Details

analyze669.0ms

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

sample41.0ms

Algorithm

intervals

Results

9.0ms	178×	body	80	valid
9.0ms	29×	body	2560	valid
6.0ms	25×	body	1280	valid
3.0ms	16×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	17×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	4×	body	320	valid

simplify261.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (258.0ms)

Iter	Nodes	Cost
0	1931	17
1	1931	17

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 30.0b

Counts

2 → 1

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
0.2b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
0.8b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
19×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `distribute-rgt-neg-in_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 75

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
9.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series72.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c))))) (.f64 2.0 a))
19.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))))
10.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify44.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5946	1448

prune137.0ms

Filtered

64 candidates to 87 candidates (-35.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	11	87
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 4.3b

Counts

88 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
2.1b	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
7.9b	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64` `associate-/l*_binary64`
11×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`pow1_binary64` `flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
4×	`div-inv_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 → 112

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
16.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
13.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series167.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
56.0ms	(/.f64 (/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)) (.f64 2.0 a))
75.0ms	(/.f64 (.f64 4.0 (.f64 a c)) (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify39.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5232	2497

prune143.0ms

Filtered

84 candidates to 124 candidates (-47.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	7	10
Picked	1	0	1
Done	0	0	0
Total	125	10	135

Merged error: 4.2b

Counts

135 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b))
0.8b	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite32.0ms

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 b) (.f64 4.0 (*.f64 a c)))) b))
5.0ms	(-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series109.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(/.f64 c (-.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)))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify72.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4943	1600
1	4943	1600

prune114.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	93	10	103

Merged error: 4.2b

Counts

103 → 10

localize14.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
2.1b	(/.f64 (.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b))) (*.f64 2.0 a))
7.9b	(.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)))
21.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

162×	`add-exp-log_binary64`
90×	`add-cbrt-cube_binary64`
85×	`prod-exp_binary64`
44×	`div-exp_binary64`
43×	`cbrt-unprod_binary64`
32×	`add-sqr-sqrt_binary64`
24×	`associate-r_binary64`
23×	`*-un-lft-identity_binary64` `cbrt-undiv_binary64`
19×	`times-frac_binary64`
15×	`add-cube-cbrt_binary64`
14×	`pow1_binary64`
9×	`1-exp_binary64` `rec-exp_binary64`
8×	`difference-of-squares_binary64`
7×	`sqrt-prod_binary64`
6×	`pow-prod-down_binary64` `add-log-exp_binary64`
4×	`distribute-lft-out--_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `un-div-inv_binary64` `div-inv_binary64` `sqrt-div_binary64`
1×	`associate-/r_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` `associate-/l_binary64` `*-commutative_binary64`

Counts

4 → 140

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
19.0ms	(/.f64 (.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b))) (*.f64 2.0 a))
18.0ms	(.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

series168.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c)))) b)
57.0ms	(/.f64 (.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b))) (*.f64 2.0 a))
71.0ms	(.f64 (.f64 4.0 (.f64 a c)) (/.f64 1 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (.f64 a c)))) b)))
22.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4.0 (*.f64 a c))))

simplify73.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4980	2867
1	4980	2867

prune96.0ms

Filtered

73 candidates to 152 candidates (-108.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	152	10	162

Merged error: 4.2b

Counts

162 → 10

regimes318.0ms

Accuracy

94.9% (1.2b remaining)

Error of 6.7b against oracle of 5.5b and baseline of 29.5b

bsearch69.0ms

Steps

Iters	Range	Point
8	6.935890742706509e+60	2.2816268548923162e+64	1.304608330782827e+64
5	2.7573175966824064e-279	7.936480566151615e-279	7.420373164236022e-279
6	-2.0168463992321823e+147	-1.7280299014924793e+146	-1.9209858444379851e+146

Iters

Range

Point

6.935890742706509e+60

2.2816268548923162e+64

1.304608330782827e+64

2.7573175966824064e-279

7.936480566151615e-279

7.420373164236022e-279

-2.0168463992321823e+147

-1.7280299014924793e+146

-1.9209858444379851e+146

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	122	61
1	122	61

end0.0ms

sample1.3s

Algorithm

intervals

Results

335.0ms	1083×	body	2560	valid
281.0ms	5145×	body	80	valid
220.0ms	869×	body	1280	valid
87.0ms	445×	body	640	valid
46.0ms	126×	body	5120	valid
36.0ms	732×	body	80	nan
32.0ms	217×	body	320	valid
20.0ms	387×	body	80	invalid
12.0ms	115×	body	160	valid

Details

analyze669.0ms

sample41.0ms

simplify261.0ms

prune6.0ms

localize15.0ms

rewrite33.0ms

series72.0ms

simplify44.0ms

prune137.0ms

localize11.0ms

rewrite46.0ms

series167.0ms

simplify39.0ms

prune143.0ms

localize12.0ms

rewrite32.0ms

series109.0ms

simplify72.0ms

prune114.0ms

localize14.0ms

rewrite57.0ms

series168.0ms

simplify73.0ms

prune96.0ms

regimes318.0ms

bsearch69.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling