Details

analyze543.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

sample23.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
1.0ms	15×	body	80	invalid

simplify204.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (201.0ms)

Iter	Nodes	Cost
0	4821	15
1	4821	15

prune4.0ms

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: 28.0b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.8b	(-.f64 (.f64 b c) (.f64 a d))
27.4b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64`
7×	`add-log-exp_binary64`
5×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-/r_binary64` `pow1_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 54

Calls

3 calls:

4.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(-.f64 (.f64 b c) (.f64 a d))
9.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

series55.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(+.f64 (.f64 c c) (.f64 d d))
12.0ms	(-.f64 (.f64 b c) (.f64 a d))
36.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (+.f64 (.f64 c c) (.f64 d d)))

simplify51.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5785	976

prune102.0ms

Filtered

49 candidates to 63 candidates (-28.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 27.1b

Counts

64 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b c) (.f64 a d))
18.9b	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
30.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
21×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64` `sqrt-prod_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3-+_binary64` `associate-/l*_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 85

Calls

4 calls:

4.0ms	(-.f64 (.f64 b c) (.f64 a d))
10.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 (.f64 b c) (.f64 a d))
45.0ms	(/.f64 (-.f64 (.f64 b c) (.f64 a d)) (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d))))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify55.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5760	1553

prune111.0ms

Filtered

77 candidates to 97 candidates (-26.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	4	97
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	96	10	106

Merged error: 23.9b

Counts

106 → 10

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 c c) (.f64 d d))
0.0b	(+.f64 (.f64 c c) (.f64 d d))
16.0b	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
18.5b	(/.f64 (.f64 a d) (+.f64 (.f64 c c) (*.f64 d d)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
6×	`associate-/r*_binary64` `times-frac_binary64`
4×	`flip3-+_binary64` `pow1_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 68

Calls

4 calls:

6.0ms	(+.f64 (.f64 c c) (.f64 d d))
4.0ms	(+.f64 (.f64 c c) (.f64 d d))
7.0ms	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
7.0ms	(/.f64 (.f64 a d) (+.f64 (.f64 c c) (*.f64 d d)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(+.f64 (.f64 c c) (.f64 d d))
7.0ms	(+.f64 (.f64 c c) (.f64 d d))
18.0ms	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
19.0ms	(/.f64 (.f64 a d) (+.f64 (.f64 c c) (*.f64 d d)))

simplify51.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4962	880
1	4962	880

prune100.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	1	7	8
Picked	1	0	1
Done	1	0	1
Total	80	10	90

Merged error: 22.0b

Counts

90 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

2.0b	(.f64 (/.f64 a (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 d (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
16.0b	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
30.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
30.1b	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

66×	`add-sqr-sqrt_binary64`
51×	`times-frac_binary64`
34×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
30×	`sqrt-prod_binary64`
24×	`associate-r_binary64` `associate-l_binary64`
21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`unswap-sqr_binary64`
8×	`pow1_binary64` `sqrt-div_binary64`
6×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
5×	`flip3-+_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/r*_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`pow-prod-down_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 130

Calls

4 calls:

26.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 d (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
7.0ms	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
4.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

series53.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(.f64 (/.f64 a (sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))) (/.f64 d (sqrt.f64 (+.f64 (.f64 c c) (*.f64 d d)))))
18.0ms	(/.f64 (.f64 b c) (+.f64 (.f64 c c) (*.f64 d d)))
7.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))
8.0ms	(sqrt.f64 (+.f64 (.f64 c c) (.f64 d d)))

simplify69.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4967	2105
1	4967	2105

prune105.0ms

Filtered

103 candidates to 142 candidates (-37.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	141	1	142
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	144	8	152

Merged error: 21.8b

Counts

152 → 8

regimes407.0ms

Accuracy

44.8% (0.7b remaining)

Error of 23.1b against oracle of 22.5b and baseline of 23.7b

bsearch38.0ms

Steps

Iters	Range		Point
9	3.578591583768455e-199	1.9224846528789776e-190	7.741980536026424e-194
7	-0.0025133320054770117	-1.8132444495535047e-05	-2.024796178527634e-05

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	93	75
1	93	75

end0.0ms

sample614.0ms

Algorithm

intervals

Results

361.0ms	8000×	body	80	valid
25.0ms	515×	body	80	invalid

Details

analyze543.0ms

sample23.0ms

simplify204.0ms

prune4.0ms

localize10.0ms

rewrite19.0ms

series55.0ms

simplify51.0ms

prune102.0ms

localize12.0ms

rewrite25.0ms

series73.0ms

simplify55.0ms

prune111.0ms

localize11.0ms

rewrite27.0ms

series50.0ms

simplify51.0ms

prune100.0ms

localize13.0ms

rewrite47.0ms

series53.0ms

simplify69.0ms

prune105.0ms

regimes407.0ms

bsearch38.0ms

simplify3.0ms

end0.0ms

sample614.0ms

Profiling