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
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

sample11.0ms

Algorithm

intervals

Results

5.0ms

256×

body

valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 27.9b

Counts

2 → 2

localize4.0ms

Local error

Found 1 expressions with local error:

27.1b

(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

series5.0ms

Counts

1 → 3

Calls

1 calls:

5.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4818	91
1	4818	91

prune34.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	12	6	18

Merged error: 0.1b

Counts

18 → 6

localize4.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 x x))
27.1b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

6×	`sqrt-prod_binary64`
4×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
3×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
2×	`flip3-+_binary64` `count-2_binary64` `distribute-lft-out_binary64` `distribute-rgt-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

2 → 32

Calls

2 calls:

4.0ms	(+.f64 (.f64 x x) (.f64 x x))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

series11.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 x x))
6.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 x x)))

simplify82.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4793	222
1	4793	222

prune32.0ms

Filtered

24 candidates to 38 candidates (-58.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	37	1	38
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	38	6	44

Merged error: 0.1b

Counts

44 → 6

localize6.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
27.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
27.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64`
71×	`pow1_binary64`
33×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-prod-down_binary64`
22×	`pow1/2_binary64`
20×	`associate-*r/_binary64`
14×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow-sqr_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
18.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series26.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
5.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
7.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4895	929
1	4895	929

prune75.0ms

Filtered

72 candidates to 136 candidates (-88.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	135	7	142

Merged error: 0.1b

Counts

142 → 7

localize7.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x))))
0.3b	(.f64 (fabs.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))
28.0b	(cbrt.f64 (*.f64 x (+.f64 x x)))
28.0b	(cbrt.f64 (*.f64 x (+.f64 x x)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64`
10×	`associate-*r/_binary64`
9×	`sqrt-prod_binary64`
8×	`cbrt-div_binary64` `*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64` `associate-r_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip-+_binary64` `cbrt-prod_binary64` `sqrt-div_binary64`
3×	`pow1/3_binary64` `associate-l_binary64`
2×	`sqrt-pow1_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 64

Calls

4 calls:

2.0ms	(sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x))))
6.0ms	(.f64 (fabs.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms	(cbrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(cbrt.f64 (*.f64 x (+.f64 x x)))

series112.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x))))
39.0ms	(.f64 (fabs.f64 (cbrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (cbrt.f64 (*.f64 x (+.f64 x x)))))
23.0ms	(cbrt.f64 (*.f64 x (+.f64 x x)))
26.0ms	(cbrt.f64 (*.f64 x (+.f64 x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4790	808
1	4790	808

prune52.0ms

Filtered

59 candidates to 76 candidates (-28.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	76	7	83

Merged error: 0.1b

Counts

83 → 7

regimes163.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 30.8b

bsearch11.0ms

Steps

Iters	Range		Point
9	-4.0303509276913107e-308	1.978313196859493e-301	-3.9001145064361e-310

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	16
1	37	16

end0.0ms

sample267.0ms

Algorithm

intervals

Results

177.0ms

8000×

body

valid

Details

analyze4.0ms

sample11.0ms

simplify5.0ms

prune6.0ms

localize4.0ms

rewrite6.0ms

series5.0ms

simplify64.0ms

prune34.0ms

localize4.0ms

rewrite9.0ms

series11.0ms

simplify82.0ms

prune32.0ms

localize6.0ms

rewrite39.0ms

series26.0ms

simplify84.0ms

prune75.0ms

localize7.0ms

rewrite20.0ms

series112.0ms

simplify44.0ms

prune52.0ms

regimes163.0ms

bsearch11.0ms

simplify2.0ms

end0.0ms

sample267.0ms

Profiling