Details

analyze3.7s

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
1.2%	98.6%	0.2%	11
1.4%	98.4%	0.2%	12
10.8%	88.9%	0.2%	13
10.8%	88.9%	0.2%	14

sample298.0ms

Algorithm

intervals

Results

192.0ms	103×	body	1280	valid
53.0ms	54×	body	640	valid
16.0ms	24×	body	320	valid
12.0ms	64×	body	80	valid
5.0ms	11×	body	160	valid

simplify31.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune13.0ms

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: 0.2b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
0.3b	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.6b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-r_binary64` `associate-l_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 45

Calls

4 calls:

1.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
6.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
2.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
4.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

series120.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
42.0ms	(.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
7.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
56.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))

simplify54.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4908	1415
1	4908	1415

prune115.0ms

Filtered

46 candidates to 57 candidates (-23.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	49	8	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	8	58

Merged error: 0.1b

Counts

58 → 8

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (cos.f64 delta) (sin.f64 phi1))
0.2b	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.3b	(.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.6b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`pow-prod-down_binary64` `associate--r+_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 60

Calls

4 calls:

5.0ms	(*.f64 (cos.f64 delta) (sin.f64 phi1))
1.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
10.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series121.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (cos.f64 delta) (sin.f64 phi1))
15.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
41.0ms	(.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
56.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4990	1345
1	4990	1345

prune99.0ms

Filtered

52 candidates to 72 candidates (-38.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	67	5	72
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	75	5	80

Merged error: 0.0b

Counts

80 → 5

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.2b	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
0.3b	(.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))
0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

22×	`pow1_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-up_binary64` `cos-mult_binary64` `pow-plus_binary64` `sqr-cos-a_binary64` `sin-mult_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
1.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
10.0ms	(.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))
5.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

series56.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
15.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
28.0ms	(.f64 (sin.f64 phi1) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))
4.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5064	833

prune111.0ms

Filtered

54 candidates to 86 candidates (-59.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.2b	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (sin.f64 delta))) (cos.f64 theta))))
0.2b	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (sin.f64 delta)))
0.3b	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1_binary64`
15×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
7×	`associate-r_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64`
1×	`pow-prod-up_binary64` `cos-mult_binary64` `pow-plus_binary64` `sqr-cos-a_binary64` `sin-mult_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 71

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
1.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (sin.f64 delta))) (cos.f64 theta))))
7.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (sin.f64 delta)))
5.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

series44.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
15.0ms	(atan2.f64 (.f64 (.f64 (sin.f64 theta) (sin.f64 delta)) (cos.f64 phi1)) (-.f64 (.f64 (cos.f64 delta) (.f64 (cos.f64 phi1) (cos.f64 phi1))) (.f64 (.f64 (sin.f64 phi1) (*.f64 (cos.f64 phi1) (sin.f64 delta))) (cos.f64 theta))))
15.0ms	(.f64 (sin.f64 phi1) (.f64 (cos.f64 phi1) (sin.f64 delta)))
4.0ms	(*.f64 (cos.f64 phi1) (cos.f64 phi1))

simplify56.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4904	737
1	4904	737

prune66.0ms

Filtered

54 candidates to 83 candidates (-53.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	83	7	90

Merged error: 0.0b

Counts

90 → 7

regimes409.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	31
1	85	31

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.6s	3056×	body	1280	valid
1.8s	1824×	body	640	valid
509.0ms	754×	body	320	valid
395.0ms	2045×	body	80	valid
136.0ms	321×	body	160	valid

Details

analyze3.7s

sample298.0ms

simplify31.0ms

prune13.0ms

localize31.0ms

rewrite14.0ms

series120.0ms

simplify54.0ms

prune115.0ms

localize25.0ms

rewrite21.0ms

series121.0ms

simplify42.0ms

prune99.0ms

localize26.0ms

rewrite22.0ms

series56.0ms

simplify54.0ms

prune111.0ms

localize26.0ms

rewrite20.0ms

series44.0ms

simplify56.0ms

prune66.0ms

regimes409.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.9s

Profiling