Details

analyze2.7s

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

sample287.0ms

Algorithm

intervals

Results

211.0ms	147×	body	1280	valid
48.0ms	59×	body	640	valid
7.0ms	14×	body	320	valid
4.0ms	25×	body	80	valid
4.0ms	11×	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: 13.0b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.0b	(cos.f64 (-.f64 lambda1 lambda2))
2.1b	(sin.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` `*-commutative_binary64`
1×	`sin-diff_binary64` `sin-sum_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `associate-*l/_binary64`

Counts

4 → 57

Calls

4 calls:

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

series182.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
107.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))
21.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify110.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4825	929
1	4825	929

prune84.0ms

Filtered

49 candidates to 69 candidates (-40.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	57	12	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	12	70

Merged error: 6.3b

Counts

70 → 12

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.3b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.0b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite28.0ms

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` `associate-l/_binary64` `-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sin-cos-mult_binary64` `cos-sum_binary64` `flip--_binary64`

Counts

4 → 68

Calls

4 calls:

9.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
7.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
6.0ms	(cos.f64 (-.f64 lambda1 lambda2))

series292.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(.f64 (-.f64 (.f64 (sin.f64 lambda1) (cos.f64 lambda2)) (*.f64 (cos.f64 lambda1) (sin.f64 lambda2))) (cos.f64 phi2))
43.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
104.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
16.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify56.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5115	1404

prune98.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	5	6	11
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 0.1b

Counts

92 → 13

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
0.2b	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
0.2b	(.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 (cos.f64 phi1) (sin.f64 phi2))
9.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
5.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
9.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

series345.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
112.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
42.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
127.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))

simplify110.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4940	1542
1	4940	1542

prune325.0ms

Filtered

58 candidates to 99 candidates (-70.7%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	93	6	99
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	97	15	112

Merged error: 0.0b

Counts

112 → 15

localize36.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
10.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
7.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1))
6.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

series300.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
118.0ms	(.f64 (.f64 (sin.f64 lambda1) (sin.f64 lambda2)) (*.f64 (sin.f64 phi1) (cos.f64 phi2)))
75.0ms	(.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (sin.f64 phi1))
44.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))

simplify120.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4945	1311
1	4945	1311

prune84.0ms

Filtered

56 candidates to 93 candidates (-66.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	2	12	14
Picked	1	0	1
Done	0	0	0
Total	94	14	108

Merged error: 0.0b

Counts

108 → 14

regimes225.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	152	99
1	152	99

end0.0ms

sample9.2s

Algorithm

intervals

Results

6.8s	4669×	body	1280	valid
1.6s	1932×	body	640	valid
303.0ms	538×	body	320	valid
113.0ms	669×	body	80	valid
69.0ms	192×	body	160	valid

Details

analyze2.7s

sample287.0ms

simplify30.0ms

prune3.0ms

localize24.0ms

rewrite21.0ms

series182.0ms

simplify110.0ms

prune84.0ms

localize33.0ms

rewrite28.0ms

series292.0ms

simplify56.0ms

prune98.0ms

localize36.0ms

rewrite31.0ms

series345.0ms

simplify110.0ms

prune325.0ms

localize36.0ms

rewrite30.0ms

series300.0ms

simplify120.0ms

prune84.0ms

regimes225.0ms

bsearch0.0ms

simplify5.0ms

end0.0ms

sample9.2s

Profiling