Details

analyze627.0ms

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

sample40.0ms

Algorithm

intervals

Results

11.0ms	174×	body	128	valid
7.0ms	31×	body	2048	valid
5.0ms	17×	body	4096	valid
2.0ms	12×	body	1024	valid
2.0ms	13×	body	512	valid
1.0ms	27×	body	128	nan
1.0ms	9×	body	256	valid
0.0ms	5×	body	128	invalid

simplify239.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	714	20
1	714	20

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: 31.7b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
9.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
11.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
116.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
57.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
116.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify80.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4957	2470
1	4957	2470

prune95.0ms

Filtered

72 candidates to 101 candidates (-40.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	93	8	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	94	8	102

Merged error: 4.6b

Counts

102 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
3.5b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`difference-of-squares_binary64`
10×	`associate-/r/_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 123

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
11.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series819.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
293.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
361.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4984	3813
1	4984	3813

prune100.0ms

Filtered

102 candidates to 135 candidates (-32.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	132	3	135
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	136	7	143

Merged error: 4.5b

Counts

143 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite33.0ms

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×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/l*_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 81

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series619.0ms

Counts

4 → 12

Calls

4 calls:

348.0ms	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))
111.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4883	2111
1	4883	2111

prune63.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 4.5b

Counts

100 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
3.5b	(/.f64 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c)) a)
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite131.0ms

Algorithm

rewrite-expression-head

Rules

831×	`times-frac_binary64`
545×	`add-sqr-sqrt_binary64`
448×	`*-un-lft-identity_binary64`
352×	`add-cube-cbrt_binary64`
96×	`difference-of-squares_binary64`
74×	`associate-/l*_binary64`
51×	`sqrt-prod_binary64`
48×	`distribute-lft-out--_binary64`
25×	`associate-/r*_binary64`
22×	`div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `associate-/r/_binary64`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 436

Calls

4 calls:

4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
12.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
29.0ms	(/.f64 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c)) a)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series844.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
366.0ms	(/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
316.0ms	(/.f64 (/.f64 a (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c)) a)
102.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify185.0ms

Algorithm

egg-herbie

Counts

448 → 448

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5049	18224

prune235.0ms

Filtered

281 candidates to 448 candidates (-59.4%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	448	0	448
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	448	7	455

Merged error: 4.5b

Counts

455 → 7

regimes194.0ms

Accuracy

95.6% (1.1b remaining)

Error of 6.6b against oracle of 5.5b and baseline of 29.7b

bsearch86.0ms

Steps

Iters	Range	Point
10	2.0918088224755456e+104	3.1908930023788663e+122	6.453375680380735e+115
7	8.16975911518364e-250	7.659173979921316e-248	3.58673047358848e-249
8	-8.041915598558936e+116	-1.7518034651143135e+112	-5.444561051956594e+115

Iters

Range

Point

2.0918088224755456e+104

3.1908930023788663e+122

6.453375680380735e+115

8.16975911518364e-250

7.659173979921316e-248

3.58673047358848e-249

-8.041915598558936e+116

-1.7518034651143135e+112

-5.444561051956594e+115

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	115	82
1	115	82

end0.0ms

sample1.1s

Algorithm

intervals

Results

253.0ms	1141×	body	2048	valid
233.0ms	5185×	body	128	valid
130.0ms	741×	body	1024	valid
112.0ms	404×	body	4096	valid
52.0ms	360×	body	512	valid
35.0ms	783×	body	128	nan
15.0ms	169×	body	256	valid
10.0ms	229×	body	128	invalid

Details

analyze627.0ms

sample40.0ms

simplify239.0ms

prune3.0ms

localize11.0ms

rewrite49.0ms

series437.0ms

simplify80.0ms

prune95.0ms

localize10.0ms

rewrite48.0ms

series819.0ms

simplify88.0ms

prune100.0ms

localize10.0ms

rewrite33.0ms

series619.0ms

simplify71.0ms

prune63.0ms

localize11.0ms

rewrite131.0ms

series844.0ms

simplify185.0ms

prune235.0ms

regimes194.0ms

bsearch86.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling