Details

analyze83.0ms

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%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
25%	21.9%	53.2%	8
25%	14%	61%	9
28.1%	10.9%	61%	10
31.6%	7.4%	61%	11
33.4%	5.7%	61%	12
35.2%	3.8%	61%	13
36.1%	2.9%	61%	14

sample18.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify84.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	4828	17
1	4828	17

prune6.0ms

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: 0.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 a a) (.f64 b b))
0.0b	(.f64 4.0 (.f64 b b))
0.0b	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (.f64 b b)))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1_binary64` `add-exp-log_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
3×	`pow-prod-down_binary64` `pow-unpow_binary64` `cbrt-unprod_binary64` `associate-l_binary64` `unpow-prod-down_binary64` `prod-exp_binary64`
2×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `associate-r_binary64` `pow-pow_binary64` `sqr-pow_binary64` `unswap-sqr_binary64` `pow-exp_binary64` `*-commutative_binary64`

Counts

4 → 58

Calls

4 calls:

5.0ms	(+.f64 (.f64 a a) (.f64 b b))
6.0ms	(.f64 4.0 (.f64 b b))
8.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (.f64 b b)))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)

series59.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 (.f64 a a) (.f64 b b))
4.0ms	(.f64 4.0 (.f64 b b))
18.0ms	(+.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 4.0 (.f64 b b)))
32.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)

simplify39.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5424	778

prune84.0ms

Filtered

51 candidates to 70 candidates (-37.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	3	71

Merged error: 0b

Counts

71 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))))
0.0b	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
0.0b	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b))))
1.5b	(.f64 (.f64 a a) (*.f64 b b))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
27×	`pow-prod-down_binary64`
21×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
4×	`pow-prod-up_binary64` `associate-l_binary64` `pow-plus_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-r_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `unswap-sqr_binary64` `associate-+r+_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))))
13.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
6.0ms	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b))))
9.0ms	(.f64 (.f64 a a) (*.f64 b b))

series45.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+.f64 (pow.f64 a 4) (+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b)))))
10.0ms	(.f64 2 (.f64 (.f64 a a) (.f64 b b)))
14.0ms	(+.f64 (pow.f64 b 4) (.f64 2 (.f64 (.f64 a a) (.f64 b b))))
7.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify43.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5453	1020

prune72.0ms

Filtered

51 candidates to 93 candidates (-82.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	93	3	96

Merged error: 0b

Counts

96 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b))))
0.0b	(.f64 4.0 (.f64 b b))
0.0b	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b)))) (.f64 4.0 (.f64 b b)))
1.5b	(.f64 (.f64 a a) (*.f64 b b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

37×	`pow1_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`pow-prod-down_binary64`
11×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`pow-prod-up_binary64` `associate-l_binary64` `pow-plus_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-r_binary64` `unswap-sqr_binary64` `pow-sqr_binary64` `+-commutative_binary64` `flip-+_binary64` `pow2_binary64` `*-commutative_binary64`
1×	`associate-+l+_binary64`

Counts

4 → 72

Calls

4 calls:

6.0ms	(+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b))))
6.0ms	(.f64 4.0 (.f64 b b))
10.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b)))) (.f64 4.0 (.f64 b b)))
9.0ms	(.f64 (.f64 a a) (*.f64 b b))

series37.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b))))
4.0ms	(.f64 4.0 (.f64 b b))
14.0ms	(+.f64 (+.f64 (pow.f64 b 4) (.f64 2.0 (.f64 (.f64 a a) (.f64 b b)))) (.f64 4.0 (.f64 b b)))
7.0ms	(.f64 (.f64 a a) (*.f64 b b))

simplify56.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4948	859
1	4948	859

prune72.0ms

Filtered

52 candidates to 84 candidates (-61.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	84	3	87

Merged error: 0b

Counts

87 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 4.0 (pow.f64 b 4))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (*.f64 2.0 2))
0.3b	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
36.8b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (.f64 2.0 2)) (.f64 4.0 (.f64 4.0 (pow.f64 b 4)))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 (*.f64 b b) 4.0)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
10×	`unpow-prod-down_binary64`
9×	`times-frac_binary64`
8×	`add-cbrt-cube_binary64`
7×	`associate-r_binary64`
6×	`pow1_binary64`
4×	`pow-unpow_binary64` `add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `associate-/r_binary64` `associate-l_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `associate-/l_binary64` `pow-exp_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `pow-pow_binary64` `associate-/r/_binary64` `flip--_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `*-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

6.0ms	(*.f64 4.0 (pow.f64 b 4))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (*.f64 2.0 2))
5.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
16.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (.f64 2.0 2)) (.f64 4.0 (.f64 4.0 (pow.f64 b 4)))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 (*.f64 b b) 4.0)))

series124.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(*.f64 4.0 (pow.f64 b 4))
29.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (*.f64 2.0 2))
27.0ms	(pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0)
63.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) (.f64 2.0 2)) (.f64 4.0 (.f64 4.0 (pow.f64 b 4)))) (-.f64 (pow.f64 (+.f64 (.f64 a a) (.f64 b b)) 2.0) (.f64 (*.f64 b b) 4.0)))

simplify50.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5870	2219

prune131.0ms

Filtered

74 candidates to 101 candidates (-36.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	101	3	104

Merged error: 0b

Counts

104 → 3

regimes139.0ms

Accuracy

0% (0.9b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 0.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	28	19
1	28	19

end0.0ms

sample494.0ms

Algorithm

intervals

Results

360.0ms	8000×	body	80	valid
0.0ms	6×	body	80	invalid

Details

analyze83.0ms

sample18.0ms

simplify84.0ms

prune6.0ms

localize10.0ms

rewrite25.0ms

series59.0ms

simplify39.0ms

prune84.0ms

localize12.0ms

rewrite41.0ms

series45.0ms

simplify43.0ms

prune72.0ms

localize13.0ms

rewrite33.0ms

series37.0ms

simplify56.0ms

prune72.0ms

localize18.0ms

rewrite35.0ms

series124.0ms

simplify50.0ms

prune131.0ms

regimes139.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample494.0ms

Profiling