Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample76.0ms

Algorithm

intervals

Results

40.0ms	112×	body	1024	valid
11.0ms	51×	body	512	valid
9.0ms	69×	body	128	valid
4.0ms	5×	body	2048	valid
3.0ms	19×	body	256	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune3.0ms

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: 13.9b

Counts

2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
2.9b	(cos.f64 (+.f64 a b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r_binary64` `add-log-exp_binary64` `associate-r_binary64` `associate-l*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `cos-sum_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

3 → 47

Calls

3 calls:

4.0ms	(*.f64 r (sin.f64 b))
6.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
5.0ms	(cos.f64 (+.f64 a b))

series315.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(*.f64 r (sin.f64 b))
232.0ms	(/.f64 (*.f64 r (sin.f64 b)) (cos.f64 (+.f64 a b)))
28.0ms	(cos.f64 (+.f64 a b))

simplify81.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5397	692

prune47.0ms

Filtered

42 candidates to 56 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
0.1b	(*.f64 r (sin.f64 b))
0.2b	(*.f64 (sin.f64 a) (sin.f64 b))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-l_binary64`
5×	`sin-mult_binary64`
4×	`cos-mult_binary64` `associate-/r/_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `div-exp_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 75

Calls

4 calls:

8.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
5.0ms	(*.f64 r (sin.f64 b))
5.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

series794.0ms

Counts

4 → 12

Calls

4 calls:

149.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 a) (sin.f64 b)))
62.0ms	(*.f64 r (sin.f64 b))
69.0ms	(*.f64 (sin.f64 a) (sin.f64 b))
513.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 a) (sin.f64 b))))

simplify70.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4947	1582
1	4947	1582

prune90.0ms

Filtered

65 candidates to 87 candidates (-33.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	75	12	87
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	82	14	96

Merged error: 0.0b

Counts

96 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
0.2b	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
20×	`associate-r_binary64`
19×	`times-frac_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-/r/_binary64`
7×	`sin-mult_binary64`
6×	`add-log-exp_binary64` `cos-mult_binary64` `associate-l_binary64`
3×	`associate-/r_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `sub-div_binary64` `flip--_binary64` `frac-sub_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-*r/_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 99

Calls

4 calls:

6.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
14.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
9.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

series997.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a)))
502.0ms	(.f64 r (/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (*.f64 (sin.f64 b) (sin.f64 a)))))
70.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
285.0ms	(/.f64 (sin.f64 b) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (.f64 (sin.f64 b) (sin.f64 a))))

simplify84.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	6090	2846

prune98.0ms

Filtered

84 candidates to 111 candidates (-32.1%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	3	10	13
Picked	0	1	1
Done	0	0	0
Total	112	13	125

Merged error: 0.0b

Counts

125 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 r (sin.f64 b))
0.2b	(*.f64 (sin.f64 b) (sin.f64 a))
0.2b	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
2.4b	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64`
5×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `cbrt-unprod_binary64` `log-prod_binary64` `log-pow_binary64` `prod-exp_binary64` `times-frac_binary64`
2×	`pow-prod-down_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-exp_binary64` `*-commutative_binary64`
1×	`flip3--_binary64` `rem-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `sin-mult_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64` `exp-to-pow_binary64` `exp-prod_binary64`

Counts

4 → 74

Calls

4 calls:

5.0ms	(*.f64 r (sin.f64 b))
5.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
10.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
2.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

series835.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(*.f64 r (sin.f64 b))
76.0ms	(*.f64 (sin.f64 b) (sin.f64 a))
560.0ms	(/.f64 (.f64 r (sin.f64 b)) (-.f64 (.f64 (cos.f64 a) (cos.f64 b)) (log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))))
146.0ms	(log.f64 (exp.f64 (*.f64 (sin.f64 b) (sin.f64 a))))

simplify71.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4987	1318
1	4987	1318

prune51.0ms

Filtered

58 candidates to 86 candidates (-48.3%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	86	13	99

Merged error: 0.0b

Counts

99 → 13

regimes85.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	26
1	42	26

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	3429×	body	1024	valid
304.0ms	1375×	body	512	valid
187.0ms	216×	body	2048	valid
159.0ms	2369×	body	128	valid
105.0ms	611×	body	256	valid
1.0ms	2×	body	1024	invalid
0.0ms	2×	body	512	invalid

Details

analyze1.0s

sample76.0ms

simplify8.0ms

prune3.0ms

localize9.0ms

rewrite18.0ms

series315.0ms

simplify81.0ms

prune47.0ms

localize15.0ms

rewrite36.0ms

series794.0ms

simplify70.0ms

prune90.0ms

localize15.0ms

rewrite46.0ms

series997.0ms

simplify84.0ms

prune98.0ms

localize18.0ms

rewrite30.0ms

series835.0ms

simplify71.0ms

prune51.0ms

regimes85.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.2s

Profiling