Details

sample58.0ms

Algorithm

intervals

Results

38.0ms

430×

body

valid

simplify108.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	69	42
1	231	42
2	900	42
3	3753	42
4	5001	42

prune9.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 0.4b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
0.1b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.3b	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

107×	`add-exp-log` `add-cbrt-cube`
70×	`prod-exp` `cbrt-unprod`
51×	`pow1`
48×	`associate-l`
42×	`add-sqr-sqrt`
38×	`times-frac`
35×	`pow-prod-down`
33×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-*l/`
13×	`sqrt-prod`
12×	`frac-add`
11×	`cbrt-undiv` `div-exp`
6×	`frac-times` `flip3-+` `associate-*r/` `flip-+`
5×	`associate-r`
4×	`add-log-exp`
3×	`*-commutative` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2`

Counts

4 → 165

Calls

4 calls:

19.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
12.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
59.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series79.0ms

Counts

4 → 10

Calls

4 calls:

58.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
7.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
13.0ms	(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify67.0ms

Algorithm

egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 1 (29.0ms)

Iter	Nodes	Cost
0	1338	4946
1	5001	4032

prune2.2s

Filtered

175 candidates to 109 candidates (37.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	168	7	175
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	169	7	176

Merged error: 0.0b

Counts

176 → 7

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (fabs x) (fabs x)) (fabs x))
0.1b	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
0.1b	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0b	(sqrt PI)

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

37×	`add-sqr-sqrt`
36×	`associate-l`
35×	`pow1` `add-exp-log` `add-cbrt-cube`
29×	`times-frac`
27×	`add-cube-cbrt` `*-un-lft-identity`
22×	`associate-*l/`
17×	`prod-exp` `cbrt-unprod`
13×	`sqrt-prod`
12×	`frac-add`
10×	`pow-prod-down`
7×	`associate-r`
6×	`frac-times` `flip3-+` `pow-plus` `associate-*r/` `pow-prod-up` `flip-+`
4×	`cbrt-undiv` `div-exp` `add-log-exp` `unswap-sqr`
3×	`*-commutative`
2×	`pow2` `pow-sqr` `div-inv`
1×	`distribute-rgt-in` `rem-sqrt-square` `distribute-lft-in` `sqrt-pow1` `pow1/2` `pow3`

Counts

4 → 135

Calls

4 calls:

6.0ms	(* (* (fabs x) (fabs x)) (fabs x))
16.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
11.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
1.0ms	(sqrt PI)

series68.0ms

Counts

4 → 10

Calls

4 calls:

5.0ms	(* (* (fabs x) (fabs x)) (fabs x))
55.0ms	(* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x))))
7.0ms	(* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))
0.0ms	(sqrt PI)

simplify50.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	977	3393
1	5001	2858

prune1.8s

Filtered

145 candidates to 95 candidates (34.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	143	2	145
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	147	5	152

Merged error: 0b

Counts

152 → 5

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (sqrt PI))) (/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))))
0.3b	(/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))))
1.0b	(sqrt PI)
1.0b	(sqrt PI)

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

517×	`times-frac`
370×	`add-sqr-sqrt`
273×	`sqrt-prod`
249×	`*-un-lft-identity`
234×	`add-cube-cbrt`
116×	`associate-r`
48×	`add-exp-log`
44×	`associate-/r/`
43×	`associate-*r/`
42×	`frac-add`
37×	`associate-/r*`
35×	`unswap-sqr`
31×	`associate-l`
30×	`add-cbrt-cube`
29×	`associate-*l/`
21×	`flip3-+` `div-exp` `flip-+`
12×	`cbrt-undiv` `prod-exp`
10×	`div-inv`
8×	`pow1`
6×	`cbrt-unprod`
4×	`add-log-exp`
3×	`rec-exp` `1-exp` `associate-/l*`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `pow-prod-down` `clear-num` `*-commutative`

Counts

4 → 404

Calls

4 calls:

83.0ms	(* (/ 1 (sqrt (sqrt PI))) (/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))))
20.0ms	(/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))))
1.0ms	(sqrt PI)
1.0ms	(sqrt PI)

series130.0ms

Counts

4 → 8

Calls

4 calls:

54.0ms	(* (/ 1 (sqrt (sqrt PI))) (/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))))))
76.0ms	(/ 1.0 (/ (sqrt (sqrt PI)) (+ (+ (* (* (/ 1.0 21.0) (pow (fabs x) 6)) (fabs x)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0)))))
0.0ms	(sqrt PI)
0.0ms	(sqrt PI)

simplify172.0ms

Algorithm

egg-herbie

Counts

412 → 412

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1782	18683
1	5001	17872

prune5.4s

Filtered

412 candidates to 247 candidates (40.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	412	0	412
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	412	5	417

Merged error: 0b

Counts

417 → 5

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) (/ 1.0 (sqrt PI)))
0.2b	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
0.3b	(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
1.0b	(sqrt PI)

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

166×	`add-exp-log`
116×	`prod-exp`
86×	`add-cbrt-cube`
52×	`cbrt-unprod`
45×	`add-sqr-sqrt`
39×	`times-frac`
36×	`associate-r`
33×	`add-cube-cbrt` `*-un-lft-identity`
21×	`pow1`
18×	`associate-*r/` `div-exp`
17×	`associate-l`
13×	`sqrt-prod`
12×	`frac-add`
10×	`cbrt-undiv` `pow-prod-down`
8×	`pow-to-exp` `pow-exp`
7×	`associate-*l/`
6×	`frac-times` `flip3-+` `flip-+`
5×	`unswap-sqr`
4×	`add-log-exp`
3×	`*-commutative` `div-inv`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 172

Calls

4 calls:

30.0ms	(* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) (/ 1.0 (sqrt PI)))
8.0ms	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
21.0ms	(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
1.0ms	(sqrt PI)

series73.0ms

Counts

4 → 10

Calls

4 calls:

56.0ms	(* (+ (+ (* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0)) (* (fabs x) (+ (* (/ 2.0 3.0) (* (fabs x) (fabs x))) 2.0))) (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (/ 1.0 5.0))) (/ 1.0 (sqrt PI)))
5.0ms	(* (/ 2.0 3.0) (* (fabs x) (fabs x)))
12.0ms	(* (* (* (pow (fabs x) 3) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (/ 1.0 21.0))
0.0ms	(sqrt PI)

simplify56.0ms

Algorithm

egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1207	4165
1	5002	3310

prune2.9s

Filtered

182 candidates to 108 candidates (40.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	182	5	187

Merged error: 0b

Counts

187 → 5

regimes120.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	33
1	41	33

end0.0ms

sample1.5s

Algorithm

intervals

Results

1.2s

14074×

body

valid

Details

sample58.0ms

simplify108.0ms

prune9.0ms

localize25.0ms

rewrite99.0ms

series79.0ms

simplify67.0ms

prune2.2s

localize26.0ms

rewrite40.0ms

series68.0ms

simplify50.0ms

prune1.8s

localize30.0ms

rewrite135.0ms

series130.0ms

simplify172.0ms

prune5.4s

localize24.0ms

rewrite69.0ms

series73.0ms

simplify56.0ms

prune2.9s

regimes120.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.5s

Profiling