Details

analyze793.0ms

Algorithm

Search

True	Other	False	Iter
0%	48.6%	51.4%	0
0%	48.6%	51.4%	1
24.3%	24.3%	51.4%	2
24.3%	24.3%	51.4%	3
30.4%	18.2%	51.4%	4
30.4%	18.2%	51.4%	5
33.4%	15.2%	51.4%	6
33.4%	15.2%	51.4%	7
34.6%	14.1%	51.4%	8
34.8%	13.9%	51.4%	9
35.4%	13.2%	51.4%	10
35.6%	13.1%	51.4%	11
35.9%	12.7%	51.4%	12
36%	12.6%	51.4%	13
36.2%	12.4%	51.4%	14

sample74.0ms

Algorithm

intervals

Results

10.0ms	31×	body	2560	valid
9.0ms	193×	body	80	valid
4.0ms	18×	body	1280	valid
2.0ms	8×	body	640	valid
0.0ms	4×	body	160	valid
0.0ms	2×	body	320	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	38	17
1	38	17

prune7.0ms

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: 13.3b

Counts

2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
6.1b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
7.1b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
20×	`add-cube-cbrt`
18×	`times-frac`
16×	`sqrt-prod`
8×	`pow1`
6×	`add-exp-log` `sqrt-div` `associate-/r*` `add-cbrt-cube` `add-log-exp`
4×	`flip3-+` `flip-+`
3×	`sqrt-pow1` `associate-/l*`
2×	`pow1/2` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `div-exp` `pow-prod-down` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 81

Calls

4 calls:

8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series61.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
14.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
30.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify71.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5576	1479

prune217.0ms

Filtered

74 candidates to 93 candidates (-25.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	83	10	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	10	94

Merged error: 13.0b

Counts

94 → 10

localize29.0ms

Local error

Found 4 expressions with local error:

7.1b	(sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))))
8.3b	(- (/ x (+ (* 4.0 (* p p)) (* x x))) (/ 1.0 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite86.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
9×	`pow1` `times-frac` `sqrt-prod`
6×	`add-cube-cbrt` `sqrt-div` `add-log-exp` `difference-of-squares`
4×	`add-exp-log` `sqrt-pow1` `add-cbrt-cube`
3×	`flip3-+` `pow1/2` `flip-+`
2×	`rem-sqrt-square` `associate-*r/` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `diff-log` `pow-prod-down` `frac-sub` `flip--`

Counts

4 → 63

Calls

4 calls:

41.0ms	(sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))))
29.0ms	(- (/ x (+ (* 4.0 (* p p)) (* x x))) (/ 1.0 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(sqrt (* 0.5 (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))))
16.0ms	(- (/ x (+ (* 4.0 (* p p)) (* x x))) (/ 1.0 (sqrt (+ (* 4.0 (* p p)) (* x x)))))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify64.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4953	1513
1	4953	1513

prune278.0ms

Filtered

61 candidates to 75 candidates (-23.0%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	75	10	85

Merged error: 13.0b

Counts

85 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

9.2b	(cbrt (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
10×	`*-un-lft-identity`
9×	`sqrt-prod`
8×	`add-cube-cbrt`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `cbrt-prod` `flip3-+` `add-cbrt-cube` `flip-+` `add-log-exp`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`cbrt-div`
1×	`pow1/3` `distribute-lft-out`

Counts

4 → 59

Calls

4 calls:

13.0ms	(cbrt (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series69.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(cbrt (+ 1.0 (/ x (sqrt (+ (* 4.0 (* p p)) (* x x))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify47.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5405	968

prune258.0ms

Filtered

60 candidates to 71 candidates (-18.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	72	9	81

Merged error: 13.0b

Counts

81 → 9

localize32.0ms

Local error

Found 4 expressions with local error:

14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
14.4b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.2b	(cbrt (+ (* 4.0 (* p p)) (* x x)))
15.2b	(cbrt (+ (* 4.0 (* p p)) (* x x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1` `cbrt-prod` `sqrt-prod`
4×	`add-exp-log` `cbrt-div` `flip3-+` `sqrt-div` `add-cbrt-cube` `flip-+` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 56

Calls

4 calls:

6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

series58.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
21.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
22.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5275	884

prune256.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	68	9	77

Merged error: 13.0b

Counts

77 → 9

regimes150.0ms

Accuracy

0% (0.3b remaining)

Error of 13.0b against oracle of 12.8b and baseline of 13.0b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	48	53
1	48	53

end0.0ms

sample1.6s

Algorithm

intervals

Results

299.0ms	6077×	body	80	valid
241.0ms	785×	body	2560	valid
149.0ms	610×	body	1280	valid
59.0ms	304×	body	640	valid
22.0ms	151×	body	320	valid
7.0ms	73×	body	160	valid

Details

analyze793.0ms

sample74.0ms

simplify4.0ms

prune7.0ms

localize17.0ms

rewrite41.0ms

series61.0ms

simplify71.0ms

prune217.0ms

localize29.0ms

rewrite86.0ms

series58.0ms

simplify64.0ms

prune278.0ms

localize23.0ms

rewrite33.0ms

series69.0ms

simplify47.0ms

prune258.0ms

localize32.0ms

rewrite27.0ms

series58.0ms

simplify52.0ms

prune256.0ms

regimes150.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample1.6s

Profiling