Details

analyze2.6s

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
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

sample273.0ms

Algorithm

intervals

Results

176.0ms	127×	body	1280	valid
55.0ms	70×	body	640	valid
16.0ms	30×	body	320	valid
9.0ms	21×	body	80	valid
3.0ms	8×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (14.0ms)

Iter	Nodes	Cost
0	384	24
1	384	24

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 13.1b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.7b	(cos.f64 (-.f64 lambda1 lambda2))
2.7b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`associate-r_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
3×	`cos-diff_binary64`
2×	`sub-neg_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 58

Calls

4 calls:

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(*.f64 (sin.f64 (-.f64 lambda1 lambda2)) (cos.f64 phi2))
25.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))
5.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify55.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4879	620
1	4879	620

prune122.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	57	13	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	13	71

Merged error: 5.9b

Counts

71 → 13

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.1b	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.7b	(cos.f64 (-.f64 lambda1 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`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`cos-diff_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `sin-cos-mult_binary64`
1×	`sub-neg_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 67

Calls

4 calls:

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

series49.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
9.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
27.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify74.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4888	648
1	4888	648

prune122.0ms

Filtered

56 candidates to 79 candidates (-41.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	72	7	79
Fresh	7	5	12
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 0.1b

Counts

92 → 12

localize35.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
15×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-r_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-l_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
5×	`sin-cos-mult_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`associate-*r/_binary64` `unswap-sqr_binary64` `sin-mult_binary64` `frac-times_binary64`
2×	`flip3-+_binary64` `cos-mult_binary64` `frac-add_binary64` `flip-+_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-*l/_binary64`

Counts

4 → 83

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
5.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
12.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
10.0ms	(*.f64 (sin.f64 lambda1) (cos.f64 lambda2))
10.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
47.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify55.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4997	1065
1	4997	1065

prune137.0ms

Filtered

66 candidates to 95 candidates (-43.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	88	7	95
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	94	13	107

Merged error: 0.0b

Counts

107 → 13

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
6.6b	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
6.6b	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
6.6b	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`pow1/3_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`cbrt-div_binary64` `sin-mult_binary64` `cbrt-prod_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `swap-sqr_binary64` `associate-r_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `associate-r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 64

Calls

4 calls:

7.0ms	(.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
4.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
4.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
4.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(.f64 (cbrt.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2))) (cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2))))
26.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
20.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))
21.0ms	(cbrt.f64 (*.f64 (sin.f64 lambda1) (sin.f64 lambda2)))

simplify55.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5183	621

prune65.0ms

Filtered

53 candidates to 76 candidates (-43.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	76	13	89

Merged error: 0.0b

Counts

89 → 13

regimes556.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	147	53
1	147	53

end0.0ms

sample8.9s

Algorithm

intervals

Results

6.6s	4586×	body	1280	valid
1.6s	1920×	body	640	valid
316.0ms	574×	body	320	valid
115.0ms	706×	body	80	valid
72.0ms	214×	body	160	valid

Details

analyze2.6s

sample273.0ms

simplify17.0ms

prune8.0ms

localize29.0ms

rewrite25.0ms

series48.0ms

simplify55.0ms

prune122.0ms

localize33.0ms

rewrite23.0ms

series49.0ms

simplify74.0ms

prune122.0ms

localize35.0ms

rewrite29.0ms

series78.0ms

simplify55.0ms

prune137.0ms

localize40.0ms

rewrite20.0ms

series100.0ms

simplify55.0ms

prune65.0ms

regimes556.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample8.9s

Profiling