Details

analyze39.0ms

Algorithm

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

sample20.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true
0.0ms	2×	pre	80	false

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5165	11

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 13.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
30.5b	(/.f64 (.f64 b b) (.f64 a a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64`
3×	`times-frac_binary64` `sqrt-prod_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `flip--_binary64`

Counts

3 → 50

Calls

3 calls:

6.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
7.0ms	(/.f64 (.f64 b b) (.f64 a a))

series32.0ms

Counts

3 → 9

Calls

3 calls:

11.0ms	(-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))
13.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (/.f64 (.f64 b b) (.f64 a a)))))
7.0ms	(/.f64 (.f64 b b) (.f64 a a))

simplify35.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5101	563

prune46.0ms

Filtered

35 candidates to 59 candidates (-68.6%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	58	2	60

Merged error: 0.0b

Counts

60 → 2

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))))
0.0b	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
11×	`*-un-lft-identity_binary64`
8×	`associate-r_binary64`
5×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64` `difference-of-squares_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`add-log-exp_binary64` `sub-neg_binary64` `associate-r/_binary64` `times-frac_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

2 → 47

Calls

2 calls:

1.0ms	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))))
18.0ms	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))

series16.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(sqrt.f64 (fabs.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))))
8.0ms	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4991	762
1	4991	762

prune52.0ms

Filtered

37 candidates to 53 candidates (-43.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	51	2	53
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	51	4	55

Merged error: 0b

Counts

55 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))))
0.0b	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))
0.0b	(pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3)
0.0b	(cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
16×	`cube-div_binary64`
15×	`*-un-lft-identity_binary64`
12×	`frac-times_binary64`
10×	`pow1_binary64`
9×	`flip3-+_binary64` `flip3--_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `flip-+_binary64`
8×	`cbrt-div_binary64` `associate-r_binary64` `cbrt-prod_binary64`
6×	`associate-r/_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64` `difference-of-squares_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `sqr-pow_binary64` `rem-cube-cbrt_binary64` `unpow-prod-down_binary64` `prod-exp_binary64` `cube-prod_binary64` `times-frac_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `unswap-sqr_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

1.0ms	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))))
18.0ms	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))
19.0ms	(pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3)
4.0ms	(cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))

series43.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))))
9.0ms	(*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a)))
18.0ms	(pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3)
9.0ms	(cbrt.f64 (pow.f64 (*.f64 (+.f64 (/.f64 b a) 1) (-.f64 1 (/.f64 b a))) 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4960	1804
1	4960	1804

prune111.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	115	3	118

Merged error: 0b

Counts

118 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))))
0.0b	(pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3)
0.0b	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
43×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
17×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
16×	`cbrt-prod_binary64`
13×	`pow1_binary64` `swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
10×	`unpow-prod-down_binary64` `cube-prod_binary64`
8×	`difference-of-squares_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `cube-div_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`pow-unpow_binary64` `sqrt-prod_binary64`
2×	`cbrt-div_binary64` `flip3--_binary64` `sqr-pow_binary64` `flip--_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow1/2_binary64` `rem-cbrt-cube_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow1/3_binary64` `pow-pow_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rem-cube-cbrt_binary64` `pow-sqr_binary64` `frac-times_binary64` `pow-exp_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 136

Calls

4 calls:

1.0ms	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))))
5.0ms	(pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3)
5.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))
11.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

series48.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(sqrt.f64 (fabs.f64 (cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))))
18.0ms	(pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3)
8.0ms	(cbrt.f64 (pow.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a))) 3))
7.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify33.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5063	1495

prune106.0ms

Filtered

90 candidates to 148 candidates (-64.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	148	3	151

Merged error: 0b

Counts

151 → 3

regimes69.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	14
1	36	14

end0.0ms

sample566.0ms

Algorithm

intervals

Results

269.0ms	8000×	body	80	valid
148.0ms	8000×	pre	80	true
2.0ms	130×	pre	80	false

Details

analyze39.0ms

sample20.0ms

simplify64.0ms

prune6.0ms

localize7.0ms

rewrite15.0ms

series32.0ms

simplify35.0ms

prune46.0ms

localize7.0ms

rewrite20.0ms

series16.0ms

simplify55.0ms

prune52.0ms

localize9.0ms

rewrite46.0ms

series43.0ms

simplify64.0ms

prune111.0ms

localize9.0ms

rewrite29.0ms

series48.0ms

simplify33.0ms

prune106.0ms

regimes69.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample566.0ms

Profiling