Details

analyze3.0s

Algorithm

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

sample294.0ms

Algorithm

intervals

Results

208.0ms	155×	body	1280	valid
50.0ms	66×	body	640	valid
12.0ms	24×	body	320	valid
7.0ms	9×	body	160	valid
0.0ms	2×	body	80	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	97	31
1	97	31

prune2.0ms

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: 14.1b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.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)
1.3b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
1.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `acos-asin_binary64` `cos-diff_binary64` `sin-mult_binary64` `cos-sum_binary64`

Counts

4 → 54

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.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)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series221.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
117.0ms	(.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)
46.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
18.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4926	1438
1	4926	1438

prune88.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	53	13	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	54	13	67

Merged error: 4.0b

Counts

67 → 13

localize32.0ms

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))
0.3b	(.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)
1.3b	(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))))))

rewrite23.0ms

Algorithm

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`
6×	`cos-mult_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`associate-r/_binary64` `sin-mult_binary64` `frac-times_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `frac-add_binary64` `unswap-sqr_binary64` `flip-+_binary64`
1×	`acos-asin_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

Counts

4 → 72

Calls

4 calls:

11.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.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)
1.0ms	(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))))))

series504.0ms

Counts

4 → 12

Calls

4 calls:

218.0ms	(.f64 (.f64 (cos.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
40.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
185.0ms	(.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)
60.0ms	(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))))))

simplify98.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5037	2773

prune110.0ms

Filtered

56 candidates to 84 candidates (-50.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	72	12	84
Fresh	9	3	12
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Merged error: 3.9b

Counts

97 → 15

localize35.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (log.f64 (exp.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)
0.4b	(exp.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)))))))
0.9b	(log.f64 (exp.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))))))))
1.3b	(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))))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`exp-prod_binary64`
8×	`pow1_binary64` `log-pow_binary64`
7×	`associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`add-log-exp_binary64`
3×	`acos-asin_binary64` `associate-r_binary64` `log-prod_binary64`
2×	`exp-diff_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `rem-exp-log_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `log-div_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(.f64 (log.f64 (exp.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)
2.0ms	(exp.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)))))))
3.0ms	(log.f64 (exp.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))))))))
1.0ms	(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))))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(.f64 (log.f64 (exp.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)
116.0ms	(exp.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)))))))
59.0ms	(log.f64 (exp.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))))))))
58.0ms	(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))))))

simplify155.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	4867	3226
1	4867	3226

prune89.0ms

Filtered

41 candidates to 70 candidates (-70.7%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	66	4	70
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	69	16	85

Merged error: 3.9b

Counts

85 → 16

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
1.3b	(acos.f64 (+.f64 (log.f64 (exp.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))))))
2.8b	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
3×	`log-prod_binary64` `log-pow_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
1×	`acos-asin_binary64` `rem-log-exp_binary64` `sin-mult_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 59

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
3.0ms	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
2.0ms	(acos.f64 (+.f64 (log.f64 (exp.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))))))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

series333.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
187.0ms	(.f64 (acos.f64 (+.f64 (log.f64 (exp.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)
62.0ms	(acos.f64 (+.f64 (log.f64 (exp.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))))))
45.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

simplify116.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4944	1901
1	4944	1901

prune53.0ms

Filtered

45 candidates to 71 candidates (-57.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	69	2	71
Fresh	1	14	15
Picked	0	1	1
Done	0	0	0
Total	70	17	87

Merged error: 3.9b

Counts

87 → 17

regimes380.0ms

Accuracy

0% (0.4b remaining)

Error of 4.1b against oracle of 3.7b and baseline of 4.1b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	47
1	33	47

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.3s	4717×	body	1280	valid
1.7s	2152×	body	640	valid
365.0ms	687×	body	320	valid
102.0ms	291×	body	160	valid
33.0ms	9×	body	2560	valid
26.0ms	144×	body	80	valid

Details

analyze3.0s

sample294.0ms

simplify16.0ms

prune2.0ms

localize24.0ms

rewrite15.0ms

series221.0ms

simplify104.0ms

prune88.0ms

localize32.0ms

rewrite23.0ms

series504.0ms

simplify98.0ms

prune110.0ms

localize35.0ms

rewrite13.0ms

series423.0ms

simplify155.0ms

prune89.0ms

localize36.0ms

rewrite14.0ms

series333.0ms

simplify116.0ms

prune53.0ms

regimes380.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample8.9s

Profiling