Details

analyze46.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	50%	50%	2
0%	50%	50%	3
25%	25%	50%	4
25%	25%	50%	5
31.2%	18.7%	50%	6
34.3%	15.6%	50%	7
39%	10.9%	50%	8
40.6%	8.6%	50.8%	9
42.9%	5.9%	51.2%	10
43.7%	4.5%	51.8%	11
44.9%	3%	52.1%	12
45.3%	2.3%	52.4%	13
45.9%	1.5%	52.6%	14

sample18.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
0.0ms	3×	body	80	invalid

simplify23.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	496	12
1	496	12

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: 0.2b

Counts

2 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
0.2b	(/.f64 y (*.f64 3 (sqrt.f64 x)))
0.2b	(*.f64 3 (sqrt.f64 x))
0.4b	(/.f64 1 (*.f64 x 9))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
18×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`add-cbrt-cube_binary64`
11×	`add-cube-cbrt_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
6×	`associate-r_binary64` `associate-/l*_binary64` `times-frac_binary64` `div-exp_binary64`
5×	`prod-exp_binary64` `distribute-lft-out--_binary64`
4×	`cbrt-undiv_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `associate-/r*_binary64` `sub-neg_binary64` `flip3--_binary64` `1-exp_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`associate--l-_binary64` `inv-pow_binary64` `difference-of-squares_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

16.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
6.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series26.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (/.f64 y (.f64 3 (sqrt.f64 x))))
10.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

simplify44.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5013	912

prune85.0ms

Filtered

70 candidates to 103 candidates (-47.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	96	7	103
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	97	8	105

Merged error: 0.0b

Counts

105 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

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

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

150×	`times-frac_binary64`
98×	`add-sqr-sqrt_binary64`
89×	`*-un-lft-identity_binary64`
82×	`add-cube-cbrt_binary64`
44×	`sqrt-prod_binary64`
19×	`add-exp-log_binary64`
16×	`associate-/l*_binary64`
13×	`add-cbrt-cube_binary64`
10×	`div-inv_binary64`
8×	`add-log-exp_binary64`
7×	`associate-/r*_binary64` `div-exp_binary64`
6×	`pow1_binary64`
5×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
3×	`diff-log_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `1-exp_binary64` `clear-num_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `inv-pow_binary64` `associate--l+_binary64`

Counts

3 → 164

Calls

3 calls:

41.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
8.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
5.0ms	(/.f64 1 (*.f64 x 9))

series22.0ms

Counts

3 → 9

Calls

3 calls:

10.0ms	(-.f64 (-.f64 1 (/.f64 1 (*.f64 x 9))) (/.f64 (/.f64 y 3) (sqrt.f64 x)))
10.0ms	(/.f64 (/.f64 y 3) (sqrt.f64 x))
2.0ms	(/.f64 1 (*.f64 x 9))

simplify72.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4929	2196
1	4929	2196

prune114.0ms

Filtered

112 candidates to 173 candidates (-54.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	170	3	173
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	173	8	181

Merged error: 0.0b

Counts

181 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

78×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
56×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64`
20×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64` `associate-/l*_binary64`
9×	`add-log-exp_binary64`
8×	`div-exp_binary64`
6×	`pow1_binary64` `associate-r_binary64` `div-inv_binary64`
5×	`cbrt-undiv_binary64`
4×	`associate-/r*_binary64` `sqrt-prod_binary64`
3×	`diff-log_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
2×	`sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `flip--_binary64` `frac-sub_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate--l-_binary64` `1-exp_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

27.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
5.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
7.0ms	(/.f64 (/.f64 1 x) 9)

series27.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 (/.f64 (/.f64 1 x) 9)) (/.f64 y (*.f64 3 (sqrt.f64 x))))
10.0ms	(/.f64 y (*.f64 3 (sqrt.f64 x)))
5.0ms	(*.f64 3 (sqrt.f64 x))
2.0ms	(/.f64 (/.f64 1 x) 9)

simplify61.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4913	1418
1	4913	1418

prune114.0ms

Filtered

102 candidates to 146 candidates (-43.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	141	5	146
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	144	10	154

Merged error: 0b

Counts

154 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
61×	`times-frac_binary64`
45×	`*-un-lft-identity_binary64`
41×	`add-cube-cbrt_binary64` `add-exp-log_binary64`
25×	`sqrt-prod_binary64`
23×	`add-cbrt-cube_binary64`
22×	`associate-r_binary64`
14×	`div-exp_binary64`
13×	`associate-l_binary64`
11×	`pow1_binary64` `prod-exp_binary64`
10×	`unswap-sqr_binary64`
9×	`add-log-exp_binary64`
8×	`frac-sub_binary64`
7×	`associate-/r*_binary64` `cbrt-undiv_binary64`
6×	`associate-/l*_binary64`
5×	`flip3--_binary64` `cbrt-unprod_binary64` `1-exp_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64`
4×	`div-inv_binary64`
3×	`diff-log_binary64` `associate-r/_binary64` `un-div-inv_binary64` `frac-times_binary64` `associate-l/_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `sqrt-pow1_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 165

Calls

4 calls:

12.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 x))
15.0ms	(*.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x)))
5.0ms	(/.f64 1 (*.f64 x 9))

series34.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (-.f64 1 (/.f64 1 (.f64 x 9))) (.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x))))
8.0ms	(/.f64 1 (sqrt.f64 x))
13.0ms	(*.f64 (/.f64 y 3) (/.f64 1 (sqrt.f64 x)))
2.0ms	(/.f64 1 (*.f64 x 9))

simplify54.0ms

Algorithm

egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5049	1682

prune95.0ms

Filtered

106 candidates to 177 candidates (-67.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	177	10	187

Merged error: 0b

Counts

187 → 10

regimes82.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	16
1	84	16

end0.0ms

sample481.0ms

Algorithm

intervals

Results

343.0ms	8000×	body	80	valid
4.0ms	94×	body	80	invalid

Details

analyze46.0ms

sample18.0ms

simplify23.0ms

prune6.0ms

localize9.0ms

rewrite35.0ms

series26.0ms

simplify44.0ms

prune85.0ms

localize9.0ms

rewrite63.0ms

series22.0ms

simplify72.0ms

prune114.0ms

localize10.0ms

rewrite50.0ms

series27.0ms

simplify61.0ms

prune114.0ms

localize10.0ms

rewrite43.0ms

series34.0ms

simplify54.0ms

prune95.0ms

regimes82.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample481.0ms

Profiling