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

sample244.0ms

Algorithm

intervals

Results

178.0ms	169×	body	1024	valid
25.0ms	42×	body	512	valid
18.0ms	7×	body	2048	valid
6.0ms	17×	body	256	valid
3.0ms	21×	body	128	valid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	385	39
1	385	39

prune10.0ms

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: 12.3b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.5b	(cos.f64 (-.f64 lambda1 lambda2))
2.6b	(sin.f64 (-.f64 lambda1 lambda2))

rewrite27.0ms

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	(cos.f64 (-.f64 lambda1 lambda2))
4.0ms	(sin.f64 (-.f64 lambda1 lambda2))

series351.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
217.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
28.0ms	(cos.f64 (-.f64 lambda1 lambda2))
36.0ms	(sin.f64 (-.f64 lambda1 lambda2))

simplify87.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4893	943
1	4893	943

prune89.0ms

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: 7.1b

Counts

71 → 10

localize37.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
0.2b	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
0.2b	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
2.5b	(cos.f64 (-.f64 lambda1 lambda2))

rewrite29.0ms

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 phi1) (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))

series378.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
67.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
213.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (cos.f64 (-.f64 lambda1 lambda2)))
30.0ms	(cos.f64 (-.f64 lambda1 lambda2))

simplify78.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5346	1049

prune89.0ms

Filtered

54 candidates to 79 candidates (-46.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	4	79
Fresh	4	5	9
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 0.1b

Counts

89 → 9

localize33.0ms

Local error

Found 4 expressions with local error:

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

rewrite38.0ms

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 phi1) (cos.f64 phi2))
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))))

series568.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(*.f64 (cos.f64 phi1) (sin.f64 phi2))
69.0ms	(*.f64 (sin.f64 phi1) (cos.f64 phi2))
68.0ms	(*.f64 (sin.f64 lambda1) (sin.f64 lambda2))
362.0ms	(.f64 (.f64 (sin.f64 phi1) (cos.f64 phi2)) (+.f64 (.f64 (cos.f64 lambda1) (cos.f64 lambda2)) (.f64 (sin.f64 lambda1) (sin.f64 lambda2))))

simplify73.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4980	1744
1	4980	1744

prune128.0ms

Filtered

64 candidates to 95 candidates (-48.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	91	13	104

Merged error: 0.1b

Counts

104 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
0.6b	(cbrt.f64 (sin.f64 lambda2))
0.6b	(cbrt.f64 (sin.f64 lambda2))
0.6b	(cbrt.f64 (sin.f64 lambda2))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
2.0ms	(cbrt.f64 (sin.f64 lambda2))
2.0ms	(cbrt.f64 (sin.f64 lambda2))
2.0ms	(cbrt.f64 (sin.f64 lambda2))

series543.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(*.f64 (cbrt.f64 (sin.f64 lambda2)) (cbrt.f64 (sin.f64 lambda2)))
125.0ms	(cbrt.f64 (sin.f64 lambda2))
134.0ms	(cbrt.f64 (sin.f64 lambda2))
121.0ms	(cbrt.f64 (sin.f64 lambda2))

simplify63.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5033	797

prune88.0ms

Filtered

55 candidates to 85 candidates (-54.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	85	13	98

Merged error: 0.1b

Counts

98 → 13

regimes230.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	164	79
1	164	79

end0.0ms

sample7.7s

Algorithm

intervals

Results

5.8s	5364×	body	1024	valid
787.0ms	1292×	body	512	valid
466.0ms	172×	body	2048	valid
153.0ms	403×	body	256	valid
133.0ms	769×	body	128	valid

Details

analyze2.7s

sample244.0ms

simplify23.0ms

prune10.0ms

localize27.0ms

rewrite27.0ms

series351.0ms

simplify87.0ms

prune89.0ms

localize37.0ms

rewrite29.0ms

series378.0ms

simplify78.0ms

prune89.0ms

localize33.0ms

rewrite38.0ms

series568.0ms

simplify73.0ms

prune128.0ms

localize41.0ms

rewrite24.0ms

series543.0ms

simplify63.0ms

prune88.0ms

regimes230.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample7.7s

Profiling