Details

analyze2.0s

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
9.4%	90.4%	0.2%	9
9.4%	90.4%	0.2%	10
10.9%	88.9%	0.2%	11
10.9%	88.9%	0.2%	12
10.9%	88.9%	0.2%	13
10.9%	88.9%	0.2%	14

sample210.0ms

Algorithm

intervals

Results

117.0ms	119×	body	1280	valid
55.0ms	78×	body	640	valid
11.0ms	29×	body	320	valid
4.0ms	15×	body	160	valid
2.0ms	15×	body	80	valid

simplify158.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	271	32
1	271	32

prune8.0ms

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: 1.3b

Counts

2 → 1

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_3127`
6×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106` `*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113` `add-log-exp_binary64_3107`
4×	`sub-neg_binary64_3146`
3×	`sin-sum_binary64_2991` `associate-l_binary64_3202` `associate-r_binary64_3201` `cos-diff_binary64_2995`
2×	`associate-+r+_binary64_3193` `distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184`
1×	`cbrt-unprod_binary64_3111` `unswap-sqr_binary64_3170` `pow-prod-down_binary64_3069` `+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `cos-sum_binary64_2992` `*-commutative_binary64_3210` `flip3-+_binary64_3140` `sin-diff_binary64_2994` `prod-exp_binary64_3093`

Counts

4 → 51

Calls

4 calls:

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

series366.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
268.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 phi2) (cos.f64 (-.f64 lambda1 lambda2))))
17.0ms	(cos.f64 (-.f64 lambda1 lambda2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify104.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5862	945

prune419.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	50	13	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	13	64

Merged error: 1.1b

Counts

64 → 13

localize43.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_3127`
8×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106` `*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
6×	`associate-l_binary64_3202` `associate-r_binary64_3201` `add-log-exp_binary64_3107`
3×	`sin-sum_binary64_2991` `sub-neg_binary64_3146`
2×	`cbrt-unprod_binary64_3111` `unswap-sqr_binary64_3170` `pow-prod-down_binary64_3069` `associate-+r+_binary64_3193` `*-commutative_binary64_3210` `distribute-rgt-in_binary64_3185` `distribute-lft-in_binary64_3184` `prod-exp_binary64_3093`
1×	`+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `flip3-+_binary64_3140` `sin-diff_binary64_2994` `sin-mult_binary64_3013`

Counts

4 → 61

Calls

4 calls:

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

series366.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(*.f64 (cos.f64 phi2) (sin.f64 (-.f64 lambda1 lambda2)))
41.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
242.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))
24.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify70.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4933	1251
1	4933	1251

prune381.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 0.1b

Counts

86 → 10

localize53.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.2b	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.5b	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_3127`
8×	`pow1_binary64_3088` `add-cbrt-cube_binary64_3114` `add-exp-log_binary64_3106` `*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113`
6×	`associate-l_binary64_3202` `associate-r_binary64_3201` `add-log-exp_binary64_3107`
2×	`cbrt-unprod_binary64_3111` `unswap-sqr_binary64_3170` `pow-prod-down_binary64_3069` `associate-+r+_binary64_3193` `associate-r/_binary64_3203` `-commutative_binary64_3210` `distribute-rgt-in_binary64_3185` `sub-neg_binary64_3146` `distribute-lft-in_binary64_3184` `prod-exp_binary64_3093`
1×	`+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `flip3-+_binary64_3140` `flip--_binary64_3168` `flip3--_binary64_3141` `sin-mult_binary64_3013`

Counts

4 → 61

Calls

4 calls:

9.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
0.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

series481.0ms

Counts

4 → 12

Calls

4 calls:

141.0ms	(.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))))
70.0ms	(atan2.f64 (.f64 (cos.f64 phi2) (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (.f64 (cos.f64 lambda1) (sin.f64 lambda2)))) (+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))))
40.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
229.0ms	(+.f64 (cos.f64 phi1) (.f64 (cos.f64 phi2) (+.f64 (.f64 (cos.f64 lambda2) (cos.f64 lambda1)) (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))))

simplify81.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4887	2051
1	4887	2051

prune410.0ms

Filtered

55 candidates to 73 candidates (-32.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	68	5	73
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.0b

Counts

83 → 11

localize43.0ms

Local error

Found 4 expressions with local error:

0.5b	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
0.6b	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
3.6b	(cos.f64 (-.f64 lambda1 lambda2))
3.8b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_3142` `add-cube-cbrt_binary64_3113` `add-log-exp_binary64_3107` `add-sqr-sqrt_binary64_3127`
5×	`pow1_binary64_3088`
4×	`add-cbrt-cube_binary64_3114` `log-pow_binary64_3063` `add-exp-log_binary64_3106` `log-prod_binary64_3060`
3×	`exp-prod_binary64_3096`
2×	`sub-neg_binary64_3146`
1×	`sin-sum_binary64_2991` `+-commutative_binary64_3209` `flip-+_binary64_3167` `sum-log_binary64_3057` `cos-sum_binary64_2992` `flip3-+_binary64_3140` `exp-sum_binary64_3101` `sin-diff_binary64_2994` `cos-diff_binary64_2995` `rem-log-exp_binary64_3105`

Counts

4 → 45

Calls

4 calls:

4.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
5.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series257.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))
111.0ms	(log.f64 (exp.f64 (+.f64 (cos.f64 phi1) (*.f64 (cos.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2)))))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
19.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify82.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5107	968

prune248.0ms

Filtered

44 candidates to 57 candidates (-29.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	57	11	68

Merged error: 0.0b

Counts

68 → 11

regimes965.0ms

Accuracy

64.3% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.9b

bsearch2.0ms

Steps

Iters	Range		Point
0	4416508646354431/4503599627370496	2228117337999147/2251799813685248	0.9850723928065103

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	214
1	141	214

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.5s	3554×	body	1280	valid
1.4s	2417×	body	640	valid
374.0ms	921×	body	320	valid
104.0ms	401×	body	160	valid
85.0ms	707×	body	80	valid

Details

analyze2.0s

sample210.0ms

simplify158.0ms

prune8.0ms

localize35.0ms

rewrite21.0ms

series366.0ms

simplify104.0ms

prune419.0ms

localize43.0ms

rewrite24.0ms

series366.0ms

simplify70.0ms

prune381.0ms

localize53.0ms

rewrite21.0ms

series481.0ms

simplify81.0ms

prune410.0ms

localize43.0ms

rewrite19.0ms

series257.0ms

simplify82.0ms

prune248.0ms

regimes965.0ms

bsearch2.0ms

simplify7.0ms

end0.0ms

sample5.9s

Profiling