Details

analyze3.5s (15%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0.8%	99%	0.2%	11
1.2%	98.6%	0.2%	12
1.8%	98%	0.2%	13
2%	97.7%	0.2%	14

Compiler

Compiled 20 to 18 computations (10% saved)

sample329.0ms (1.4%)

Algorithm

1×

intervals

Results

237.0ms	178×	body	1024	valid
34.0ms	47×	body	512	valid
27.0ms	8×	body	2048	valid
7.0ms	17×	body	256	valid
1.0ms	6×	body	128	valid

Compiler

Compiled 39 to 40 computations (-2.6% saved)

simplify372.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	78	31
1	78	31

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: 16.0b

Counts

2 → 1

Compiler

Compiled 38 to 34 computations (10.5% saved)

localize41.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
3.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
10×	`add-sqr-sqrt_binary64_100`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`associate-r_binary64_18`
4×	`associate-l_binary64_19` `add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `cos-sum_binary64_212`
3×	`cancel-sign-sub-inv_binary64_44` `cos-diff_binary64_215`
2×	`*-commutative_binary64_9`
1×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `acos-asin_binary64_259` `associate-*l/_binary64_21` `unswap-sqr_binary64_46` `cos-mult_binary64_232` `sub-neg_binary64_71`

Counts

4 → 59

Calls

4 calls:

8.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))

series686.0ms (2.9%)

Counts

4 → 12

Calls

4 calls:

298.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2))))) R)
253.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
103.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
32.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify159.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (132.0ms)

Iter	Nodes	Cost
0	4821	1724
1	4821	1724

prune137.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 3.8b

Counts

72 → 13

Compiler

Compiled 2209 to 528 computations (76.1% saved)

localize63.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

rewrite49.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116` `pow1_binary64_139`
9×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19`
6×	`cos-mult_binary64_232`
5×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
4×	`add-log-exp_binary64_117`
3×	`-commutative_binary64_9` `frac-times_binary64_88` `sin-mult_binary64_233` `associate-r/_binary64_20`
2×	`frac-add_binary64_86` `flip-+_binary64_52` `unswap-sqr_binary64_46` `flip3-+_binary64_81`
1×	`distribute-lft-in_binary64_27` `distribute-rgt-in_binary64_28` `acos-asin_binary64_259` `associate-*l/_binary64_21`

Counts

4 → 72

Calls

4 calls:

20.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
8.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
3.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

series1.3s (5.5%)

Counts

4 → 12

Calls

4 calls:

541.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
535.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))) R)
118.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
111.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))

simplify90.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5063	2773

prune176.0ms (0.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	70	14	84
Fresh	11	1	12
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Merged error: 3.7b

Counts

97 → 15

Compiler

Compiled 3581 to 733 computations (79.5% saved)

localize47.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))

rewrite38.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `pow1_binary64_139`
12×	`add-sqr-sqrt_binary64_100`
10×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149`
8×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
7×	`associate-l_binary64_19` `associate-r_binary64_18`
4×	`add-log-exp_binary64_117`
3×	`*-commutative_binary64_9` `sin-mult_binary64_233`
2×	`unswap-sqr_binary64_46` `cos-mult_binary64_232`
1×	`acos-asin_binary64_259` `frac-times_binary64_88` `associate-l/_binary64_21` `associate-r/_binary64_20`

Counts

4 → 70

Calls

4 calls:

10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
4.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
1.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))

series1.1s (4.7%)

Counts

4 → 12

Calls

4 calls:

455.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2)))))) R)
372.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2)))
148.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (cos.f64 phi1) (cos.f64 phi2))))))
128.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify116.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	4916	2261
1	4916	2261

prune154.0ms (0.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	13	14
Picked	1	0	1
Done	0	0	0
Total	83	14	97

Merged error: 3.7b

Counts

97 → 14

Compiler

Compiled 3605 to 691 computations (80.8% saved)

localize45.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
1.2b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
3.1b	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite43.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
8×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
5×	`add-log-exp_binary64_117`
3×	`log-prod_binary64_164` `log-pow_binary64_167`
2×	`*-commutative_binary64_9` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46`
1×	`acos-asin_binary64_259` `exp-to-pow_binary64_140` `rem-log-exp_binary64_119` `sin-mult_binary64_233` `exp-prod_binary64_130`

Counts

4 → 59

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
7.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
6.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
2.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))

series1.2s (5%)

Counts

4 → 12

Calls

4 calls:

507.0ms	(log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
448.0ms	(.f64 (acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))))) R)
140.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (+.f64 (.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 phi1) (cos.f64 phi2))) (log.f64 (exp.f64 (.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))))
77.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))

simplify136.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4971	2068
1	4971	2068

prune94.0ms (0.4%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	12	13
Picked	0	1	1
Done	0	0	0
Total	71	14	85

Merged error: 3.7b

Counts

85 → 14

Compiler

Compiled 2683 to 298 computations (88.9% saved)

regimes1.9s (8.2%)

Compiler: Compiled 20996 to 12918 computations (38.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	43
1	31	43

end0.0ms (0%)

sample11.7s (49.6%)

Algorithm

1×

intervals

Results

7.0s	5475×	body	1024	valid
1.1s	1437×	body	512	valid
848.0ms	277×	body	2048	valid
243.0ms	514×	body	256	valid
69.0ms	297×	body	128	valid

Compiler

Compiled 2007 to 1235 computations (38.5% saved)

Details

analyze3.5s (15%)

sample329.0ms (1.4%)

simplify372.0ms (1.6%)

prune6.0ms (0%)

localize41.0ms (0.2%)

rewrite25.0ms (0.1%)

series686.0ms (2.9%)

simplify159.0ms (0.7%)

prune137.0ms (0.6%)

localize63.0ms (0.3%)

rewrite49.0ms (0.2%)

series1.3s (5.5%)

simplify90.0ms (0.4%)

prune176.0ms (0.7%)

localize47.0ms (0.2%)

rewrite38.0ms (0.2%)

series1.1s (4.7%)

simplify116.0ms (0.5%)

prune154.0ms (0.7%)

localize45.0ms (0.2%)

rewrite43.0ms (0.2%)

series1.2s (5%)

simplify136.0ms (0.6%)

prune94.0ms (0.4%)

regimes1.9s (8.2%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample11.7s (49.6%)

Profiling