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

sample292.0ms

Algorithm

intervals

Results

172.0ms	97×	body	1280	valid
68.0ms	64×	body	640	valid
17.0ms	27×	body	320	valid
11.0ms	60×	body	80	valid
3.0ms	8×	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

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: 0.1b

Counts

2 → 1

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(*.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))))
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)))))))

series122.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
46.0ms	(.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))))
57.0ms	(-.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 (43.0ms)

Iter	Nodes	Cost
0	4978	1213
1	4978	1213

prune123.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	62	7	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	7	70

Merged error: 0.0b

Counts

70 → 7

localize37.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
0.3b	(*.f64 (sin.f64 theta) (sin.f64 delta))
0.4b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
2.9b	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sin-sum_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`acos-asin_binary64` `associate--r-_binary64`
4×	`associate--r+_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `sin-mult_binary64` `flip--_binary64` `*-commutative_binary64`
1×	`distribute-lft-out--_binary64` `times-frac_binary64`

Counts

4 → 72

Calls

4 calls:

13.0ms	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
5.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
5.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
9.0ms	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series117.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
12.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
52.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (sin.f64 (-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))))
10.0ms	(-.f64 (/.f64 PI.f64 2) (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

simplify79.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4823	1698
1	4823	1698

prune112.0ms

Filtered

65 candidates to 84 candidates (-29.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	84	7	91

Merged error: 0.0b

Counts

91 → 7

localize33.0ms

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))))
0.4b	(-.f64 (cos.f64 delta) (.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)))))))
0.5b	(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.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))
0.6b	(pow.f64 (-.f64 (cos.f64 delta) (.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)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`cube-div_binary64`
3×	`pow-unpow_binary64` `flip3--_binary64` `flip--_binary64`
2×	`cbrt-div_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `asin-acos_binary64` `diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64` `rem-cube-cbrt_binary64` `pow-exp_binary64`

Counts

4 → 67

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))))
4.0ms	(-.f64 (cos.f64 delta) (.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)))))))
4.0ms	(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.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))
5.0ms	(pow.f64 (-.f64 (cos.f64 delta) (.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)

series218.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
52.0ms	(-.f64 (cos.f64 delta) (.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)))))))
55.0ms	(cbrt.f64 (pow.f64 (-.f64 (cos.f64 delta) (.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))
103.0ms	(pow.f64 (-.f64 (cos.f64 delta) (.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)

simplify51.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5009	2275

prune89.0ms

Filtered

50 candidates to 79 candidates (-58.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	79	7	86

Merged error: 0.0b

Counts

86 → 7

localize38.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
0.6b	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
0.6b	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
0.6b	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

rewrite12.0ms

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:

6.0ms	(.f64 (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
1.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
1.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
1.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

series166.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(.f64 (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))) (cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))))
34.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
39.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
35.0ms	(cbrt.f64 (asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5612	1717

prune64.0ms

Filtered

51 candidates to 85 candidates (-66.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

regimes412.0ms

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	68	37
1	68	37

end0.0ms

sample8.9s

Algorithm

intervals

Results

5.5s	3092×	body	1280	valid
1.9s	1898×	body	640	valid
481.0ms	717×	body	320	valid
389.0ms	1988×	body	80	valid
129.0ms	305×	body	160	valid

Details

analyze3.6s

sample292.0ms

simplify31.0ms

prune10.0ms

localize30.0ms

rewrite18.0ms

series122.0ms

simplify53.0ms

prune123.0ms

localize37.0ms

rewrite34.0ms

series117.0ms

simplify79.0ms

prune112.0ms

localize33.0ms

rewrite16.0ms

series218.0ms

simplify51.0ms

prune89.0ms

localize38.0ms

rewrite12.0ms

series166.0ms

simplify67.0ms

prune64.0ms

regimes412.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample8.9s

Profiling