Details

analyze459.0ms

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
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample37.0ms

Algorithm

intervals

Results

8.0ms	169×	body	128	valid
6.0ms	26×	body	2048	valid
5.0ms	17×	body	4096	valid
4.0ms	23×	body	1024	valid
2.0ms	16×	body	512	valid
1.0ms	13×	body	128	nan
0.0ms	10×	body	128	invalid
0.0ms	5×	body	256	valid

simplify303.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (296.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune4.0ms

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: 34.6b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite32.0ms

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-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_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:

9.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
116.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
65.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify88.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4902	2018
1	4902	2018

prune115.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	74	9	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	9	84

Merged error: 8.0b

Counts

84 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
3.3b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.8b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`difference-of-squares_binary64`
10×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`clear-num_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 → 127

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
16.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
15.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series905.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
316.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
416.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5330	4666

prune152.0ms

Filtered

102 candidates to 139 candidates (-36.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	140	8	148

Merged error: 7.9b

Counts

148 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite37.0ms

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:

9.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
7.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series696.0ms

Counts

4 → 12

Calls

4 calls:

382.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
135.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
116.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4899	2450
1	4899	2450

prune93.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	93	8	101

Merged error: 7.9b

Counts

101 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
0.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

102×	`times-frac_binary64`
82×	`*-un-lft-identity_binary64`
57×	`add-sqr-sqrt_binary64`
56×	`add-cube-cbrt_binary64`
18×	`associate-/r*_binary64`
13×	`distribute-lft-out_binary64`
12×	`add-exp-log_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64`
5×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`div-exp_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `rec-exp_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `+-commutative_binary64` `pow-flip_binary64` `sum-log_binary64`

Counts

4 → 132

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series506.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(/.f64 1 (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
72.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify97.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4893	4446
1	4893	4446

prune120.0ms

Filtered

91 candidates to 144 candidates (-58.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	144	8	152

Merged error: 7.9b

Counts

152 → 8

regimes123.0ms

Accuracy

95.1% (1.2b remaining)

Error of 6.9b against oracle of 5.7b and baseline of 29.8b

bsearch108.0ms

Steps

Iters	Range	Point
7	8.325952084587279e+91	1.2552859941331094e+94	1.1846201307114041e+94
10	9.205375923004052e-298	2.372728704595599e-284	1.715311830575204e-291
9	-1.0963414683130536e+161	-6.0827360795700886e+153	-6.161738829450185e+153

Iters

Range

Point

8.325952084587279e+91

1.2552859941331094e+94

1.1846201307114041e+94

9.205375923004052e-298

2.372728704595599e-284

1.715311830575204e-291

-1.0963414683130536e+161

-6.0827360795700886e+153

-6.161738829450185e+153

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	109	98
1	109	98

end0.0ms

sample1.1s

Algorithm

intervals

Results

276.0ms	1135×	body	2048	valid
254.0ms	5190×	body	128	valid
139.0ms	731×	body	1024	valid
121.0ms	390×	body	4096	valid
54.0ms	381×	body	512	valid
32.0ms	643×	body	128	nan
19.0ms	384×	body	128	invalid
18.0ms	173×	body	256	valid

Details

analyze459.0ms

sample37.0ms

simplify303.0ms

prune4.0ms

localize15.0ms

rewrite32.0ms

series453.0ms

simplify88.0ms

prune115.0ms

localize12.0ms

rewrite58.0ms

series905.0ms

simplify72.0ms

prune152.0ms

localize13.0ms

rewrite37.0ms

series696.0ms

simplify74.0ms

prune93.0ms

localize15.0ms

rewrite46.0ms

series506.0ms

simplify97.0ms

prune120.0ms

regimes123.0ms

bsearch108.0ms

simplify4.0ms

end0.0ms

sample1.1s

Profiling