Details

analyze602.0ms

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample38.0ms

Algorithm

intervals

Results

10.0ms	34×	body	2048	valid
8.0ms	177×	body	128	valid
4.0ms	23×	body	1024	valid
2.0ms	8×	body	4096	valid
1.0ms	10×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	13×	body	128	invalid
0.0ms	4×	body	256	valid

simplify246.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms

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: 33.1b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
14.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series471.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
122.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
114.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify72.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5716	2155

prune96.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	83	11	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	83	12	95

Merged error: 6.6b

Counts

95 → 12

localize11.0ms

Local error

Found 4 expressions with local error:

0.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
2.9b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
11.2b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
15.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series884.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
285.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
368.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify113.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5773	8137

prune168.0ms

Filtered

175 candidates to 229 candidates (-30.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	6	4	10
Picked	1	0	1
Done	0	1	1
Total	234	7	241

Merged error: 6.6b

Counts

241 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_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` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series599.0ms

Counts

4 → 12

Calls

4 calls:

323.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
118.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
104.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify68.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4948	1690
1	4948	1690

prune53.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 6.6b

Counts

90 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.7b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
16.8b	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
22.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`associate-/l*_binary64` `times-frac_binary64`
5×	`pow1_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `associate-/r/_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `sum-log_binary64`

Counts

4 → 69

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series558.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
113.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
283.0ms	(/.f64 (neg.f64 (.f64 a c)) (.f64 a (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
101.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify59.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5107	1554

prune51.0ms

Filtered

64 candidates to 81 candidates (-26.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	81	7	88

Merged error: 6.6b

Counts

88 → 7

regimes129.0ms

Accuracy

95.7% (1.0b remaining)

Error of 6.8b against oracle of 5.8b and baseline of 29.8b

bsearch77.0ms

Steps

Iters	Range	Point
6	3.30075912834621e+93	1.6427805606474683e+94	1.5027731307248138e+94
9	-1.9650228055801083e-293	-1.224383724922962e-299	-1.0770271972015288e-294
6	-2.5062439911161653e+154	-3.0003694483523168e+153	-3.2825768280390323e+153

Iters

Range

Point

3.30075912834621e+93

1.6427805606474683e+94

1.5027731307248138e+94

-1.9650228055801083e-293

-1.224383724922962e-299

-1.0770271972015288e-294

-2.5062439911161653e+154

-3.0003694483523168e+153

-3.2825768280390323e+153

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	102	79
1	102	79

end0.0ms

sample965.0ms

Algorithm

intervals

Results

238.0ms	1150×	body	2048	valid
217.0ms	5250×	body	128	valid
113.0ms	715×	body	1024	valid
87.0ms	351×	body	4096	valid
44.0ms	362×	body	512	valid
31.0ms	818×	body	128	nan
14.0ms	172×	body	256	valid
10.0ms	248×	body	128	invalid

Details

analyze602.0ms

sample38.0ms

simplify246.0ms

prune6.0ms

localize10.0ms

rewrite47.0ms

series471.0ms

simplify72.0ms

prune96.0ms

localize11.0ms

rewrite63.0ms

series884.0ms

simplify113.0ms

prune168.0ms

localize11.0ms

rewrite29.0ms

series599.0ms

simplify68.0ms

prune53.0ms

localize12.0ms

rewrite32.0ms

series558.0ms

simplify59.0ms

prune51.0ms

regimes129.0ms

bsearch77.0ms

simplify3.0ms

end0.0ms

sample965.0ms

Profiling