Details

analyze3.6s

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
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

sample267.0ms

Algorithm

intervals

Results

164.0ms	95×	body	1280	valid
43.0ms	44×	body	640	valid
23.0ms	28×	body	320	valid
14.0ms	78×	body	80	valid
5.0ms	11×	body	160	valid

simplify32.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	462	33
1	462	33

prune9.0ms

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: 0.1b

Counts

2 → 1

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))
0.4b	(-.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)))))))

rewrite18.0ms

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` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64`

Counts

4 → 57

Calls

4 calls:

5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
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))))
5.0ms	(-.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)))))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
45.0ms	(.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)))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4892	1209
1	4892	1209

prune146.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	56	13	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	13	70

Merged error: 0.0b

Counts

70 → 13

localize41.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`asin-acos_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `sqr-cos-a_binary64` `flip--_binary64` `associate--l+_binary64`

Counts

4 → 36

Calls

4 calls:

2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
8.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

series217.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
6.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
197.0ms	(-.f64 (.f64 (cos.f64 delta) (cos.f64 delta)) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (pow.f64 (sin.f64 phi1) 2))))

simplify51.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4954	1401
1	4954	1401

prune118.0ms

Filtered

37 candidates to 48 candidates (-29.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	50	11	61

Merged error: 0.0b

Counts

61 → 11

localize53.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(pow.f64 (sin.f64 phi1) 3)
0.3b	(-.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (sin.f64 phi1) 4)) (.f64 (sin.f64 delta) (+.f64 (.f64 (sin.f64 delta) (.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (cos.f64 theta) 2)))) (.f64 2 (.f64 (cos.f64 phi1) (.f64 (pow.f64 (sin.f64 phi1) 3) (*.f64 (cos.f64 delta) (cos.f64 theta)))))))))
0.4b	(pow.f64 (sin.f64 phi1) 4)

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
9×	`add-log-exp_binary64` `add-cube-cbrt_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64`
5×	`add-cbrt-cube_binary64`
4×	`difference-of-squares_binary64`
3×	`sqr-pow_binary64` `cube-prod_binary64`
2×	`pow-to-exp_binary64` `diff-log_binary64` `pow-pow_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `asin-acos_binary64` `associate--r+_binary64` `flip3--_binary64` `unpow2_binary64` `rem-cube-cbrt_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

4 → 66

Calls

4 calls:

2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
3.0ms	(pow.f64 (sin.f64 phi1) 3)
14.0ms	(-.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (sin.f64 phi1) 4)) (.f64 (sin.f64 delta) (+.f64 (.f64 (sin.f64 delta) (.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (cos.f64 theta) 2)))) (.f64 2 (.f64 (cos.f64 phi1) (.f64 (pow.f64 (sin.f64 phi1) 3) (*.f64 (cos.f64 delta) (cos.f64 theta)))))))))
3.0ms	(pow.f64 (sin.f64 phi1) 4)

series193.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms	(pow.f64 (sin.f64 phi1) 3)
172.0ms	(-.f64 (pow.f64 (cos.f64 delta) 2) (+.f64 (.f64 (pow.f64 (cos.f64 delta) 2) (pow.f64 (sin.f64 phi1) 4)) (.f64 (sin.f64 delta) (+.f64 (.f64 (sin.f64 delta) (.f64 (pow.f64 (cos.f64 phi1) 2) (.f64 (pow.f64 (sin.f64 phi1) 2) (pow.f64 (cos.f64 theta) 2)))) (.f64 2 (.f64 (cos.f64 phi1) (.f64 (pow.f64 (sin.f64 phi1) 3) (*.f64 (cos.f64 delta) (cos.f64 theta)))))))))
8.0ms	(pow.f64 (sin.f64 phi1) 4)

simplify59.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4946	1853
1	4946	1853

prune161.0ms

Filtered

48 candidates to 78 candidates (-62.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	78	11	89

Merged error: 0.0b

Counts

89 → 11

localize59.0ms

Local error

Found 4 expressions with local error:

0.3b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.3b	(pow.f64 (sin.f64 phi1) 3)
0.3b	(+.f64 (neg.f64 (pow.f64 (sin.f64 phi1) 4)) 1)
0.4b	(pow.f64 (sin.f64 phi1) 4)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
9×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
6×	`pow-unpow_binary64` `pow1_binary64` `add-exp-log_binary64` `unpow-prod-down_binary64`
5×	`add-cbrt-cube_binary64`
3×	`cube-prod_binary64`
2×	`pow-to-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-exp_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `asin-acos_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `distribute-rgt-neg-in_binary64` `rem-cube-cbrt_binary64` `neg-log_binary64` `+-commutative_binary64` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 63

Calls

4 calls:

2.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
3.0ms	(pow.f64 (sin.f64 phi1) 3)
9.0ms	(+.f64 (neg.f64 (pow.f64 (sin.f64 phi1) 4)) 1)
3.0ms	(pow.f64 (sin.f64 phi1) 4)

series34.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms	(pow.f64 (sin.f64 phi1) 3)
8.0ms	(+.f64 (neg.f64 (pow.f64 (sin.f64 phi1) 4)) 1)
8.0ms	(pow.f64 (sin.f64 phi1) 4)

simplify57.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4935	581
1	4935	581

prune104.0ms

Filtered

47 candidates to 75 candidates (-59.6%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	75	11	86

Merged error: 0.0b

Counts

86 → 11

regimes538.0ms

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 (3.0ms)

Iter	Nodes	Cost
0	220	82
1	220	82

end0.0ms

sample8.8s

Algorithm

intervals

Results

5.4s	3073×	body	1280	valid
2.0s	1909×	body	640	valid
442.0ms	660×	body	320	valid
400.0ms	2057×	body	80	valid
133.0ms	301×	body	160	valid

Details

analyze3.6s

sample267.0ms

simplify32.0ms

prune9.0ms

localize36.0ms

rewrite18.0ms

series118.0ms

simplify53.0ms

prune146.0ms

localize41.0ms

rewrite14.0ms

series217.0ms

simplify51.0ms

prune118.0ms

localize53.0ms

rewrite24.0ms

series193.0ms

simplify59.0ms

prune161.0ms

localize59.0ms

rewrite18.0ms

series34.0ms

simplify57.0ms

prune104.0ms

regimes538.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample8.8s

Profiling