Details

analyze49.0ms

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%	74.9%	25.1%	4
12.5%	62.4%	25.1%	5
31.2%	31.2%	37.6%	6
37.5%	25%	37.6%	7
40.6%	15.6%	43.8%	8
42.9%	11.7%	45.4%	9
44.1%	7.4%	48.5%	10
45.1%	5.7%	49.3%	11
45.6%	3.6%	50.8%	12
46%	2.8%	51.2%	13
46.2%	1.8%	52%	14

sample17.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	6×	body	80	nan
0.0ms	1×	body	80	invalid

simplify160.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (151.0ms)

Iter	Nodes	Cost
0	1584	18
1	1584	18

prune7.0ms

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: 0.4b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 1 (*.f64 x 9)))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
0.3b	(/.f64 1 (*.f64 x 9))
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
21×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
15×	`associate-r_binary64`
14×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
7×	`prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow-prod-down_binary64` `cbrt-unprod_binary64`
4×	`distribute-lft-out_binary64` `associate-l_binary64` `div-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `div-inv_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `pow-flip_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/r*_binary64` `flip3--_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 93

Calls

4 calls:

5.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
14.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
5.0ms	(/.f64 1 (*.f64 x 9))
5.0ms	(*.f64 3 (sqrt.f64 x))

series85.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+.f64 y (/.f64 1 (*.f64 x 9)))
39.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 1 (*.f64 x 9))) 1))
11.0ms	(/.f64 1 (*.f64 x 9))
17.0ms	(*.f64 3 (sqrt.f64 x))

simplify48.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5031	1291

prune99.0ms

Filtered

66 candidates to 105 candidates (-59.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	93	12	105
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 0.0b

Counts

107 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 1/9 x) y)
0.3b	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
0.3b	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
0.4b	(/.f64 1/9 x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
11×	`pow1_binary64`
9×	`associate-l_binary64` `times-frac_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `associate-*r/_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 91

Calls

4 calls:

7.0ms	(+.f64 (/.f64 1/9 x) y)
12.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
13.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
3.0ms	(/.f64 1/9 x)

series100.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+.f64 (/.f64 1/9 x) y)
31.0ms	(*.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y)))
41.0ms	(.f64 3 (.f64 (sqrt.f64 x) (+.f64 -1 (+.f64 (/.f64 1/9 x) y))))
12.0ms	(/.f64 1/9 x)

simplify112.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	4867	1555
1	4867	1555

prune86.0ms

Filtered

68 candidates to 103 candidates (-51.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	100	3	103
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	104	11	115

Merged error: 0.0b

Counts

115 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 y (/.f64 (/.f64 1 x) 9))
0.2b	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
0.2b	(/.f64 (/.f64 1 x) 9)
0.3b	(*.f64 3 (sqrt.f64 x))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac_binary64`
58×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
50×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64`
14×	`associate-r_binary64`
13×	`associate-/l*_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `div-exp_binary64`
5×	`div-inv_binary64`
4×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `prod-exp_binary64` `sqrt-prod_binary64`
3×	`associate-/r*_binary64` `cbrt-undiv_binary64`
2×	`sub-neg_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `associate--l+_binary64` `-commutative_binary64`
1×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 135

Calls

4 calls:

13.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
23.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
6.0ms	(/.f64 (/.f64 1 x) 9)
5.0ms	(*.f64 3 (sqrt.f64 x))

series89.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 y (/.f64 (/.f64 1 x) 9))
39.0ms	(.f64 (.f64 3 (sqrt.f64 x)) (-.f64 (+.f64 y (/.f64 (/.f64 1 x) 9)) 1))
13.0ms	(/.f64 (/.f64 1 x) 9)
17.0ms	(*.f64 3 (sqrt.f64 x))

simplify85.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4933	2077
1	4933	2077

prune127.0ms

Filtered

98 candidates to 147 candidates (-50.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	0	9	9
Picked	1	0	1
Done	0	1	1
Total	147	11	158

Merged error: 0b

Counts

158 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 x) 9)
0.3b	(/.f64 1 (sqrt.f64 x))
0.3b	(*.f64 3 (sqrt.f64 x))
0.3b	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

76×	`times-frac_binary64`
59×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
38×	`sqrt-prod_binary64`
34×	`add-exp-log_binary64`
25×	`associate-/l*_binary64`
22×	`add-cbrt-cube_binary64`
14×	`div-exp_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64`
6×	`prod-exp_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `div-inv_binary64`
3×	`1-exp_binary64` `rec-exp_binary64` `pow-flip_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `inv-pow_binary64`

Counts

4 → 157

Calls

4 calls:

5.0ms	(*.f64 (sqrt.f64 x) 9)
7.0ms	(/.f64 1 (sqrt.f64 x))
5.0ms	(*.f64 3 (sqrt.f64 x))
10.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

series82.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(*.f64 (sqrt.f64 x) 9)
31.0ms	(/.f64 1 (sqrt.f64 x))
17.0ms	(*.f64 3 (sqrt.f64 x))
18.0ms	(/.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (sqrt.f64 x) 9))

simplify99.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4931	2024
1	4931	2024

prune112.0ms

Filtered

101 candidates to 169 candidates (-67.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	169	11	180

Merged error: 0b

Counts

180 → 11

regimes51.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	28
1	29	28

end0.0ms

sample488.0ms

Algorithm

intervals

Results

346.0ms	8000×	body	80	valid
6.0ms	142×	body	80	nan
3.0ms	67×	body	80	invalid

Details

analyze49.0ms

sample17.0ms

simplify160.0ms

prune7.0ms

localize10.0ms

rewrite31.0ms

series85.0ms

simplify48.0ms

prune99.0ms

localize9.0ms

rewrite38.0ms

series100.0ms

simplify112.0ms

prune86.0ms

localize10.0ms

rewrite52.0ms

series89.0ms

simplify85.0ms

prune127.0ms

localize11.0ms

rewrite32.0ms

series82.0ms

simplify99.0ms

prune112.0ms

regimes51.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample488.0ms

Profiling