Details

sample240.0ms

Algorithm

intervals

Results

52.0ms	110×	body	1280	valid
49.0ms	77×	body	1280	nan
31.0ms	74×	body	640	nan
27.0ms	48×	body	10240	exit
24.0ms	73×	body	640	valid
10.0ms	40×	body	320	nan
10.0ms	234×	body	80	nan
7.0ms	32×	body	320	valid
5.0ms	104×	body	80	valid
2.0ms	14×	body	160	nan
1.0ms	11×	body	160	valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	35	6
2	85	6
3	249	6
4	911	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize9.0ms

Local error

Found 1 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

66×	`unpow-prod-down`
56×	`*-un-lft-identity` `prod-diff`
45×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
22×	`sqr-pow`
9×	`distribute-lft-out` `difference-of-squares`
8×	`fma-neg`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 90

Calls

1 calls:

15.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series282.0ms

Counts

1 → 3

Calls

1 calls:

282.0ms

(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify50.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	413	1840
1	1182	1320
2	5002	1316

prune169.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.8b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
177×	`*-un-lft-identity`
168×	`prod-diff`
149×	`add-sqr-sqrt`
101×	`add-cube-cbrt`
72×	`sqr-pow`
36×	`difference-of-squares`
28×	`distribute-lft-out`
24×	`fma-neg`
15×	`cbrt-prod`
12×	`distribute-lft-out--`
10×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 297

Calls

4 calls:

9.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts

4 → 12

Calls

4 calls:

585.0ms	(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
288.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify91.0ms

Algorithm

egg-herbie

Counts

309 → 309

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	554	5996
1	1534	4421
2	5001	4401

prune739.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.7b

localize29.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
4.3b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

234×	`unpow-prod-down`
192×	`prod-diff`
184×	`*-un-lft-identity`
155×	`add-sqr-sqrt`
114×	`add-cube-cbrt`
70×	`sqr-pow`
30×	`difference-of-squares`
29×	`distribute-lft-out`
27×	`sqrt-prod`
24×	`fma-neg`
10×	`add-log-exp`
7×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`fma-udef`

Counts

4 → 305

Calls

4 calls:

13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.2s

Counts

4 → 12

Calls

4 calls:

475.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
299.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
292.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify123.0ms

Algorithm

egg-herbie

Counts

317 → 317

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	923	7382
1	2887	5237
2	5002	5220

prune1.1s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 22.7b

localize35.0ms

Local error

Found 4 expressions with local error:

2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
2.2b	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))
4.3b	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

267×	`unpow-prod-down`
213×	`prod-diff`
193×	`*-un-lft-identity`
174×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
74×	`sqr-pow`
62×	`sqrt-prod`
33×	`difference-of-squares`
28×	`distribute-lft-out`
27×	`fma-neg`
10×	`add-log-exp`
5×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`fma-udef`

Counts

4 → 330

Calls

4 calls:

15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
13.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
14.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))
1.0ms	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

series2.4s

Counts

4 → 12

Calls

4 calls:

290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
473.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow (sqrt x) (* 2 (/ 1.0 n))))
482.0ms	(- (pow (sqrt (+ x 1.0)) (/ 1.0 n)) (pow x (/ (/ 1.0 n) 2)))
1.1s	(fma (pow (sqrt x) (/ 1.0 n)) (- (pow (sqrt x) (/ 1.0 n))) (pow (sqrt x) (* 2 (/ 1.0 n))))

simplify166.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	1342	8707
1	4159	6045
2	5001	6035

prune1.5s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 22.7b

regimes262.0ms

Accuracy

81.4% (1.9b remaining)

Error of 24.4b against oracle of 22.5b and baseline of 33.0b

bsearch3.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	91	119
1	93	119
2	93	119

end0.0ms

sample6.7s

Algorithm

intervals

Results

1.9s	3923×	body	1280	valid
1.4s	2258×	body	1280	nan
739.0ms	1811×	body	640	nan
646.0ms	1446×	body	10240	exit
612.0ms	1792×	body	640	valid
279.0ms	6286×	body	80	nan
226.0ms	918×	body	320	nan
194.0ms	891×	body	320	valid
159.0ms	3191×	body	80	valid
73.0ms	478×	body	160	nan
64.0ms	466×	body	160	valid