Details

sample1.4s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

14.0ms	186×	body	80	valid
8.0ms	26×	body	2560	valid
5.0ms	20×	body	1280	valid
5.0ms	256×	pre	80	true
2.0ms	11×	body	640	valid
1.0ms	8×	body	320	valid
1.0ms	5×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	9
1	34	9
2	38	9
3	40	9
4	41	9
5	41	9

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 14.7b

Counts

2 → 1

localize12.0ms

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))))
1.3b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite30.0ms

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:

5.0ms	(+ (* (* 4.0 p) p) (* x x))
7.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
11.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series38.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ (* (* 4.0 p) p) (* x x))
10.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify149.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4232	757
3	5001	757

prune204.0ms

Filtered

67 candidates to 91 candidates (-35.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	78	13	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	13	92

Merged error: 14.4b

Counts

92 → 13

localize21.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.3b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

37.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
8.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	352	1043
1	1550	965
2	5001	964

prune432.0ms

Filtered

81 candidates to 110 candidates (-35.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	107	3	110
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 14.4b

Counts

123 → 14

localize24.0ms

Local error

Found 4 expressions with local error:

1.3b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
2.3b	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
16×	`unpow-prod-down`
9×	`add-exp-log`
8×	`associate-/l*`
6×	`pow1` `sqrt-prod` `add-cbrt-cube` `add-log-exp`
5×	`distribute-lft-out`
4×	`flip3-+` `sqrt-div` `cube-prod` `flip-+` `unpow2` `sqr-pow`
3×	`div-exp` `associate-/r*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `sum-cubes` `div-inv`

Counts

4 → 98

Calls

4 calls:

36.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
7.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series39.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3))
8.0ms	(/ (pow x 2) (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	352	1043
1	1550	965
2	5001	964

prune429.0ms

Filtered

81 candidates to 110 candidates (-35.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	106	4	110
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	111	13	124

Merged error: 14.4b

Counts

124 → 13

localize32.0ms

Local error

Found 4 expressions with local error:

10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
10.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite22.0ms

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:

7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series29.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
7.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify80.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	98	500
1	283	484
2	827	484
3	2050	484
4	5001	484

prune450.0ms

Filtered

64 candidates to 72 candidates (-12.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	70	2	72
Fresh	1	11	12
Picked	1	0	1
Done	0	0	0
Total	72	13	85

Merged error: 14.4b

Counts

85 → 13

regimes287.0ms

Accuracy

0% (0.7b remaining)

Error of 13.5b against oracle of 12.8b and baseline of 13.5b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	57
1	48	57

end0.0ms

sample2.6s

Algorithm

intervals

sampling

Space saved by range analysis: 51.314837%

Space saved by search: 51.314837%

Guaranteed chance to sample good point: 74.54834%

Results

327.0ms	6047×	body	80	valid
267.0ms	792×	body	2560	valid
167.0ms	622×	body	1280	valid
149.0ms	8000×	pre	80	true
67.0ms	313×	body	640	valid
22.0ms	144×	body	320	valid
8.0ms	82×	body	160	valid

Details

sample1.4s

simplify9.0ms

prune3.0ms

localize12.0ms

rewrite30.0ms

series38.0ms

simplify149.0ms

prune204.0ms

localize21.0ms

rewrite57.0ms

series37.0ms

simplify54.0ms

prune432.0ms

localize24.0ms

rewrite55.0ms

series39.0ms

simplify52.0ms

prune429.0ms

localize32.0ms

rewrite22.0ms

series29.0ms

simplify80.0ms

prune450.0ms

regimes287.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

Profiling