Details

analyze1.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
100%	0%	0%	1

sample36.0ms

Algorithm

intervals

Results

19.0ms	89×	body	1280	valid
5.0ms	129×	body	80	valid
3.0ms	18×	body	640	valid
1.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	44	10
1	44	10

prune5.0ms

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: 17.0b

Counts

2 → 1

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
0.0b	(/.f64 1/2 (hypot.f64 1 x))
0.0b	(hypot.f64 1 x)
2.8b	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
2×	`distribute-lft-out_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 68

Calls

4 calls:

7.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
3.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)
9.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x))))
5.0ms	(/.f64 1/2 (hypot.f64 1 x))
1.0ms	(hypot.f64 1 x)
17.0ms	(-.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4987	797
1	4987	797

prune76.0ms

Filtered

53 candidates to 80 candidates (-50.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	77	4	81

Merged error: 16.5b

Counts

81 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot.f64 1 x)
0.0b	(hypot.f64 1 x)
0.0b	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
2.4b	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
8×	`add-log-exp_binary64`
4×	`pow1_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`difference-of-squares_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `times-frac_binary64` `+-commutative_binary64` `flip--_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 42

Calls

4 calls:

1.0ms	(hypot.f64 1 x)
1.0ms	(hypot.f64 1 x)
8.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
7.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

series23.0ms

Counts

4 → 12

Calls

4 calls:

1.0ms	(hypot.f64 1 x)
1.0ms	(hypot.f64 1 x)
13.0ms	(+.f64 1 (sqrt.f64 (+.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))))
9.0ms	(-.f64 1/2 (/.f64 1/2 (hypot.f64 1 x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5040	477

prune59.0ms

Filtered

37 candidates to 54 candidates (-45.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	53	1	54
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	54	4	58

Merged error: 16.5b

Counts

58 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.1b	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
0.5b	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
2.3b	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
46×	`sqrt-prod_binary64`
32×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
12×	`difference-of-squares_binary64`
11×	`associate-r_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-l_binary64`
4×	`flip3--_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `frac-times_binary64`
3×	`flip3-+_binary64` `sub-neg_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `div-inv_binary64` `sqrt-div_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
22.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
10.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

series77.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
12.0ms	(sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))
38.0ms	(*.f64 (+.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))) (-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x)))))
15.0ms	(-.f64 (sqrt.f64 1/2) (sqrt.f64 (/.f64 1/2 (hypot.f64 1 x))))

simplify60.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5450	1627

prune205.0ms

Filtered

84 candidates to 119 candidates (-41.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	0	1	1
Picked	1	0	1
Done	1	1	2
Total	119	4	123

Merged error: 16.5b

Counts

123 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2)) (+.f64 1 (sqrt.f64 (/.f64 1 (hypot.f64 1 x)))))
0.1b	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
0.1b	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
2.4b	(+.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

32×	`add-sqr-sqrt_binary64`
28×	`sqrt-prod_binary64`
25×	`*-un-lft-identity_binary64`
22×	`times-frac_binary64`
20×	`add-cube-cbrt_binary64`
10×	`pow1_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
4×	`frac-times_binary64`
3×	`distribute-lft-out_binary64` `associate-l_binary64` `div-inv_binary64`
2×	`pow1/2_binary64` `associate-r/_binary64` `inv-pow_binary64` `pow-flip_binary64` `sqrt-div_binary64` `associate-l/_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

12.0ms	(.f64 (+.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2)) (+.f64 1 (sqrt.f64 (/.f64 1 (hypot.f64 1 x)))))
3.0ms	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
3.0ms	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
3.0ms	(+.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2))

series52.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(.f64 (+.f64 1/2 (.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2)) (+.f64 1 (sqrt.f64 (/.f64 1 (hypot.f64 1 x)))))
8.0ms	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
8.0ms	(sqrt.f64 (/.f64 1 (hypot.f64 1 x)))
12.0ms	(+.f64 1/2 (*.f64 (sqrt.f64 (/.f64 1 (hypot.f64 1 x))) -1/2))

simplify60.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5026	1251

prune151.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	111	3	114

Merged error: 16.5b

Counts

114 → 3

regimes57.0ms

Accuracy

0% (0.0b remaining)

Error of 14.9b against oracle of 14.9b and baseline of 14.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	29	18
1	29	18

end0.0ms

sample1.1s

Algorithm

intervals

Results

643.0ms	2899×	body	1280	valid
160.0ms	4050×	body	80	valid
106.0ms	595×	body	640	valid
37.0ms	305×	body	320	valid
12.0ms	151×	body	160	valid

Details

analyze1.0ms

sample36.0ms

simplify6.0ms

prune5.0ms

localize6.0ms

rewrite21.0ms

series35.0ms

simplify60.0ms

prune76.0ms

localize11.0ms

rewrite17.0ms

series23.0ms

simplify51.0ms

prune59.0ms

localize16.0ms

rewrite41.0ms

series77.0ms

simplify60.0ms

prune205.0ms

localize15.0ms

rewrite27.0ms

series52.0ms

simplify60.0ms

prune151.0ms

regimes57.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling