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

sample317.0ms

Algorithm

intervals

Results

215.0ms	118×	body	1280	valid
56.0ms	55×	body	640	valid
17.0ms	25×	body	320	valid
10.0ms	51×	body	80	valid
3.0ms	7×	body	160	valid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	464	55
1	464	55

prune4.0ms

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	(*.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))))
0.6b	(-.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)))))))

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` `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))))))
1.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
7.0ms	(-.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)))))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(*.f64 (sin.f64 theta) (sin.f64 delta))
165.0ms	(.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))))))
27.0ms	(asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
215.0ms	(-.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)))))))

simplify93.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	5060	2029

prune116.0ms

Filtered

55 candidates to 69 candidates (-25.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	60	9	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	9	70

Merged error: 0.0b

Counts

70 → 9

localize47.0ms

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 (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))
0.5b	(pow.f64 (cos.f64 delta) 3)
0.5b	(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)

rewrite22.0ms

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:

1.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
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))
3.0ms	(pow.f64 (cos.f64 delta) 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)

series2.0s

Counts

4 → 12

Calls

4 calls:

25.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
1.6s	(-.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))
27.0ms	(pow.f64 (cos.f64 delta) 3)
350.0ms	(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)

simplify86.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5158	3170

prune170.0ms

Filtered

59 candidates to 87 candidates (-47.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	85	2	87
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	86	10	96

Merged error: 0.0b

Counts

96 → 10

localize34.0ms

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))))
0.5b	(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	(-.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)))))))
0.6b	(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)

rewrite18.0ms

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:

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

series880.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(asin.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
208.0ms	(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))
212.0ms	(-.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)))))))
434.0ms	(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)

simplify92.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5046	3816

prune105.0ms

Filtered

48 candidates to 79 candidates (-64.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	76	3	79
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	80	9	89

Merged error: 0.0b

Counts

89 → 9

localize57.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (pow.f64 (cos.f64 delta) 3) (log.f64 (exp.f64 (pow.f64 (.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)))))) 3))))
0.5b	(pow.f64 (cos.f64 delta) 3)
0.5b	(pow.f64 (.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)))))) 3)
3.5b	(log.f64 (exp.f64 (pow.f64 (.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)))))) 3)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

15.0ms	(-.f64 (pow.f64 (cos.f64 delta) 3) (log.f64 (exp.f64 (pow.f64 (.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)))))) 3))))
3.0ms	(pow.f64 (cos.f64 delta) 3)
6.0ms	(pow.f64 (.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)))))) 3)
4.0ms	(log.f64 (exp.f64 (pow.f64 (.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)))))) 3)))

series2.3s

Counts

4 → 12

Calls

4 calls:

1.6s	(-.f64 (pow.f64 (cos.f64 delta) 3) (log.f64 (exp.f64 (pow.f64 (.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)))))) 3))))
27.0ms	(pow.f64 (cos.f64 delta) 3)
336.0ms	(pow.f64 (.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)))))) 3)
339.0ms	(log.f64 (exp.f64 (pow.f64 (.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)))))) 3)))

simplify85.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5165	3313

prune165.0ms

Filtered

67 candidates to 98 candidates (-46.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	97	10	107

Merged error: 0.0b

Counts

107 → 10

regimes197.0ms

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 (1.0ms)

Iter	Nodes	Cost
0	56	148
1	56	148

end0.0ms

sample9.1s

Algorithm

intervals

Results

5.8s	3130×	body	1280	valid
1.9s	1825×	body	640	valid
483.0ms	718×	body	320	valid
420.0ms	2047×	body	80	valid
129.0ms	280×	body	160	valid

Details

analyze3.6s

sample317.0ms

simplify52.0ms

prune4.0ms

localize31.0ms

rewrite21.0ms

series448.0ms

simplify93.0ms

prune116.0ms

localize47.0ms

rewrite22.0ms

series2.0s

simplify86.0ms

prune170.0ms

localize34.0ms

rewrite18.0ms

series880.0ms

simplify92.0ms

prune105.0ms

localize57.0ms

rewrite29.0ms

series2.3s

simplify85.0ms

prune165.0ms

regimes197.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample9.1s

Profiling