Details

analyze491.0ms

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

sample50.0ms

Algorithm

intervals

Results

11.0ms	36×	body	2560	valid
10.0ms	30×	body	1280	valid
8.0ms	152×	body	80	valid
4.0ms	18×	body	640	valid
3.0ms	7×	body	5120	valid
1.0ms	19×	body	80	nan
1.0ms	18×	body	80	invalid
1.0ms	8×	body	160	valid
1.0ms	5×	body	320	valid

simplify254.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (250.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune6.0ms

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: 39.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
1.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite27.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
9.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4931	1327
1	4931	1327

prune102.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	72	11	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	73	11	84

Merged error: 7.2b

Counts

84 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.2b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.2b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_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 → 130

Calls

4 calls:

7.0ms	(-.f64 b (sqrt.f64 (-.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))))

series163.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
54.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
75.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify55.0ms

Algorithm

egg-herbie

Counts

142 → 142

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4975	3165
1	4975	3165

prune118.0ms

Filtered

105 candidates to 142 candidates (-35.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	138	4	142
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	144	9	153

Merged error: 7.2b

Counts

153 → 9

localize15.0ms

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 (.f64 b b) (.f64 4 (*.f64 a c)))
1.0b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms

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

series103.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5070	1600

prune81.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 7.2b

Counts

102 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
1.0b	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
1.0b	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
25.9b	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

rewrite30.0ms

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`
3×	`associate-/l*_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_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 → 81

Calls

4 calls:

10.0ms	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
5.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
7.0ms	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

series104.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(/.f64 c (-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))))
9.0ms	(+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))
17.0ms	(-.f64 b (sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4)))))
18.0ms	(sqrt.f64 (+.f64 (.f64 b b) (.f64 a (*.f64 c -4))))

simplify88.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4897	1595
1	4897	1595

prune63.0ms

Filtered

68 candidates to 93 candidates (-36.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	91	2	93
Fresh	1	7	8
Picked	0	1	1
Done	0	0	0
Total	92	10	102

Merged error: 7.2b

Counts

102 → 10

regimes235.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.2b against oracle of 5.9b and baseline of 30.2b

bsearch106.0ms

Steps

Iters	Range		Point
11	1157442434.4076512	2.648929221680175e+28	2.6178552751939085e+28
9	1.3063408785013982e-233	7.458122188517929e-227	6.117566134779201e-229
9	-3.1541505566043017e+119	-2.525464646816111e+112	-3.8933131748243174e+118

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	74	64
1	74	64

end0.0ms

sample1.3s

Algorithm

intervals

Results

339.0ms	1043×	body	2560	valid
292.0ms	5146×	body	80	valid
229.0ms	884×	body	1280	valid
92.0ms	448×	body	640	valid
47.0ms	117×	body	5120	valid
38.0ms	248×	body	320	valid
36.0ms	689×	body	80	nan
24.0ms	434×	body	80	invalid
12.0ms	114×	body	160	valid

Details

analyze491.0ms

sample50.0ms

simplify254.0ms

prune6.0ms

localize10.0ms

rewrite27.0ms

series64.0ms

simplify52.0ms

prune102.0ms

localize12.0ms

rewrite49.0ms

series163.0ms

simplify55.0ms

prune118.0ms

localize15.0ms

rewrite29.0ms

series103.0ms

simplify52.0ms

prune81.0ms

localize13.0ms

rewrite30.0ms

series104.0ms

simplify88.0ms

prune63.0ms

regimes235.0ms

bsearch106.0ms

simplify3.0ms

end0.0ms

sample1.3s

Profiling