Details

analyze460.0ms

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

13.0ms	36×	body	2560	valid
8.0ms	163×	body	80	valid
6.0ms	23×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	24×	body	80	nan
1.0ms	3×	body	5120	valid
1.0ms	12×	body	80	invalid
0.0ms	2×	body	160	valid

simplify256.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (253.0ms)

Iter	Nodes	Cost
0	1833	16
1	1833	16

prune8.0ms

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: 37.4b

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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.5b	(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:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))) a)
17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
13.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify51.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4931	1327
1	4931	1327

prune129.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	75	8	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	9	84

Merged error: 7.0b

Counts

84 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.9b	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
11.7b	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
26.5b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite39.0ms

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:

4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
14.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
12.0ms	(/.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))))

series173.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
55.0ms	(/.f64 (/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))) a)
88.0ms	(/.f64 (.f64 4 (.f64 a c)) (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify42.0ms

Algorithm

egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	4997	3057
1	4997	3057

prune160.0ms

Filtered

102 candidates to 139 candidates (-36.3%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	136	3	139
Fresh	4	3	7
Picked	0	1	1
Done	0	1	1
Total	140	8	148

Merged error: 6.9b

Counts

148 → 8

localize13.0ms

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))))))
1.2b	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.5b	(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:

9.0ms	(/.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))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

63.0ms	(/.f64 c (-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))))
19.0ms	(-.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
13.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5070	1600

prune106.0ms

Filtered

69 candidates to 93 candidates (-34.8%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	93	8	101

Merged error: 6.9b

Counts

101 → 8

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))
1.0b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
1.4b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
26.5b	(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))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c))))) (/.f64 1 a))
18.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))))
12.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify54.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4910	1351
1	4910	1351

prune82.0ms

Filtered

66 candidates to 91 candidates (-37.9%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	91	8	99

Merged error: 6.9b

Counts

99 → 8

regimes306.0ms

Accuracy

94.9% (1.3b remaining)

Error of 6.9b against oracle of 5.6b and baseline of 30.1b

bsearch91.0ms

Steps

Iters	Range	Point
7	2.1244901091466005e+48	2.2767001911669423e+50	2.2272767242843476e+50
7	3.5591382758316196e-227	5.0477177829490085e-225	1.4168306912023101e-226
9	-3.586326328619297e+155	-1.5727980192684642e+150	-1.277061339333756e+154

Iters

Range

Point

2.1244901091466005e+48

2.2767001911669423e+50

2.2272767242843476e+50

3.5591382758316196e-227

5.0477177829490085e-225

1.4168306912023101e-226

-3.586326328619297e+155

-1.5727980192684642e+150

-1.277061339333756e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	106	64
1	106	64

end0.0ms

sample1.2s

Algorithm

intervals

Results

318.0ms	1053×	body	2560	valid
268.0ms	5165×	body	80	valid
236.0ms	926×	body	1280	valid
92.0ms	445×	body	640	valid
43.0ms	119×	body	5120	valid
35.0ms	658×	body	80	nan
31.0ms	198×	body	320	valid
18.0ms	355×	body	80	invalid
9.0ms	94×	body	160	valid

Details

analyze460.0ms

sample45.0ms

simplify256.0ms

prune8.0ms

localize10.0ms

rewrite25.0ms

series69.0ms

simplify51.0ms

prune129.0ms

localize12.0ms

rewrite39.0ms

series173.0ms

simplify42.0ms

prune160.0ms

localize13.0ms

rewrite27.0ms

series112.0ms

simplify54.0ms

prune106.0ms

localize12.0ms

rewrite29.0ms

series70.0ms

simplify54.0ms

prune82.0ms

regimes306.0ms

bsearch91.0ms

simplify3.0ms

end0.0ms

sample1.2s

Profiling