Details

analyze478.0ms

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

sample45.0ms

Algorithm

intervals

Results

9.0ms	30×	body	2560	valid
9.0ms	167×	body	80	valid
8.0ms	30×	body	1280	valid
3.0ms	17×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	nan
1.0ms	5×	body	320	valid
1.0ms	12×	body	80	invalid
0.0ms	3×	body	160	valid

simplify248.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (245.0ms)

Iter	Nodes	Cost
0	1931	16
1	1931	16

prune10.0ms

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: 38.2b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) (.f64 a 2.0))
21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
19.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5340	1316

prune130.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 7.6b

Counts

83 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (/.f64 1 a) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) 2.0))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

56×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
32×	`*-un-lft-identity_binary64`
26×	`add-exp-log_binary64`
22×	`associate-r_binary64` `add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
13×	`associate-l_binary64`
8×	`add-log-exp_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `div-exp_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`unswap-sqr_binary64`
4×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

19.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) 2.0))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(.f64 (/.f64 1 a) (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b) 2.0))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
14.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify61.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4968	1950
1	4968	1950

prune132.0ms

Filtered

83 candidates to 117 candidates (-41.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	115	2	117
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	116	10	126

Merged error: 7.5b

Counts

126 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
11.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5246	824

prune95.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	64	10	74

Merged error: 7.5b

Counts

74 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
1.2b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

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

series59.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
11.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5246	824

prune74.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	64	10	74

Merged error: 7.5b

Counts

74 → 10

regimes323.0ms

Accuracy

83.2% (4.8b remaining)

Error of 10.6b against oracle of 5.7b and baseline of 34.4b

bsearch52.0ms

Steps

Iters	Range		Point
9	1.3879349606251492e-149	4.462847075293778e-140	4.333101729627981e-140
8	-3.476586232975515e+112	-9.977119098877996e+107	-5.948493915058576e+108

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	92	40
1	92	40

end0.0ms

sample1.3s

Algorithm

intervals

Results

318.0ms	1039×	body	2560	valid
282.0ms	5148×	body	80	valid
235.0ms	919×	body	1280	valid
97.0ms	460×	body	640	valid
39.0ms	106×	body	5120	valid
34.0ms	671×	body	80	nan
34.0ms	230×	body	320	valid
21.0ms	396×	body	80	invalid
10.0ms	98×	body	160	valid

Details

analyze478.0ms

sample45.0ms

simplify248.0ms

prune10.0ms

localize11.0ms

rewrite31.0ms

series82.0ms

simplify43.0ms

prune130.0ms

localize12.0ms

rewrite40.0ms

series94.0ms

simplify61.0ms

prune132.0ms

localize14.0ms

rewrite20.0ms

series59.0ms

simplify40.0ms

prune95.0ms

localize14.0ms

rewrite20.0ms

series59.0ms

simplify40.0ms

prune74.0ms

regimes323.0ms

bsearch52.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling