Details

analyze24.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
50%	50%	0.1%	2
50%	50%	0.1%	3
74.9%	25%	0.1%	4
74.9%	25%	0.1%	5
87.4%	12.5%	0.1%	6
87.4%	12.5%	0.1%	7
93.7%	6.2%	0.1%	8
93.7%	6.2%	0.1%	9
96.8%	3.1%	0.1%	10
96.8%	3.1%	0.1%	11
98.3%	1.6%	0.1%	12
98.3%	1.6%	0.1%	13
99.1%	0.8%	0.1%	14

sample14.0ms

Algorithm

intervals

Results

6.0ms	243×	body	80	valid
1.0ms	5×	body	2560	valid
0.0ms	4×	body	1280	valid
0.0ms	3×	body	640	valid
0.0ms	1×	body	320	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (13.0ms)

Iter	Nodes	Cost
0	181	8
1	181	8

prune3.0ms

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: 0.1b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
1×	`flip3-+_binary64` `pow1_binary64` `distribute-lft-out_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

1 → 12

Calls

1 calls:

6.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))

series6.0ms

Counts

1 → 3

Calls

1 calls:

6.0ms

(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))

simplify65.0ms

Algorithm

egg-herbie

Counts

15 → 15

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4944	171
1	4944	171

prune24.0ms

Filtered

11 candidates to 15 candidates (-36.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	12	3	15
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	4	16

Merged error: 0.0b

Counts

16 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.5b	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

36×	`cbrt-prod_binary64`
35×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `distribute-lft-out_binary64` `pow1/3_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 95

Calls

4 calls:

6.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
6.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
6.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
15.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
25.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
25.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
33.0ms	(*.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

simplify45.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	4998	2037
1	4998	2037

prune131.0ms

Filtered

80 candidates to 107 candidates (-33.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	107	4	111

Merged error: 0.0b

Counts

111 → 4

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.0b	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.4b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

34×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
28×	`add-sqr-sqrt_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`add-cube-cbrt_binary64`
11×	`swap-sqr_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `distribute-lft-out_binary64` `flip-+_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 106

Calls

4 calls:

6.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))
6.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
6.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
19.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

series49.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))
19.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
19.0ms	(sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
6.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))

simplify39.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	4979	1678
1	4979	1678

prune94.0ms

Filtered

67 candidates to 118 candidates (-76.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	116	2	118
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	116	6	122

Merged error: 0.0b

Counts

122 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
0.3b	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
0.5b	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
14×	`sqrt-div_binary64`
13×	`associate-r_binary64`
12×	`add-cube-cbrt_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
11×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`cbrt-div_binary64` `associate-*l/_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`associate-l_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `prod-exp_binary64` `frac-times_binary64`
2×	`associate-r/_binary64` `pow1/3_binary64` `unswap-sqr_binary64` `-commutative_binary64`

Counts

4 → 86

Calls

4 calls:

18.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
9.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
6.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
6.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))

series148.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(.f64 (.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))))) (sqrt.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
39.0ms	(*.f64 (sqrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0))) (fabs.f64 (cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))))
27.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))
25.0ms	(cbrt.f64 (+.f64 x (/.f64 (fabs.f64 (-.f64 y x)) 2.0)))

simplify63.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4957	2842
1	4957	2842

prune132.0ms

Filtered

76 candidates to 98 candidates (-28.9%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	97	7	104

Merged error: 0.0b

Counts

104 → 7

regimes159.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	18	8
1	18	8

end0.0ms

sample350.0ms

Algorithm

intervals

Results

190.0ms	7672×	body	80	valid
15.0ms	128×	body	1280	valid
7.0ms	53×	body	2560	valid
7.0ms	81×	body	640	valid
3.0ms	42×	body	320	valid
1.0ms	24×	body	160	valid
0.0ms	4×	body	80	invalid

Details

analyze24.0ms

sample14.0ms

simplify16.0ms

prune3.0ms

localize5.0ms

rewrite7.0ms

series6.0ms

simplify65.0ms

prune24.0ms

localize9.0ms

rewrite36.0ms

series109.0ms

simplify45.0ms

prune131.0ms

localize8.0ms

rewrite41.0ms

series49.0ms

simplify39.0ms

prune94.0ms

localize14.0ms

rewrite42.0ms

series148.0ms

simplify63.0ms

prune132.0ms

regimes159.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample350.0ms

Profiling