Details

analyze469.0ms

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

sample42.0ms

Algorithm

intervals

Results

9.0ms	30×	body	2560	valid
9.0ms	167×	body	80	valid
7.0ms	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

simplify221.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (217.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune7.0ms

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms

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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5261	1302

prune128.0ms

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

14.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
21.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify64.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4947	1460
1	4947	1460

prune103.0ms

Filtered

68 candidates to 91 candidates (-33.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 7.6b

Counts

100 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
27.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite19.0ms

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 (*.f64 a c)))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series68.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
28.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	4931	814
1	4931	814

prune127.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	64	8	72

Merged error: 7.6b

Counts

72 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.4b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
27.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
27.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `cbrt-prod_binary64`
4×	`cbrt-div_binary64` `pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `pow1/3_binary64`

Counts

4 → 48

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
9.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
36.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) b)
26.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
28.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4988	1074
1	4988	1074

prune77.0ms

Filtered

53 candidates to 60 candidates (-13.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	60	8	68

Merged error: 7.6b

Counts

68 → 8

regimes358.0ms

Accuracy

83.3% (4.8b remaining)

Error of 10.6b against oracle of 5.8b and baseline of 34.4b

bsearch50.0ms

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	91	35
1	91	35

end0.0ms

sample1.3s

Algorithm

intervals

Results

325.0ms	1039×	body	2560	valid
280.0ms	5148×	body	80	valid
226.0ms	919×	body	1280	valid
90.0ms	460×	body	640	valid
38.0ms	106×	body	5120	valid
34.0ms	671×	body	80	nan
34.0ms	230×	body	320	valid
23.0ms	396×	body	80	invalid
10.0ms	98×	body	160	valid

Details

analyze469.0ms

sample42.0ms

simplify221.0ms

prune7.0ms

localize10.0ms

rewrite33.0ms

series79.0ms

simplify41.0ms

prune128.0ms

localize12.0ms

rewrite33.0ms

series80.0ms

simplify64.0ms

prune103.0ms

localize13.0ms

rewrite19.0ms

series68.0ms

simplify41.0ms

prune127.0ms

localize14.0ms

rewrite24.0ms

series104.0ms

simplify51.0ms

prune77.0ms

regimes358.0ms

bsearch50.0ms

simplify2.0ms

end0.0ms

sample1.3s

Profiling