Details

analyze5.0ms

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

sample36.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify99.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5202	29

prune6.0ms

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

localize25.0ms

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)))))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite57.0ms

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:

7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
31.0ms	(.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)))))
13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series73.0ms

Counts

4 → 10

Calls

4 calls:

9.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
55.0ms	(.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)))))
9.0ms	(.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 (44.0ms)

Iter	Nodes	Cost
0	4952	2987
1	4952	2987

prune185.0ms

Filtered

96 candidates to 149 candidates (-55.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	147	2	149
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	147	4	151

Merged error: 0b

Counts

151 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(.f64 (+.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))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
42×	`associate-r_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
16×	`sqrt-prod_binary64`
14×	`unswap-sqr_binary64`
12×	`add-cbrt-cube_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
11×	`times-frac_binary64`
10×	`prod-exp_binary64`
6×	`pow1_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cube-prod_binary64` `*-commutative_binary64`
3×	`pow-to-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-*r/_binary64` `div-inv_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 120

Calls

4 calls:

6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
19.0ms	(.f64 (+.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))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

series92.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
12.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
57.0ms	(.f64 (+.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))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify58.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5169	2208

prune144.0ms

Filtered

87 candidates to 132 candidates (-51.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	132	4	136

Merged error: 0b

Counts

136 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`associate-r_binary64`
18×	`times-frac_binary64`
16×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-/r_binary64` `associate-l*_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_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` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
14.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
1.0ms	(sqrt.f64 PI.f64)

series77.0ms

Counts

4 → 10

Calls

4 calls:

12.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
56.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)

simplify47.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5165	2386

prune114.0ms

Filtered

77 candidates to 120 candidates (-55.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	120	4	124

Merged error: 0b

Counts

124 → 4

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.2b	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
0.4b	(.f64 (sqrt.f64 (+.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))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
40×	`sqrt-div_binary64`
31×	`associate-r_binary64`
29×	`sqrt-prod_binary64`
28×	`associate-l_binary64`
26×	`*-un-lft-identity_binary64`
24×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
18×	`frac-times_binary64`
16×	`pow1_binary64` `unswap-sqr_binary64`
15×	`add-cbrt-cube_binary64`
14×	`flip3-+_binary64` `flip-+_binary64`
13×	`associate-*r/_binary64` `times-frac_binary64`
10×	`pow-prod-down_binary64` `prod-exp_binary64`
8×	`unpow-prod-down_binary64` `cube-prod_binary64`
6×	`cbrt-unprod_binary64` `associate-*l/_binary64`
5×	`pow1/2_binary64` `sqrt-pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `*-commutative_binary64`
3×	`sqrt-unprod_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`div-inv_binary64`

Counts

4 → 152

Calls

4 calls:

7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
19.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
32.0ms	(.f64 (sqrt.f64 (+.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))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))

series156.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
79.0ms	(.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7)))))
61.0ms	(.f64 (sqrt.f64 (+.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))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7)))) (.f64 (sqrt.f64 (/.f64 1 PI.f64)) (sqrt.f64 (+.f64 (+.f64 (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 (fabs.f64 x) 2)) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))))))

simplify56.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4995	5095
1	4995	5095

prune325.0ms

Filtered

109 candidates to 164 candidates (-50.5%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	164	4	168

Merged error: 0b

Counts

168 → 4

regimes136.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	31
1	34	31

end0.0ms

sample929.0ms

Algorithm

intervals

Results

738.0ms	8000×	body	80	valid
83.0ms	8002×	pre	80	true
0.0ms	2×	body	80	invalid

Details

analyze5.0ms

sample36.0ms

simplify99.0ms

prune6.0ms

localize25.0ms

rewrite57.0ms

series73.0ms

simplify66.0ms

prune185.0ms

localize19.0ms

rewrite41.0ms

series92.0ms

simplify58.0ms

prune144.0ms

localize21.0ms

rewrite31.0ms

series77.0ms

simplify47.0ms

prune114.0ms

localize31.0ms

rewrite71.0ms

series156.0ms

simplify56.0ms

prune325.0ms

regimes136.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample929.0ms

Profiling