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

sample310.0ms

Algorithm

intervals

Results

203.0ms	110×	body	1280	valid
59.0ms	58×	body	640	valid
15.0ms	24×	body	320	valid
11.0ms	58×	body	80	valid
3.0ms	6×	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

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))))))
0.4b	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.7b	(-.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)))))))

rewrite19.0ms

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)))))))

series107.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
41.0ms	(.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))))))
6.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
51.0ms	(-.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

prune132.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	59	10	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	10	70

Merged error: 0.0b

Counts

70 → 10

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
0.4b	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.7b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
3.4b	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

15×	`log-prod_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate--r+_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`log-pow_binary64`
3×	`associate-r_binary64` `associate-l_binary64` `exp-prod_binary64`
2×	`asin-acos_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `rem-log-exp_binary64` `exp-diff_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `log-div_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 66

Calls

4 calls:

8.0ms	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (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))))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
3.0ms	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

series99.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (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))))
50.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))))
6.0ms	(log.f64 (exp.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

simplify73.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4865	2091
1	4865	2091

prune108.0ms

Filtered

52 candidates to 78 candidates (-50.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	78	10	88

Merged error: 0.0b

Counts

88 → 10

localize46.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64` `sqr-pow_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`
2×	`pow-to-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-prod-down_binary64` `difference-cubes_binary64` `sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cube-div_binary64` `prod-exp_binary64` `sin-mult_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 75

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 (cos.f64 delta) 3)
10.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3))
6.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)

series395.0ms

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))))
6.0ms	(pow.f64 (cos.f64 delta) 3)
309.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3))
74.0ms	(pow.f64 (.f64 (sin.f64 phi1) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) 3)

simplify47.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5118	1924

prune140.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	8	8
Picked	1	0	1
Done	0	1	1
Total	86	11	97

Merged error: 0.0b

Counts

97 → 11

localize53.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
3×	`pow-unpow_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
2×	`pow-prod-down_binary64` `pow3_binary64`
1×	`pow-to-exp_binary64` `difference-cubes_binary64` `sub-neg_binary64` `asin-acos_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `sqr-pow_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `sin-mult_binary64` `sqr-sin-a_binary64` `pow-sqr_binary64` `flip--_binary64` `pow-exp_binary64` `pow2_binary64` `unpow3_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

4 → 70

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 (cos.f64 delta) 3)
22.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
7.0ms	(.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

series356.0ms

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))))
6.0ms	(pow.f64 (cos.f64 delta) 3)
303.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (.f64 (.f64 (.f64 (sin.f64 phi1) (sin.f64 phi1)) (sin.f64 phi1)) (.f64 (.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
42.0ms	(.f64 (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (sin.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4962	1547
1	4962	1547

prune87.0ms

Filtered

53 candidates to 82 candidates (-54.7%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	82	11	93

Merged error: 0.0b

Counts

93 → 11

regimes533.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	58	35
1	58	35

end0.0ms

sample9.0s

Algorithm

intervals

Results

5.6s	3146×	body	1280	valid
1.9s	1895×	body	640	valid
516.0ms	717×	body	320	valid
389.0ms	1947×	body	80	valid
140.0ms	295×	body	160	valid

Details

analyze3.7s

sample310.0ms

simplify31.0ms

prune9.0ms

localize36.0ms

rewrite19.0ms

series107.0ms

simplify53.0ms

prune132.0ms

localize34.0ms

rewrite20.0ms

series99.0ms

simplify73.0ms

prune108.0ms

localize46.0ms

rewrite23.0ms

series395.0ms

simplify47.0ms

prune140.0ms

localize53.0ms

rewrite36.0ms

series356.0ms

simplify53.0ms

prune87.0ms

regimes533.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.0s

Profiling