Details

sample37.0ms

Algorithm

intervals

Results

11.0ms	202×	body	80	valid
6.0ms	24×	body	2560	valid
4.0ms	256×	pre	80	true
3.0ms	18×	body	1280	valid
1.0ms	6×	body	640	valid
0.0ms	4×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

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

Filtered

1 candidates to 0 candidates (0.0%)

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: 11.4b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite32.0ms

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

series231.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* (* 4.0 p) p) (* x x))
53.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
80.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify148.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	278	822
1	1014	772
2	4246	757
3	5001	757

prune286.0ms

Filtered

91 candidates to 67 candidates (73.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	77	14	91
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	14	92

Merged error: 11.2b

Counts

92 → 14

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.4b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.4b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 83

Calls

4 calls:

11.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
13.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series375.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
182.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify74.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 3 (64.0ms)

Iter	Nodes	Cost
0	279	952
1	796	884
2	2317	872
3	5001	871

prune337.0ms

Filtered

95 candidates to 69 candidates (72.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	92	3	95
Fresh	6	7	13
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 8.0b

Counts

109 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x))))))
3.9b	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

51×	`*-un-lft-identity`
35×	`log-prod`
30×	`times-frac`
23×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
15×	`distribute-lft-out`
12×	`add-exp-log` `unpow-prod-down` `cube-prod`
9×	`add-cbrt-cube`
7×	`pow1`
6×	`sqrt-prod` `associate-/r/`
4×	`flip3-+` `sqrt-div` `flip-+` `add-log-exp`
3×	`div-exp` `associate-/r*` `sum-cubes`
2×	`cbrt-undiv` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `rem-log-exp` `frac-add` `div-inv`
1×	`log-div` `flip3--` `frac-2neg` `prod-exp` `clear-num` `log-pow` `flip--` `cbrt-unprod` `associate-/l*`

Counts

4 → 99

Calls

4 calls:

63.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x))))))
9.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
6.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series594.0ms

Counts

4 → 12

Calls

4 calls:

423.0ms	(log (/ (+ (pow 1.0 3) (pow (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))) 3)) (+ (* 1.0 (- 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))) (/ (* x x) (+ (* (* 4.0 p) p) (* x x))))))
49.0ms	(/ (* x x) (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
61.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify67.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	532	2613
1	2072	2494
2	5002	2486

prune499.0ms

Filtered

111 candidates to 77 candidates (69.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	1	8	9
Picked	1	0	1
Done	0	0	0
Total	111	10	121

Merged error: 8.0b

Counts

121 → 10

localize30.0ms

Local error

Found 4 expressions with local error:

13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))
13.5b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite23.0ms

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:

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

series234.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
56.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
60.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))
58.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify84.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 1 (5.0ms)

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

prune548.0ms

Filtered

72 candidates to 64 candidates (88.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	72	10	82

Merged error: 8.0b

Counts

82 → 10

regimes144.0ms

Accuracy

0% (3.9b remaining)

Error of 12.9b against oracle of 9.0b and baseline of 12.9b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	86
1	35	86

end0.0ms

sample837.0ms

Algorithm

intervals

Results

219.0ms	6124×	body	80	valid
175.0ms	760×	body	2560	valid
113.0ms	592×	body	1280	valid
109.0ms	8000×	pre	80	true
43.0ms	291×	body	640	valid
17.0ms	158×	body	320	valid
5.0ms	75×	body	160	valid