b

Counts

92 → 11

Compiler

Compiled 3365 to 577 computations (82.9% saved)

localize34.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite35.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`associate-r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `flip--_binary64`

Counts

4 → 84

Calls

4 calls:

12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
8.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series99.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
33.0ms	(.f64 (-.f64 (.f64 (cos.f64 lambda2) (sin.f64 lambda1)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

simplify84.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5024	2099

prune113.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	89	7	96
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	93	14	107

Merged error: 0.0b

Counts

107 → 14

Compiler

Compiled 4997 to 811 computations (83.8% saved)

localize37.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`sin-mult_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 87

Calls

4 calls:

10.0ms	(.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)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))

series81.0ms (0.5%)

Counts

4 → 12

Calls

4 calls:

31.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
29.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
11.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify98.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	5059	1542

prune57.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	101	12	113

Merged error: 0.0b

Counts

113 → 12

Compiler

Compiled 4716 to 468 computations (90.1% saved)

regimes411.0ms (2.7%)

Compiler: Compiled 2865 to 1665 computations (41.9% saved)

bsearch0.0ms (0%)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	130	77
1	130	77

end0.0ms (0%)

sample10.4s (69.4%)

Algorithm

1×

intervals

Results

6.9s	4723×	body	1280	valid
1.5s	1885×	body	640	valid
292.0ms	540×	body	320	valid
114.0ms	658×	body	80	valid
65.0ms	194×	body	160	valid

Compiler

Compiled 629 to 364 computations (42.1% saved)

Details

analyze2.6s (17.3%)

sample298.0ms (2%)

simplify31.0ms (0.2%)

prune6.0ms (0%)

localize30.0ms (0.2%)

rewrite23.0ms (0.2%)

series44.0ms (0.3%)

simplify118.0ms (0.8%)

prune96.0ms (0.6%)

localize35.0ms (0.2%)

rewrite27.0ms (0.2%)

series73.0ms (0.5%)

simplify55.0ms (0.4%)

prune90.0ms (0.6%)

localize34.0ms (0.2%)

rewrite35.0ms (0.2%)

series99.0ms (0.7%)

simplify84.0ms (0.6%)

prune113.0ms (0.7%)

localize37.0ms (0.2%)

rewrite32.0ms (0.2%)

series81.0ms (0.5%)

simplify98.0ms (0.7%)

prune57.0ms (0.4%)

regimes411.0ms (2.7%)

bsearch0.0ms (0%)

simplify6.0ms (0%)

end0.0ms (0%)

sample10.4s (69.4%)

Profiling