Details

analyze7.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample26.0ms

Algorithm

intervals

Results

8.0ms	56×	body	640	valid
5.0ms	136×	body	80	valid
5.0ms	26×	body	1280	valid
3.0ms	25×	body	320	valid
1.0ms	13×	body	160	valid

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	193	22
1	193	22

prune2.0ms

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: 8.9b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
1.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64`
58×	`add-sqr-sqrt_binary64`
56×	`times-frac_binary64`
25×	`add-cube-cbrt_binary64`
18×	`distribute-lft-out--_binary64`
17×	`distribute-lft-out_binary64`
14×	`difference-of-squares_binary64`
12×	`add-exp-log_binary64`
11×	`associate-/r*_binary64` `add-log-exp_binary64`
8×	`add-cbrt-cube_binary64` `div-inv_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`difference-of-sqr-1_binary64` `associate-/r/_binary64` `div-exp_binary64`
3×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64` `sum-log_binary64`
1×	`associate-+l+_binary64` `associate-+l-_binary64` `+-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

20.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
6.0ms	(/.f64 1 (+.f64 x 1))
6.0ms	(/.f64 1 (-.f64 x 1))
36.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
9.0ms	(/.f64 1 (+.f64 x 1))
9.0ms	(/.f64 1 (-.f64 x 1))
54.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify104.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5069	2576

prune131.0ms

Filtered

88 candidates to 147 candidates (-67.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	145	3	148

Merged error: 0.1b

Counts

148 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
42×	`associate-*r/_binary64`
35×	`*-un-lft-identity_binary64`
32×	`flip3--_binary64` `frac-add_binary64` `flip--_binary64`
27×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64` `frac-times_binary64`
18×	`flip3-+_binary64` `associate-/l/_binary64` `difference-of-squares_binary64` `flip-+_binary64`
10×	`associate-*l/_binary64`
9×	`associate-/r*_binary64`
8×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-l_binary64`
6×	`pow1_binary64`
5×	`sub-neg_binary64` `distribute-lft-out--_binary64`
4×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `unpow3_binary64`
3×	`associate-r_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-/l*_binary64`
2×	`associate-+l+_binary64` `associate-/r/_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 145

Calls

4 calls:

11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
19.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
3.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
11.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
28.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
15.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
4.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

simplify154.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4943	6609
1	4943	6609

prune289.0ms

Filtered

126 candidates to 157 candidates (-24.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	155	2	157
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	158	2	160

Merged error: 0.1b

Counts

160 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (pow.f64 x 3) x)
0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt_binary64`
31×	`*-un-lft-identity_binary64`
27×	`times-frac_binary64`
20×	`difference-of-squares_binary64`
16×	`add-cube-cbrt_binary64`
9×	`associate-/r*_binary64`
5×	`distribute-rgt-out--_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `distribute-lft-out--_binary64` `unpow3_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/l*_binary64`
2×	`pow1_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

2 → 70

Calls

2 calls:

9.0ms	(-.f64 (pow.f64 x 3) x)
9.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

series71.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(-.f64 (pow.f64 x 3) x)
25.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

simplify79.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4925	1312
1	4925	1312

prune61.0ms

Filtered

56 candidates to 76 candidates (-35.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	74	4	78

Merged error: 0.0b

Counts

78 → 4

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (*.f64 x x) 1)
0.1b	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
0.8b	(/.f64 2 (-.f64 (*.f64 x x) 1))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
52×	`times-frac_binary64`
41×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64`
24×	`associate-r_binary64`
17×	`add-cbrt-cube_binary64`
16×	`difference-of-squares_binary64`
13×	`associate-l_binary64`
9×	`div-exp_binary64`
8×	`difference-of-sqr-1_binary64` `prod-exp_binary64`
6×	`associate-/r*_binary64` `unswap-sqr_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `cbrt-undiv_binary64`
4×	`cbrt-unprod_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
2×	`1-exp_binary64` `rec-exp_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 122

Calls

3 calls:

4.0ms	(-.f64 (*.f64 x x) 1)
18.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
7.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

series72.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(-.f64 (*.f64 x x) 1)
27.0ms	(.f64 (/.f64 1 x) (/.f64 2 (-.f64 (.f64 x x) 1)))
21.0ms	(/.f64 2 (-.f64 (*.f64 x x) 1))

simplify101.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5020	2028

prune86.0ms

Filtered

89 candidates to 131 candidates (-47.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	130	1	131
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	131	4	135

Merged error: 0b

Counts

135 → 4

regimes10.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample764.0ms

Algorithm

intervals

Results

276.0ms	1944×	body	640	valid
155.0ms	4132×	body	80	valid
105.0ms	590×	body	1280	valid
97.0ms	893×	body	320	valid
33.0ms	441×	body	160	valid
0.0ms	2×	body	80	invalid

Details

analyze7.0ms

sample26.0ms

simplify19.0ms

prune2.0ms

localize14.0ms

rewrite73.0ms

series86.0ms

simplify104.0ms

prune131.0ms

localize13.0ms

rewrite52.0ms

series58.0ms

simplify154.0ms

prune289.0ms

localize5.0ms

rewrite20.0ms

series71.0ms

simplify79.0ms

prune61.0ms

localize9.0ms

rewrite34.0ms

series72.0ms

simplify101.0ms

prune86.0ms

regimes10.0ms

bsearch0.0ms

simplify4.0ms

end0.0ms

sample764.0ms

Profiling