Details

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

sample33.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

simplify95.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5202	29

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 0.0b

Counts

2 → 2

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64`
36×	`associate-l_binary64`
35×	`pow1_binary64` `add-cbrt-cube_binary64`
31×	`times-frac_binary64`
29×	`*-un-lft-identity_binary64`
27×	`add-cube-cbrt_binary64`
19×	`prod-exp_binary64`
17×	`cbrt-unprod_binary64`
14×	`sqrt-prod_binary64` `associate-*l/_binary64`
12×	`frac-add_binary64`
10×	`pow-prod-down_binary64`
7×	`associate-r_binary64`
6×	`flip3-+_binary64` `pow-prod-up_binary64` `associate-*r/_binary64` `pow-plus_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64`
5×	`div-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64`
3×	`*-commutative_binary64`
2×	`div-inv_binary64` `pow-sqr_binary64` `pow2_binary64`
1×	`pow1/2_binary64` `1-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow3_binary64` `rec-exp_binary64`

Counts

4 → 139

Calls

4 calls:

6.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
26.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series89.0ms

Counts

4 → 10

Calls

4 calls:

7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
69.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify66.0ms

Algorithm

egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4952	2987
1	4952	2987

prune217.0ms

Filtered

96 candidates to 149 candidates (-55.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	148	3	151

Merged error: 0b

Counts

151 → 3

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
1.0b	(/.f64 1/21 (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
30×	`sqrt-prod_binary64`
12×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 106

Calls

4 calls:

12.0ms	(/.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
4.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series229.0ms

Counts

4 → 6

Calls

4 calls:

229.0ms	(/.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x))) (*.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (sqrt.f64 PI.f64))
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify75.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4907	1897
1	4907	1897

prune144.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	112	3	115

Merged error: 0b

Counts

115 → 3

localize26.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5))))
0.4b	(.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105))
1.0b	(sqrt.f64 PI.f64)
27.6b	(/.f64 (+.f64 (.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))))) (.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

66×	`associate-*r/_binary64`
23×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
19×	`flip3--_binary64` `flip--_binary64`
18×	`associate-/l/_binary64`
16×	`frac-add_binary64`
15×	`pow1_binary64`
12×	`frac-times_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`flip3-+_binary64` `-un-lft-identity_binary64` `add-cube-cbrt_binary64` `flip-+_binary64` `associate-l/_binary64`
9×	`cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64`
6×	`pow-prod-down_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
2×	`associate-r_binary64` `associate-/r/_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 109

Calls

4 calls:

21.0ms	(.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5))))
10.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105))
1.0ms	(sqrt.f64 PI.f64)
35.0ms	(/.f64 (+.f64 (.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))))) (.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105)))

series261.0ms

Counts

4 → 10

Calls

4 calls:

65.0ms	(.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5))))
27.0ms	(.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105))
0.0ms	(sqrt.f64 PI.f64)
169.0ms	(/.f64 (+.f64 (.f64 21 (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (+.f64 (.f64 5 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (pow.f64 (fabs.f64 x) 5)))) (.f64 (pow.f64 (fabs.f64 x) 7) (.f64 5 (-.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3)))))) (.f64 (sqrt.f64 PI.f64) (.f64 (-.f64 (.f64 2 (fabs.f64 x)) (*.f64 2/3 (pow.f64 (fabs.f64 x) 3))) 105)))

simplify44.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5075	4913

prune498.0ms

Filtered

89 candidates to 119 candidates (-33.7%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	119	3	122

Merged error: 0b

Counts

122 → 3

regimes181.0ms

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	42	61
1	42	61

end0.0ms

sample941.0ms

Algorithm

intervals

Results

744.0ms	8000×	body	80	valid
90.0ms	8000×	pre	80	true

Details

analyze7.0ms

sample33.0ms

simplify95.0ms

prune8.0ms

localize27.0ms

rewrite52.0ms

series89.0ms

simplify66.0ms

prune217.0ms

localize19.0ms

rewrite23.0ms

series229.0ms

simplify75.0ms

prune144.0ms

localize26.0ms

rewrite73.0ms

series261.0ms

simplify44.0ms

prune498.0ms

regimes181.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample941.0ms

Profiling