Details

analyze599.0ms

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
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

sample45.0ms

Algorithm

intervals

Results

7.0ms	28×	body	2560	valid
7.0ms	158×	body	80	valid
7.0ms	32×	body	1280	valid
4.0ms	22×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	13×	body	80	invalid
1.0ms	8×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	6×	body	160	valid

simplify477.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	713	12
1	713	12

prune11.0ms

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: 34.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
1.0b	(- (* b_2 b_2) (* a c))
1.8b	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
26×	`*-un-lft-identity`
18×	`times-frac`
16×	`add-cube-cbrt`
10×	`difference-of-squares`
8×	`sqrt-prod` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube` `associate-/l*`
5×	`pow1` `distribute-lft-out--`
4×	`flip3--` `flip--`
3×	`associate-/r*`
2×	`sub-neg` `sqrt-div` `diff-log` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 82

Calls

4 calls:

10.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
10.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
8.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(- (sqrt (- (* b_2 b_2) (* a c))) b_2)
21.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify52.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5743	1403

prune139.0ms

Filtered

70 candidates to 94 candidates (-34.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	84	10	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	11	95

Merged error: 6.0b

Counts

95 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
2.1b	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
10.0b	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

50×	`times-frac`
40×	`*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
11×	`associate-/l*`
10×	`associate-/r/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `distribute-lft-out`
6×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
5×	`pow1`
3×	`distribute-frac-neg` `sqrt-prod`
2×	`frac-2neg` `sqrt-div` `prod-exp` `clear-num` `distribute-rgt-neg-out` `cbrt-unprod`
1×	`+-commutative` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `sum-log` `flip--` `associate-/l/`

Counts

4 → 114

Calls

4 calls:

5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
11.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
9.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series119.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
41.0ms	(/ (/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c))))) a)
49.0ms	(/ (* a (neg c)) (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
16.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4948	2297
1	4948	2297

prune131.0ms

Filtered

98 candidates to 126 candidates (-28.6%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	128	9	137

Merged error: 5.9b

Counts

137 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
1.0b	(- (* b_2 b_2) (* a c))
1.2b	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
12×	`times-frac`
8×	`add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-lft-out`
4×	`associate-/r*`
3×	`sqrt-prod` `associate-/l*`
2×	`flip3--` `flip3-+` `sqrt-div` `associate-/r/` `flip--` `flip-+`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

4 → 71

Calls

4 calls:

7.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
6.0ms	(- (* b_2 b_2) (* a c))
5.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series78.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ c (+ b_2 (sqrt (- (* b_2 b_2) (* a c)))))
7.0ms	(- (* b_2 b_2) (* a c))
13.0ms	(+ b_2 (sqrt (- (* b_2 b_2) (* a c))))
13.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5326	1109

prune96.0ms

Filtered

64 candidates to 83 candidates (-29.7%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	2	4	6
Picked	0	1	1
Done	1	1	2
Total	83	9	92

Merged error: 5.9b

Counts

92 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.2b	(+ b_2 (cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3)))
21.7b	(sqrt (- (* b_2 b_2) (* a c)))
32.3b	(cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
12×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
9×	`sqrt-prod`
8×	`add-log-exp`
6×	`unpow-prod-down` `cube-prod`
5×	`pow1`
4×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
3×	`flip3--` `flip--`
2×	`cube-div` `cbrt-div`
1×	`+-commutative` `cube-mult` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `unpow3` `sum-log` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `sqr-pow`

Counts

4 → 67

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
9.0ms	(+ b_2 (cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3)))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))
8.0ms	(cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3))

series46.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- (* b_2 b_2) (* a c))
14.0ms	(+ b_2 (cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3)))
12.0ms	(sqrt (- (* b_2 b_2) (* a c)))
13.0ms	(cbrt (pow (sqrt (- (* b_2 b_2) (* a c))) 3))

simplify37.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4984	935
1	4984	935

prune85.0ms

Filtered

55 candidates to 79 candidates (-43.6%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	77	2	79
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	78	10	88

Merged error: 5.9b

Counts

88 → 10

regimes278.0ms

Accuracy

95.3% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 29.6b

bsearch89.0ms

Steps

Iters	Range	Point
10	2.5312074942013306e+65	6.858297407647118e+76	2.7571448887910518e+76
10	-1.9079492435933748e-207	-1.6520971582118183e-217	-5.520617265234985e-215
6	-7.422906298983545e+122	-8.113432939405366e+121	-1.6939938219367456e+122

Iters

Range

Point

2.5312074942013306e+65

6.858297407647118e+76

2.7571448887910518e+76

-1.9079492435933748e-207

-1.6520971582118183e-217

-5.520617265234985e-215

-7.422906298983545e+122

-8.113432939405366e+121

-1.6939938219367456e+122

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	55
1	80	55

end0.0ms

sample1.1s

Algorithm

intervals

Results

259.0ms	1020×	body	2560	valid
232.0ms	5162×	body	80	valid
179.0ms	864×	body	1280	valid
76.0ms	475×	body	640	valid
35.0ms	797×	body	80	nan
35.0ms	112×	body	5120	valid
30.0ms	229×	body	320	valid
12.0ms	266×	body	80	invalid
12.0ms	138×	body	160	valid

Details

analyze599.0ms

sample45.0ms

simplify477.0ms

prune11.0ms

localize10.0ms

rewrite38.0ms

series65.0ms

simplify52.0ms

prune139.0ms

localize12.0ms

rewrite33.0ms

series119.0ms

simplify54.0ms

prune131.0ms

localize9.0ms

rewrite24.0ms

series78.0ms

simplify47.0ms

prune96.0ms

localize13.0ms

rewrite27.0ms

series46.0ms

simplify37.0ms

prune85.0ms

regimes278.0ms

bsearch89.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling