Details

analyze2.6s (16.6%)

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)

sample240.0ms (1.6%)

Algorithm

1×

intervals

Results

176.0ms	158×	body	1024	valid
26.0ms	43×	body	512	valid
14.0ms	5×	body	2048	valid
6.0ms	35×	body	128	valid
5.0ms	15×	body	256	valid

Compiler

Compiled 49 to 39 computations (20.4% saved)

simplify186.0ms (1.2%)

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: 14.9b

Counts

2 → 1

Compiler

Compiled 48 to 34 computations (29.2% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.1b	(sin.f64 (-.f64 lambda1 lambda2))
4.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite30.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
7×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `cancel-sign-sub-inv_binary64_2109` `*-un-lft-identity_binary64_2143`
6×	`add-log-exp_binary64_2182`
5×	`cos-diff_binary64_2280`
4×	`sin-sum_binary64_2276` `cos-sum_binary64_2277`
3×	`sub-neg_binary64_2136` `associate-r_binary64_2083` `cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
2×	`distribute-rgt-in_binary64_2093` `associate--r+_binary64_2079` `distribute-lft-in_binary64_2092`
1×	`sin-diff_binary64_2279` `diff-log_binary64_2235` `sin-cos-mult_binary64_2299` `flip--_binary64_2118` `associate-l_binary64_2084` `flip3--_binary64_2147` `associate-l/_binary64_2086` `-commutative_binary64_2074`

Counts

4 → 59

Calls

4 calls:

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

series624.0ms (4%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(-.f64 (.f64 (cos.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))
215.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
34.0ms	(sin.f64 (-.f64 lambda1 lambda2))
33.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5374	1384

prune350.0ms (2.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	60	11	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	11	72

Merged error: 7.2b

Counts

72 → 11

Compiler

Compiled 7329 to 3478 computations (52.5% saved)

localize36.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.1b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_2165`
13×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
10×	`add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`associate-r_binary64_2083`
7×	`associate-l_binary64_2084`
5×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
4×	`add-log-exp_binary64_2182` `cos-sum_binary64_2277`
3×	`cos-diff_binary64_2280` `cancel-sign-sub-inv_binary64_2109` `*-commutative_binary64_2074`
2×	`unswap-sqr_binary64_2111`
1×	`sin-cos-mult_binary64_2299` `distribute-rgt-in_binary64_2093` `sub-neg_binary64_2136` `associate-*l/_binary64_2086` `distribute-lft-in_binary64_2092`

Counts

4 → 69

Calls

4 calls:

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

series387.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
69.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
63.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
31.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify99.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4864	1089
1	4864	1089

prune303.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	4	81
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	82	10	92

Merged error: 0.0b

Counts

92 → 10

Compiler

Compiled 7215 to 2711 computations (62.4% saved)

localize43.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.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)))

rewrite49.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
18×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
12×	`add-sqr-sqrt_binary64_2165`
8×	`associate-r_binary64_2083` `associate-l_binary64_2084` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182` `sin-cos-mult_binary64_2299` `*-commutative_binary64_2074`
3×	`sin-mult_binary64_2298`
2×	`cos-mult_binary64_2297` `frac-times_binary64_2153` `associate-l/_binary64_2086` `associate-r/_binary64_2085` `unswap-sqr_binary64_2111`

Counts

4 → 87

Calls

4 calls:

15.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
11.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

series591.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

241.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
212.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
71.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
67.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

simplify78.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4966	1542
1	4966	1542

prune453.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	94	5	99
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	96	13	109

Merged error: 0.0b

Counts

109 → 13

Compiler

Compiled 11867 to 4252 computations (64.2% saved)

localize38.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))
0.2b	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (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 phi1) (cos.f64 phi2)) (sin.f64 lambda2))

rewrite46.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`pow1_binary64_2204` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
18×	`cbrt-unprod_binary64_2176` `pow-prod-down_binary64_2214` `prod-exp_binary64_2192`
10×	`add-sqr-sqrt_binary64_2165`
8×	`associate-r_binary64_2083` `associate-l_binary64_2084` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
4×	`add-log-exp_binary64_2182` `sin-cos-mult_binary64_2299` `*-commutative_binary64_2074`
3×	`associate-*l/_binary64_2086`
2×	`cos-mult_binary64_2297` `associate-*r/_binary64_2085`
1×	`frac-times_binary64_2153` `unswap-sqr_binary64_2111`

Counts

4 → 84

Calls

4 calls:

11.0ms	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2)))
10.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

series661.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

234.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
222.0ms	(.f64 (sin.f64 lambda1) (.f64 (*.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2)))
134.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (sin.f64 lambda2))
70.0ms	(*.f64 (cos.f64 lambda2) (sin.f64 lambda1))

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4948	1555
1	4948	1555

prune119.0ms (0.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	96	13	109

Merged error: 0.0b

Counts

109 → 13

Compiler

Compiled 4562 to 464 computations (89.8% saved)

regimes231.0ms (1.5%)

Compiler: Compiled 3186 to 1728 computations (45.8% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	136	63
1	136	63

end0.0ms (0%)

sample8.1s (52.6%)

Algorithm

1×

intervals

Results

5.8s	5378×	body	1024	valid
762.0ms	1232×	body	512	valid
462.0ms	158×	body	2048	valid
155.0ms	417×	body	256	valid
148.0ms	815×	body	128	valid

Compiler

Compiled 649 to 360 computations (44.5% saved)

Details

analyze2.6s (16.6%)

sample240.0ms (1.6%)

simplify186.0ms (1.2%)

prune4.0ms (0%)

localize24.0ms (0.2%)

rewrite30.0ms (0.2%)

series624.0ms (4%)

simplify79.0ms (0.5%)

prune350.0ms (2.3%)

localize36.0ms (0.2%)

rewrite31.0ms (0.2%)

series387.0ms (2.5%)

simplify99.0ms (0.6%)

prune303.0ms (2%)

localize43.0ms (0.3%)

rewrite49.0ms (0.3%)

series591.0ms (3.8%)

simplify78.0ms (0.5%)

prune453.0ms (2.9%)

localize38.0ms (0.2%)

rewrite46.0ms (0.3%)

series661.0ms (4.3%)

simplify82.0ms (0.5%)

prune119.0ms (0.8%)

regimes231.0ms (1.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample8.1s (52.6%)

Profiling