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
12.5%	87.4%	0.1%	7
18.7%	81.1%	0.1%	8
26.5%	72.9%	0.5%	9
38.2%	60.7%	1.1%	10
41.7%	54.9%	3.4%	11
47.6%	47.4%	5%	12
53.4%	39.4%	7.2%	13
54.9%	34.5%	10.6%	14

sample58.0ms

Algorithm

intervals

Results

16.0ms	190×	body	128	valid
13.0ms	36×	body	1024	valid
4.0ms	4×	body	1024	invalid
4.0ms	53×	body	128	invalid
4.0ms	15×	body	512	valid
3.0ms	15×	body	256	valid
2.0ms	7×	body	512	invalid
1.0ms	4×	body	256	invalid

simplify162.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (155.0ms)

Iter	Nodes	Cost
0	7277	24

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: 28.4b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
3.0b	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0b	(*.f64 x (pow.f64 s 2))
21.1b	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

122×	`add-exp-log_binary64`
82×	`prod-exp_binary64`
34×	`add-cbrt-cube_binary64`
18×	`pow-to-exp_binary64` `add-sqr-sqrt_binary64` `pow-exp_binary64`
16×	`cbrt-unprod_binary64` `div-exp_binary64`
12×	`-un-lft-identity_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64`
7×	`unpow-prod-down_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64`
3×	`unpow2_binary64` `sqr-pow_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
1×	`pow-prod-down_binary64` `associate-/r*_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `cos-2_binary64`

Counts

4 → 119

Calls

4 calls:

12.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
6.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
6.0ms	(*.f64 x (pow.f64 s 2))
10.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

series344.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (pow.f64 c 2) (.f64 (.f64 x (pow.f64 s 2)) x)))
48.0ms	(.f64 (.f64 x (pow.f64 s 2)) x)
45.0ms	(*.f64 x (pow.f64 s 2))
113.0ms	(.f64 (pow.f64 c 2) (.f64 (*.f64 x (pow.f64 s 2)) x))

simplify60.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4973	2228
1	4973	2228

prune95.0ms

Filtered

68 candidates to 131 candidates (-92.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	122	9	131
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Merged error: 1.9b

Counts

132 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
0.6b	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

21×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`associate-l_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow-prod-down_binary64`
5×	`associate-r_binary64`
4×	`add-log-exp_binary64`
3×	`swap-sqr_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64`
1×	`associate-/r*_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-sqr_binary64` `cos-2_binary64` `pow2_binary64`

Counts

4 → 83

Calls

4 calls:

4.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))

series366.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (*.f64 c x))))
214.0ms	(/.f64 (cos.f64 (.f64 2 x)) (.f64 (fabs.f64 (.f64 s (.f64 c x))) (fabs.f64 (.f64 s (.f64 c x)))))
49.0ms	(.f64 s (.f64 c x))
53.0ms	(.f64 s (.f64 c x))

simplify72.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4951	1303
1	4951	1303

prune96.0ms

Filtered

57 candidates to 95 candidates (-66.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	85	10	95
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	90	14	104

Merged error: 1.3b

Counts

104 → 14

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
0.4b	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac_binary64`
56×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`associate-/l*_binary64`
14×	`pow1_binary64`
6×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-l*_binary64` `prod-exp_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
2×	`associate-r_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64`

Counts

4 → 133

Calls

4 calls:

7.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
4.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))

series420.0ms

Counts

4 → 12

Calls

4 calls:

206.0ms	(/.f64 (/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (.f64 c x)))) (fabs.f64 (.f64 s (*.f64 c x))))
109.0ms	(/.f64 (cos.f64 (.f64 x 2)) (fabs.f64 (.f64 s (*.f64 c x))))
45.0ms	(.f64 s (.f64 c x))
60.0ms	(.f64 s (.f64 c x))

simplify96.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4942	4037
1	4942	4037

prune133.0ms

Filtered

96 candidates to 145 candidates (-51.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	138	7	145
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	145	14	159

Merged error: 1.3b

Counts

159 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
3.8b	(.f64 s (.f64 c x))
3.8b	(.f64 s (.f64 c x))
14.2b	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`times-frac_binary64`
19×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
15×	`pow1_binary64`
12×	`unpow-prod-down_binary64`
7×	`associate-/r*_binary64`
6×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`associate-/l*_binary64` `div-exp_binary64` `sqrt-prod_binary64`
2×	`associate-r_binary64` `*-commutative_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 94

Calls

4 calls:

5.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
5.0ms	(.f64 s (.f64 c x))
5.0ms	(.f64 s (.f64 c x))
1.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

407.0ms	(/.f64 (cos.f64 (.f64 x 2)) (pow.f64 (fabs.f64 (.f64 s (*.f64 c x))) 3/2))
47.0ms	(.f64 s (.f64 c x))
53.0ms	(.f64 s (.f64 c x))
43.0ms	(sqrt.f64 (fabs.f64 (.f64 s (.f64 c x))))

simplify92.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4936	2146
1	4936	2146

prune93.0ms

Filtered

70 candidates to 106 candidates (-51.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	104	2	106
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	107	13	120

Merged error: 1.3b

Counts

120 → 13

regimes119.0ms

Accuracy

0% (1.3b remaining)

Error of 2.8b against oracle of 1.6b and baseline of 2.8b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	51
1	20	51

end0.0ms

sample1.7s

Algorithm

intervals

Results

525.0ms	6110×	body	128	valid
370.0ms	969×	body	1024	valid
160.0ms	595×	body	512	valid
159.0ms	1852×	body	128	invalid
70.0ms	199×	body	1024	invalid
60.0ms	325×	body	256	valid
55.0ms	225×	body	512	invalid
31.0ms	166×	body	256	invalid
1.0ms	1×	body	2048	valid

Details

analyze1.0s

sample58.0ms

simplify162.0ms

prune3.0ms

localize13.0ms

rewrite51.0ms

series344.0ms

simplify60.0ms

prune95.0ms

localize11.0ms

rewrite27.0ms

series366.0ms

simplify72.0ms

prune96.0ms

localize11.0ms

rewrite36.0ms

series420.0ms

simplify96.0ms

prune133.0ms

localize18.0ms

rewrite27.0ms

series551.0ms

simplify92.0ms

prune93.0ms

regimes119.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.7s

Profiling