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

sample308.0ms

Algorithm

intervals

Results

169.0ms	87×	body	1280	valid
90.0ms	84×	body	640	valid
16.0ms	22×	body	320	valid
12.0ms	56×	body	80	valid
3.0ms	7×	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

prune7.0ms

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

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(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))))
0.5b	(-.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)))))))

rewrite15.0ms

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`
2×	`asin-acos_binary64`
1×	`pow-prod-down_binary64` `sin-diff_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sin-asin_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `sin-mult_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

4 → 47

Calls

4 calls:

2.0ms	(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)))))))

series126.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sin.f64 (asin.f64 (+.f64 (.f64 (sin.f64 phi1) (cos.f64 delta)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
36.0ms	(.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))))
54.0ms	(-.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

59 → 59

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4884	1256
1	4884	1256

prune84.0ms

Filtered

48 candidates to 59 candidates (-22.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	52	7	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	7	60

Merged error: 0.0b

Counts

60 → 7

localize34.0ms

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	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.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))))))))
3.1b	(-.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)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 61

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)))))))
2.0ms	(acos.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 (-.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)))))

series113.0ms

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)))))))
6.0ms	(acos.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 (-.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))))))))
11.0ms	(-.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)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4933	1746
1	4933	1746

prune68.0ms

Filtered

56 candidates to 73 candidates (-30.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	72	1	73
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	73	7	80

Merged error: 0.0b

Counts

80 → 7

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
0.5b	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
13.8b	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
58.2b	(cos.f64 (/.f64 PI.f64 2))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `acos-asin_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`cos-diff_binary64`
2×	`associate--r+_binary64`
1×	`cos-PI/2_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cos-acos_binary64` `flip--_binary64`

Counts

4 → 38

Calls

4 calls:

2.0ms	(acos.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) (cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
4.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
3.0ms	(cos.f64 (/.f64 PI.f64 2))

series82.0ms

Counts

4 → 10

Calls

4 calls:

6.0ms	(acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta))))
48.0ms	(-.f64 (cos.f64 delta) (.f64 (sin.f64 phi1) (cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))))
27.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
0.0ms	(cos.f64 (/.f64 PI.f64 2))

simplify95.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4841	849
1	4841	849

prune69.0ms

Filtered

40 candidates to 48 candidates (-20.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	2	3	5
Picked	1	0	1
Done	0	1	1
Total	48	7	55

Merged error: 0.0b

Counts

55 → 7

localize57.0ms

Local error

Found 4 expressions with local error:

13.8b	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
13.8b	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
13.8b	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
58.2b	(cos.f64 (/.f64 PI.f64 2))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64`
3×	`acos-asin_binary64` `cos-diff_binary64` `cos-acos_binary64`
1×	`cos-PI/2_binary64`

Counts

4 → 35

Calls

4 calls:

2.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
3.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
3.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
3.0ms	(cos.f64 (/.f64 PI.f64 2))

series83.0ms

Counts

4 → 10

Calls

4 calls:

29.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
27.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
27.0ms	(cos.f64 (acos.f64 (+.f64 (.f64 (cos.f64 delta) (sin.f64 phi1)) (.f64 (*.f64 (cos.f64 phi1) (sin.f64 delta)) (cos.f64 theta)))))
0.0ms	(cos.f64 (/.f64 PI.f64 2))

simplify46.0ms

Algorithm

egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4851	659
1	4851	659

prune55.0ms

Filtered

39 candidates to 45 candidates (-15.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	44	1	45
Fresh	0	5	5
Picked	1	0	1
Done	0	1	1
Total	45	7	52

Merged error: 0.0b

Counts

52 → 7

regimes340.0ms

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

sample9.3s

Algorithm

intervals

Results

5.6s	3172×	body	1280	valid
1.9s	1871×	body	640	valid
609.0ms	1946×	body	80	valid
532.0ms	724×	body	320	valid
143.0ms	287×	body	160	valid

Details

analyze3.7s

sample308.0ms

simplify31.0ms

prune7.0ms

localize31.0ms

rewrite15.0ms

series126.0ms

simplify53.0ms

prune84.0ms

localize34.0ms

rewrite30.0ms

series113.0ms

simplify62.0ms

prune68.0ms

localize43.0ms

rewrite15.0ms

series82.0ms

simplify95.0ms

prune69.0ms

localize57.0ms

rewrite11.0ms

series83.0ms

simplify46.0ms

prune55.0ms

regimes340.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample9.3s

Profiling