Details

analyze15.0ms

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
49.9%	49.9%	0.1%	5
74.9%	25%	0.1%	6
87.4%	12.5%	0.1%	7
93.6%	6.2%	0.1%	8
96.7%	3.1%	0.1%	9
98.3%	1.6%	0.1%	10
99.1%	0.8%	0.1%	11
99.5%	0.4%	0.1%	12
99.7%	0.2%	0.1%	13
99.8%	0.1%	0.1%	14

sample19.0ms

Algorithm

intervals

Results

11.0ms

256×

body

valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	21	14
1	21	14

prune8.0ms

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: 39.2b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.3b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
36.1b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
13×	`sqrt-prod_binary64`
11×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64`
4×	`sum-log_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `+-commutative_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `sqrt-pow1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-exp_binary64` `sqrt-div_binary64`

Counts

4 → 78

Calls

4 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
10.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
6.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

series65.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(+.f64 (.f64 x x) (.f64 y y))
11.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
15.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3)
31.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) 3))

simplify69.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4920	1455
1	4920	1455

prune75.0ms

Filtered

69 candidates to 90 candidates (-30.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	84	6	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	85	6	91

Merged error: 16.7b

Counts

91 → 6

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.4b	(.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3)
36.1b	(sqrt.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
10.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
9.0ms	(.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3)
7.0ms	(sqrt.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3))

series61.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 y y))
11.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
14.0ms	(.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3)
30.0ms	(sqrt.f64 (.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 z z)) 1/3))

simplify53.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5273	927

prune38.0ms

Filtered

47 candidates to 69 candidates (-46.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	69	6	75

Merged error: 16.7b

Counts

75 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.4b	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
36.3b	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`sqrt-prod_binary64`
36×	`times-frac_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
6×	`associate-/r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
2×	`associate-/l/_binary64` `+-commutative_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `associate-+l+_binary64` `sqrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 102

Calls

4 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
10.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
6.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+.f64 (.f64 x x) (.f64 y y))
11.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
34.0ms	(/.f64 (sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))) (sqrt.f64 3))
24.0ms	(sqrt.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)))

simplify56.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5247	2173

prune57.0ms

Filtered

71 candidates to 114 candidates (-60.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	111	9	120

Merged error: 16.6b

Counts

120 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
0.1b	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))
0.5b	(.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))
36.4b	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

90×	`add-sqr-sqrt_binary64`
75×	`times-frac_binary64` `sqrt-prod_binary64`
53×	`*-un-lft-identity_binary64`
49×	`add-cube-cbrt_binary64`
35×	`cbrt-prod_binary64`
25×	`associate-r_binary64`
16×	`unswap-sqr_binary64`
10×	`associate-l_binary64`
9×	`add-log-exp_binary64` `pow1_binary64`
8×	`add-exp-log_binary64`
7×	`add-cbrt-cube_binary64`
6×	`associate-/r*_binary64`
5×	`sqrt-div_binary64`
4×	`div-inv_binary64`
3×	`pow-prod-down_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64` `sum-log_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip-+_binary64`
1×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `associate-+l+_binary64` `sqrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-exp_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 157

Calls

4 calls:

7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
10.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))
24.0ms	(.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))
8.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z))
22.0ms	(/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))
49.0ms	(.f64 (sqrt.f64 (/.f64 1 (.f64 (cbrt.f64 3) (cbrt.f64 3)))) (sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3))))
49.0ms	(sqrt.f64 (/.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 z z)) (cbrt.f64 3)))

simplify68.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4942	4093
1	4942	4093

prune144.0ms

Filtered

132 candidates to 169 candidates (-28.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	167	2	169
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	167	11	178

Merged error: 16.6b

Counts

178 → 11

regimes629.0ms

Accuracy

55.8% (8.7b remaining)

Error of 27.1b against oracle of 18.4b and baseline of 38.2b

bsearch55.0ms

Steps

Iters	Range		Point
10	5.5818334407294036e+119	3.724207892005642e+132	2.0671969795246543e+127
6	2.47280149909341e-146	1.5021806300678813e-145	2.514104751174992e-146
6	1.8997158450737766e-264	8.295962969762243e-264	8.163804980003783e-264
10	-9.926535117811378e+73	-4.7999022850741395e+60	-9.804340525800049e+73

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	70
1	83	70

end0.0ms

sample522.0ms

Algorithm

intervals

Results

363.0ms

8000×

body

valid

Details

analyze15.0ms

sample19.0ms

simplify6.0ms

prune8.0ms

localize9.0ms

rewrite30.0ms

series65.0ms

simplify69.0ms

prune75.0ms

localize9.0ms

rewrite33.0ms

series61.0ms

simplify53.0ms

prune38.0ms

localize11.0ms

rewrite31.0ms

series74.0ms

simplify56.0ms

prune57.0ms

localize16.0ms

rewrite56.0ms

series132.0ms

simplify68.0ms

prune144.0ms

regimes629.0ms

bsearch55.0ms

simplify3.0ms

end0.0ms

sample522.0ms

Profiling