Details

analyze766.0ms

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

sample42.0ms

Algorithm

intervals

Results

11.0ms	27×	body	2560	valid
10.0ms	195×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
2.0ms	12×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	2×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	200	17
1	200	17

prune8.0ms

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: 12.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
15.9b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
8.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
10.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5043	1385

prune215.0ms

Filtered

71 candidates to 91 candidates (-28.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	83	8	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	84	8	92

Merged error: 12.2b

Counts

92 → 8

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
2.8b	(/ x (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

37.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
10.0ms	(/ x (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series44.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
9.0ms	(/ x (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
9.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify66.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4958	1316
1	4958	1316

prune304.0ms

Filtered

70 candidates to 88 candidates (-25.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	88	8	96

Merged error: 12.2b

Counts

96 → 8

localize34.0ms

Local error

Found 4 expressions with local error:

15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series32.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify104.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4745	840
1	4745	840

prune450.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	1	72
Fresh	1	6	7
Picked	1	0	1
Done	0	0	0
Total	73	7	80

Merged error: 12.2b

Counts

80 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

3.0b	(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
15.9b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 56

Calls

4 calls:

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

series43.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+ 1.0 (* (* (cbrt x) (/ (cbrt x) (* (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x))))))) (/ (cbrt x) (cbrt (sqrt (+ (* 4.0 (* p p)) (* x x)))))))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4986	810
1	4986	810

prune190.0ms

Filtered

57 candidates to 68 candidates (-19.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	67	8	75

Merged error: 12.2b

Counts

75 → 8

regimes138.0ms

Accuracy

0% (0.9b remaining)

Error of 13.6b against oracle of 12.7b and baseline of 13.6b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	62
1	81	62

end0.0ms

sample1.1s

Algorithm

intervals

Results

315.0ms	6064×	body	80	valid
235.0ms	777×	body	2560	valid
140.0ms	561×	body	1280	valid
139.0ms	8000×	pre	80	true
67.0ms	330×	body	640	valid
25.0ms	173×	body	320	valid
11.0ms	95×	body	160	valid

Details

analyze766.0ms

sample42.0ms

simplify8.0ms

prune8.0ms

localize11.0ms

rewrite34.0ms

series39.0ms

simplify46.0ms

prune215.0ms

localize22.0ms

rewrite61.0ms

series44.0ms

simplify66.0ms

prune304.0ms

localize34.0ms

rewrite28.0ms

series32.0ms

simplify104.0ms

prune450.0ms

localize24.0ms

rewrite25.0ms

series43.0ms

simplify51.0ms

prune190.0ms

regimes138.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample1.1s

Profiling