Details

sample51.0ms

Algorithm

intervals

Results

15.0ms	194×	body	80	valid
10.0ms	31×	body	2560	valid
5.0ms	256×	pre	80	true
5.0ms	18×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	4×	body	160	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: 12.5b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.0b	(+ (* (* 4.0 p) p) (* x x))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
18.0b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-log-exp`
7×	`*-un-lft-identity`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt`
4×	`add-exp-log` `flip3-+` `sqrt-div` `sqrt-prod` `add-cbrt-cube` `flip-+`
3×	`sqrt-pow1`
2×	`+-commutative` `pow1/2` `associate-*r/` `sum-log`
1×	`rem-sqrt-square` `pow-prod-down` `distribute-lft-out`

Counts

4 → 51

Calls

4 calls:

14.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
5.0ms	(+ (* (* 4.0 p) p) (* x x))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
6.0ms	(+ (* (* 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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5214	875

prune148.0ms

Filtered

55 candidates to 63 candidates (-14.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	54	9	63
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	9	64

Merged error: 12.3b

Counts

64 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
4.9b	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

38.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
11.0ms	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
6.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
7.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

series41.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ (pow 1.0 3) (pow (/ x (sqrt (+ (* 4.0 (* p p)) (* x x)))) 3))
8.0ms	(/ (* x x) (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5047	1187

prune251.0ms

Filtered

64 candidates to 82 candidates (-28.1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	80	2	82
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	82	9	91

Merged error: 12.3b

Counts

91 → 9

localize37.0ms

Local error

Found 4 expressions with local error:

18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))

rewrite27.0ms

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

series31.0ms

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)))

simplify74.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4774	840
1	4774	840

prune415.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	69	3	72
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	71	10	81

Merged error: 12.3b

Counts

81 → 10

localize41.0ms

Local error

Found 4 expressions with local error:

18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.0b	(sqrt (+ (* 4.0 (* p p)) (* x x)))
18.8b	(cbrt (+ (* 4.0 (* p p)) (* x x)))
18.8b	(cbrt (+ (* 4.0 (* p p)) (* x x)))

rewrite26.0ms

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)))
6.0ms	(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)))

series63.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
8.0ms	(sqrt (+ (* 4.0 (* p p)) (* x x)))
26.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))
22.0ms	(cbrt (+ (* 4.0 (* p p)) (* x x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5275	884

prune404.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	68	10	78

Merged error: 12.3b

Counts

78 → 10

regimes165.0ms

Accuracy

0% (0.5b remaining)

Error of 13.6b against oracle of 13.1b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	50
1	22	50

end0.0ms

sample1.2s

Algorithm

intervals

Results

306.0ms	6009×	body	80	valid
245.0ms	778×	body	2560	valid
160.0ms	635×	body	1280	valid
140.0ms	8000×	pre	80	true
68.0ms	334×	body	640	valid
25.0ms	171×	body	320	valid
7.0ms	73×	body	160	valid

Details

sample51.0ms

simplify4.0ms

prune7.0ms

localize11.0ms

rewrite41.0ms

series57.0ms

simplify42.0ms

prune148.0ms

localize21.0ms

rewrite64.0ms

series41.0ms

simplify44.0ms

prune251.0ms

localize37.0ms

rewrite27.0ms

series31.0ms

simplify74.0ms

prune415.0ms

localize41.0ms

rewrite26.0ms

series63.0ms

simplify51.0ms

prune404.0ms

regimes165.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling