Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
81.2%	18.7%	0%	5
90.6%	9.4%	0%	6
95.3%	4.7%	0%	7
97.6%	2.3%	0%	8
98.8%	1.2%	0%	9
99.4%	0.6%	0%	10
99.7%	0.3%	0%	11
99.8%	0.1%	0%	12
99.9%	0.1%	0%	13
99.9%	0%	0%	14

sample17.0ms

Algorithm

intervals

Results

6.0ms	64×	body	640	valid
3.0ms	127×	body	80	valid
2.0ms	38×	body	320	valid
1.0ms	27×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	72	9
1	72	9

prune3.0ms

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: 15.3b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (+.f64 x 1))
3.3b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
39×	`add-sqr-sqrt_binary64`
36×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out--_binary64`
9×	`difference-of-squares_binary64`
7×	`distribute-lft-out_binary64`
6×	`add-exp-log_binary64`
5×	`div-inv_binary64`
4×	`associate-/r*_binary64` `add-log-exp_binary64` `add-cbrt-cube_binary64`
3×	`pow1_binary64` `associate-/l*_binary64`
2×	`associate-/r/_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `flip-+_binary64` `frac-sub_binary64`

Counts

2 → 68

Calls

2 calls:

10.0ms	(/.f64 1 (+.f64 x 1))
19.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

series5.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(/.f64 1 (+.f64 x 1))
3.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 1 x))

simplify87.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4839	787
1	4839	787

prune37.0ms

Filtered

45 candidates to 74 candidates (-64.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	2	75

Merged error: 0.2b

Counts

75 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.1b	(/.f64 -1 (pow.f64 x 4))
0.3b	(/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x))
10.8b	(+.f64 (/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

33×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
29×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
12×	`unpow-prod-down_binary64`
11×	`associate-/l*_binary64`
10×	`add-cbrt-cube_binary64`
8×	`associate-/r*_binary64`
6×	`difference-of-sqr--1_binary64`
5×	`add-log-exp_binary64` `distribute-lft-out_binary64` `div-exp_binary64`
4×	`sqr-pow_binary64` `div-inv_binary64`
3×	`pow1_binary64` `cbrt-undiv_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `cbrt-unprod_binary64` `frac-add_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

3 → 91

Calls

3 calls:

5.0ms	(/.f64 -1 (pow.f64 x 4))
12.0ms	(/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x))
27.0ms	(+.f64 (/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))

series14.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(/.f64 -1 (pow.f64 x 4))
6.0ms	(/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x))
4.0ms	(+.f64 (/.f64 (+.f64 (/.f64 1 x) -1) (*.f64 x x)) (/.f64 -1 (pow.f64 x 4)))

simplify51.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5603	1110

prune61.0ms

Filtered

65 candidates to 100 candidates (-53.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	98	4	102

Merged error: 0.0b

Counts

102 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 (/.f64 1 x) -1) x)
0.1b	(/.f64 -1 (pow.f64 x 4))
0.2b	(/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x)
10.8b	(+.f64 (/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x) (/.f64 -1 (pow.f64 x 4)))

rewrite145.0ms

Algorithm

rewrite-expression-head

Rules

259×	`times-frac_binary64`
180×	`*-un-lft-identity_binary64`
174×	`add-sqr-sqrt_binary64`
110×	`add-cube-cbrt_binary64`
48×	`difference-of-sqr--1_binary64`
39×	`associate-/l*_binary64`
34×	`distribute-lft-out_binary64`
23×	`div-inv_binary64`
16×	`add-exp-log_binary64`
13×	`associate-/r*_binary64` `add-cbrt-cube_binary64`
12×	`unpow-prod-down_binary64`
7×	`div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`cbrt-undiv_binary64`
4×	`pow1_binary64` `sqr-pow_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `frac-add_binary64` `+-commutative_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 238

Calls

4 calls:

11.0ms	(/.f64 (+.f64 (/.f64 1 x) -1) x)
5.0ms	(/.f64 -1 (pow.f64 x 4))
16.0ms	(/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x)
101.0ms	(+.f64 (/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x) (/.f64 -1 (pow.f64 x 4)))

series21.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(/.f64 (+.f64 (/.f64 1 x) -1) x)
7.0ms	(/.f64 -1 (pow.f64 x 4))
6.0ms	(/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x)
4.0ms	(+.f64 (/.f64 (/.f64 (+.f64 (/.f64 1 x) -1) x) x) (/.f64 -1 (pow.f64 x 4)))

simplify82.0ms

Algorithm

egg-herbie

Counts

250 → 250

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4925	3444
1	4925	3444

prune160.0ms

Filtered

146 candidates to 250 candidates (-71.2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	247	3	250
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	247	7	254

Merged error: 0.0b

Counts

254 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow.f64 (cbrt.f64 x) 2)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
10.8b	(+.f64 (.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (cbrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (pow.f64 (cbrt.f64 x) 2))) (/.f64 -1 (pow.f64 x 4)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
7×	`frac-add_binary64`
6×	`add-log-exp_binary64` `unpow-prod-down_binary64`
5×	`pow1_binary64` `add-exp-log_binary64` `frac-times_binary64` `associate-*l/_binary64`
4×	`add-cbrt-cube_binary64`
3×	`pow-unpow_binary64` `associate-*r/_binary64` `pow1/3_binary64`
2×	`pow-pow_binary64`
1×	`pow-to-exp_binary64` `flip3-+_binary64` `unpow2_binary64` `sqr-pow_binary64` `+-commutative_binary64` `flip-+_binary64` `pow-exp_binary64` `sum-log_binary64`

Counts

4 → 62

Calls

4 calls:

3.0ms	(pow.f64 (cbrt.f64 x) 2)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)
53.0ms	(+.f64 (.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (cbrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (pow.f64 (cbrt.f64 x) 2))) (/.f64 -1 (pow.f64 x 4)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(pow.f64 (cbrt.f64 x) 2)
14.0ms	(cbrt.f64 x)
17.0ms	(cbrt.f64 x)
5.0ms	(+.f64 (.f64 (.f64 (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (cbrt.f64 x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) x)) (/.f64 (cbrt.f64 (+.f64 (/.f64 1 x) -1)) (pow.f64 (cbrt.f64 x) 2))) (/.f64 -1 (pow.f64 x 4)))

simplify25.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5447	658

prune70.0ms

Filtered

58 candidates to 74 candidates (-27.6%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	74	7	81

Merged error: 0.0b

Counts

81 → 7

regimes73.0ms

Accuracy

95.3% (0.6b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 13.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	49
1	36	49

end0.0ms

sample471.0ms

Algorithm

intervals

Results

172.0ms	1914×	body	640	valid
105.0ms	4231×	body	80	valid
80.0ms	1213×	body	320	valid
28.0ms	642×	body	160	valid

Details

analyze4.0ms

sample17.0ms

simplify7.0ms

prune3.0ms

localize5.0ms

rewrite32.0ms

series5.0ms

simplify87.0ms

prune37.0ms

localize9.0ms

rewrite48.0ms

series14.0ms

simplify51.0ms

prune61.0ms

localize9.0ms

rewrite145.0ms

series21.0ms

simplify82.0ms

prune160.0ms

localize17.0ms

rewrite60.0ms

series60.0ms

simplify25.0ms

prune70.0ms

regimes73.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample471.0ms

Profiling