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

sample284.0ms

Algorithm

intervals

Results

190.0ms	149×	body	1280	valid
60.0ms	71×	body	640	valid
11.0ms	23×	body	320	valid
3.0ms	9×	body	160	valid
1.0ms	4×	body	80	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	95	19
1	95	19

prune12.0ms

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: 13.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

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)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.9b	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
2.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite16.0ms

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:

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)
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))

series60.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(.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)
11.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
10.0ms	(acos.f64 (+.f64 (.f64 (sin.f64 phi1) (sin.f64 phi2)) (.f64 (*.f64 (cos.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))))
5.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify61.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4943	876
1	4943	876

prune133.0ms

Filtered

49 candidates to 66 candidates (-34.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	52	14	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	14	67

Merged error: 3.0b

Counts

67 → 14

localize29.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
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)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.9b	(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))))))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`
2×	`sin-mult_binary64`
1×	`acos-asin_binary64`

Counts

4 → 64

Calls

4 calls:

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

series92.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
54.0ms	(.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)
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
17.0ms	(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))))))

simplify51.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5164	1173

prune134.0ms

Filtered

51 candidates to 76 candidates (-49.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	75	15	90

Merged error: 3.0b

Counts

90 → 15

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.3b	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
0.9b	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
30.8b	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `associate-r_binary64` `associate-l_binary64` `sin-mult_binary64`
2×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `cube-div_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`cbrt-div_binary64` `pow-to-exp_binary64` `rem-cbrt-cube_binary64` `acos-asin_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 68

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
5.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
2.0ms	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
5.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

series57.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
20.0ms	(pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3)
16.0ms	(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)) (cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))))))
11.0ms	(cbrt.f64 (pow.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)) 3))

simplify42.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	4978	795
1	4978	795

prune135.0ms

Filtered

54 candidates to 80 candidates (-48.1%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	79	1	80
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	79	16	95

Merged error: 2.9b

Counts

95 → 16

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(.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)
0.2b	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
0.9b	(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))))))
3.6b	(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:

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)
5.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
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))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(.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)
10.0ms	(*.f64 (sin.f64 phi1) (sin.f64 phi2))
18.0ms	(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))))))
10.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 phi1) (sin.f64 phi2))))

simplify72.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4996	1145
1	4996	1145

prune50.0ms

Filtered

46 candidates to 71 candidates (-54.3%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	14	14
Picked	0	1	1
Done	0	1	1
Total	71	16	87

Merged error: 2.9b

Counts

87 → 16

regimes1.0s

Accuracy

0% (0.3b remaining)

Error of 3.7b against oracle of 3.4b and baseline of 3.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	29
1	33	29

end0.0ms

sample9.2s

Algorithm

intervals

Results

6.6s	4876×	body	1280	valid
1.6s	2056×	body	640	valid
366.0ms	675×	body	320	valid
89.0ms	259×	body	160	valid
29.0ms	129×	body	80	valid
18.0ms	5×	body	2560	valid
1.0ms	1×	body	1280	invalid

Details

analyze3.0s

sample284.0ms

simplify8.0ms

prune12.0ms

localize24.0ms

rewrite16.0ms

series60.0ms

simplify61.0ms

prune133.0ms

localize29.0ms

rewrite17.0ms

series92.0ms

simplify51.0ms

prune134.0ms

localize34.0ms

rewrite19.0ms

series57.0ms

simplify42.0ms

prune135.0ms

localize33.0ms

rewrite14.0ms

series91.0ms

simplify72.0ms

prune50.0ms

regimes1.0s

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.2s

Profiling