Details

analyze466.0ms

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

10.0ms	173×	body	80	valid
9.0ms	31×	body	2560	valid
7.0ms	28×	body	1280	valid
3.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	17×	body	80	nan
1.0ms	15×	body	80	invalid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify357.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (348.0ms)

Iter	Nodes	Cost
0	1835	24
1	1835	24

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: 31.6b

Counts

2 → 1

localize11.0ms

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)
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite25.0ms

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)
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series232.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
37.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify89.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4945	2018
1	4945	2018

prune111.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	8	84

Merged error: 6.9b

Counts

84 → 8

localize12.0ms

Local error

Found 4 expressions with local error:

0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.4b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.1b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

66×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
27×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`associate-/l*_binary64`
12×	`difference-of-squares_binary64`
10×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
9×	`associate-/r*_binary64` `sqrt-prod_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64` `distribute-lft-out--_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 → 127

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
15.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
13.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series487.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
167.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
223.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify76.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5329	4666

prune153.0ms

Filtered

102 candidates to 139 candidates (-36.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	140	7	147

Merged error: 6.8b

Counts

147 → 7

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))))))
0.3b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite27.0ms

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:

8.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.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	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series351.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
70.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify136.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	4895	2450
1	4895	2450

prune92.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	93	7	100

Merged error: 6.8b

Counts

100 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
0.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.7b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

12.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series237.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
33.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify89.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4968	2052
1	4968	2052

prune76.0ms

Filtered

66 candidates to 91 candidates (-37.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	91	7	98

Merged error: 6.8b

Counts

98 → 7

regimes88.0ms

Accuracy

95% (1.2b remaining)

Error of 6.7b against oracle of 5.6b and baseline of 28.7b

bsearch115.0ms

Steps

Iters	Range		Point
8	3.413419671611925e+96	3.194645308723527e+100	2.70585956042705e+98
10	4.4213538941992515e-195	2.7788311674158627e-181	4.9581933950094135e-195
9	-4.017204298093521e+88	-3.399204905230493e+79	-3.9235974648770365e+88

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	110	98
1	110	98

end0.0ms

sample1.3s

Algorithm

intervals

Results

334.0ms	1061×	body	2560	valid
279.0ms	5041×	body	80	valid
234.0ms	911×	body	1280	valid
97.0ms	474×	body	640	valid
48.0ms	117×	body	5120	valid
37.0ms	249×	body	320	valid
35.0ms	674×	body	80	nan
21.0ms	386×	body	80	invalid
17.0ms	147×	body	160	valid

Details

analyze466.0ms

sample41.0ms

simplify357.0ms

prune7.0ms

localize11.0ms

rewrite25.0ms

series232.0ms

simplify89.0ms

prune111.0ms

localize12.0ms

rewrite41.0ms

series487.0ms

simplify76.0ms

prune153.0ms

localize15.0ms

rewrite27.0ms

series351.0ms

simplify136.0ms

prune92.0ms

localize12.0ms

rewrite29.0ms

series237.0ms

simplify89.0ms

prune76.0ms

regimes88.0ms

bsearch115.0ms

simplify5.0ms

end0.0ms

sample1.3s

Profiling