Details

analyze485.0ms

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
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample41.0ms

Algorithm

intervals

Results

9.0ms	166×	body	80	valid
9.0ms	28×	body	2560	valid
7.0ms	29×	body	1280	valid
3.0ms	17×	body	640	valid
2.0ms	11×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	17×	body	80	nan
0.0ms	2×	body	160	valid
0.0ms	3×	body	80	invalid

simplify309.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (300.0ms)

Iter	Nodes	Cost
0	1803	24
1	1803	24

prune5.0ms

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: 31.3b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 3 a) c)
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
14×	`*-un-lft-identity_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`pow1_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 77

Calls

4 calls:

5.0ms	(.f64 (.f64 3 a) c)
11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series252.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(.f64 (.f64 3 a) c)
112.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
61.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4939	1898
1	4939	1898

prune112.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	10	90

Merged error: 3.4b

Counts

90 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

693×	`times-frac_binary64`
439×	`add-sqr-sqrt_binary64`
364×	`*-un-lft-identity_binary64`
290×	`add-cube-cbrt_binary64`
74×	`difference-of-squares_binary64`
71×	`associate-/r*_binary64`
40×	`sqrt-prod_binary64`
37×	`distribute-lft-out--_binary64`
30×	`add-exp-log_binary64`
18×	`add-cbrt-cube_binary64`
17×	`div-inv_binary64`
15×	`div-exp_binary64`
11×	`pow1_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64`
5×	`associate-/r/_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `associate-r_binary64` `1-exp_binary64` `prod-exp_binary64` `rec-exp_binary64` `associate-/l*_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 359

Calls

4 calls:

22.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
6.0ms	(.f64 (.f64 3 a) c)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 1 (/.f64 3 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) a)))
16.0ms	(.f64 (.f64 3 a) c)
64.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify199.0ms

Algorithm

egg-herbie

Counts

371 → 371

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4989	16230
1	4989	16230

prune369.0ms

Filtered

197 candidates to 371 candidates (-88.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	370	1	371
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	370	11	381

Merged error: 3.4b

Counts

381 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
0.2b	(.f64 (.f64 3 a) c)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`add-sqr-sqrt_binary64`
95×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/l*_binary64`
16×	`sqrt-prod_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`distribute-lft-out--_binary64`
10×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`div-inv_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
2×	`flip3--_binary64` `div-sub_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-l_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 154

Calls

4 calls:

13.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
6.0ms	(.f64 (.f64 3 a) c)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series251.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(/.f64 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b) 3) a)
15.0ms	(.f64 (.f64 3 a) c)
60.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
66.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5308	5702

prune167.0ms

Filtered

113 candidates to 166 candidates (-46.9%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	166	11	177

Merged error: 3.4b

Counts

177 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
19.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
19.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `distribute-lft-out--_binary64`

Counts

4 → 58

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series248.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
62.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify75.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5001	1542

prune86.0ms

Filtered

56 candidates to 70 candidates (-25.0%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	70	11	81

Merged error: 3.4b

Counts

81 → 11

regimes216.0ms

Accuracy

83.7% (4.6b remaining)

Error of 10.2b against oracle of 5.6b and baseline of 33.6b

bsearch42.0ms

Steps

Iters	Range		Point
3	1.2552653880170457e-60	1.76157985671008e-60	1.2869100423103602e-60
9	-6.185495569244337e+161	-4.038212711806056e+152	-4.100503925456705e+152

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	116	65
1	116	65

end0.0ms

sample1.3s

Algorithm

intervals

Results

329.0ms	1008×	body	2560	valid
307.0ms	5241×	body	80	valid
232.0ms	844×	body	1280	valid
99.0ms	460×	body	640	valid
44.0ms	112×	body	5120	valid
39.0ms	246×	body	320	valid
36.0ms	665×	body	80	nan
22.0ms	389×	body	80	invalid
9.0ms	89×	body	160	valid

Details

analyze485.0ms

sample41.0ms

simplify309.0ms

prune5.0ms

localize14.0ms

rewrite31.0ms

series252.0ms

simplify92.0ms

prune112.0ms

localize12.0ms

rewrite69.0ms

series251.0ms

simplify199.0ms

prune369.0ms

localize11.0ms

rewrite39.0ms

series251.0ms

simplify106.0ms

prune167.0ms

localize15.0ms

rewrite30.0ms

series248.0ms

simplify75.0ms

prune86.0ms

regimes216.0ms

bsearch42.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling