Details

analyze2.5s

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

sample286.0ms

Algorithm

intervals

Results

213.0ms	152×	body	1280	valid
47.0ms	62×	body	640	valid
8.0ms	15×	body	320	valid
3.0ms	20×	body	80	valid
2.0ms	7×	body	160	valid

simplify30.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	386	39
1	386	39

prune3.0ms

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: 13.7b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.7b	(sin.f64 (-.f64 lambda1 lambda2))
4.8b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite21.0ms

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:

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

series180.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
106.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
18.0ms	(sin.f64 (-.f64 lambda1 lambda2))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify108.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4890	943
1	4890	943

prune80.0ms

Filtered

50 candidates to 70 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	60	10	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 6.9b

Counts

71 → 10

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.8b	(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 (sin.f64 phi1) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
8.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
4.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series261.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
41.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
165.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
19.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify91.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5069	1049

prune80.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	81	8	89

Merged error: 0.1b

Counts

89 → 8

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.3b	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

32×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
4×	`add-log-exp_binary64` `sin-cos-mult_binary64` `*-commutative_binary64`
3×	`sin-mult_binary64`
2×	`cos-mult_binary64` `associate-r/_binary64` `unswap-sqr_binary64` `frac-times_binary64` `associate-l/_binary64`

Counts

4 → 87

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

series320.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
40.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
112.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
125.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify95.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4959	1542
1	4959	1542

prune112.0ms

Filtered

58 candidates to 99 candidates (-70.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	96	11	107

Merged error: 0.1b

Counts

107 → 11

localize34.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

29×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
13×	`add-sqr-sqrt_binary64`
10×	`associate-l_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-r_binary64`
4×	`add-log-exp_binary64` `*-commutative_binary64`
3×	`associate-*r/_binary64` `sin-mult_binary64` `sin-cos-mult_binary64`
2×	`unswap-sqr_binary64`
1×	`frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 84

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 lambda2) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))
5.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

series321.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
129.0ms	(.f64 (cos.f64 lambda1) (.f64 (cos.f64 lambda2) (*.f64 (sin.f64 phi1) (cos.f64 phi2))))
37.0ms	(*.f64 (cos.f64 lambda1) (sin.f64 lambda2))
114.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify96.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4936	1468
1	4936	1468

prune87.0ms

Filtered

61 candidates to 96 candidates (-57.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	95	1	96
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	98	9	107

Merged error: 0.1b

Counts

107 → 9

regimes152.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	77
1	130	77

end0.0ms

sample8.8s

Algorithm

intervals

Results

6.5s	4657×	body	1280	valid
1.5s	1957×	body	640	valid
281.0ms	547×	body	320	valid
98.0ms	641×	body	80	valid
69.0ms	198×	body	160	valid

Details

analyze2.5s

sample286.0ms

simplify30.0ms

prune3.0ms

localize30.0ms

rewrite21.0ms

series180.0ms

simplify108.0ms

prune80.0ms

localize36.0ms

rewrite23.0ms

series261.0ms

simplify91.0ms

prune80.0ms

localize36.0ms

rewrite31.0ms

series320.0ms

simplify95.0ms

prune112.0ms

localize34.0ms

rewrite32.0ms

series321.0ms

simplify96.0ms

prune87.0ms

regimes152.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample8.8s

Profiling