Details

sample133.0ms

Algorithm

intervals

Results

53.0ms	107×	body	1280	valid
15.0ms	45×	body	640	valid
10.0ms	19×	body	1280	nan
9.0ms	29×	body	10240	exit
7.0ms	131×	body	80	valid
7.0ms	24×	body	640	nan
6.0ms	29×	body	320	valid
5.0ms	152×	body	80	nan
2.0ms	11×	body	320	nan
2.0ms	15×	body	160	valid
0.0ms	3×	body	160	nan

simplify35.0ms

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: 31.3b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 149

Calls

3 calls:

3.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series474.0ms

Counts

3 → 9

Calls

3 calls:

59.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify66.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	654	2164
1	2164	1642
2	5002	1637

prune333.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 300

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 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)))

series966.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
271.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
272.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	542	5691
1	1694	4129
2	5001	4126

prune730.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow (+ x 1.0) (/ 1.0 n))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

208×	`unpow-prod-down`
189×	`prod-diff`
188×	`*-un-lft-identity`
163×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
73×	`sqrt-prod`
71×	`sqr-pow`
30×	`difference-of-squares`
27×	`fma-neg` `distribute-lft-out`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 325

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
15.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
14.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.1s

Counts

4 → 12

Calls

4 calls:

152.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
394.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify119.0ms

Algorithm

egg-herbie

Counts

337 → 337

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	894	6898
1	2735	4844
2	5002	4804

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.8b

localize24.0ms

Local error

Found 4 expressions with local error:

1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.9b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.4b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

266×	`unpow-prod-down`
245×	`prod-diff`
231×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
146×	`add-cube-cbrt`
91×	`sqr-pow`
73×	`sqrt-prod`
61×	`log-prod`
58×	`exp-sum`
39×	`difference-of-squares`
34×	`distribute-lft-out`
27×	`fma-neg`
16×	`log-pow`
15×	`exp-prod`
10×	`distribute-lft-out--` `add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 383

Calls

4 calls:

12.0ms	(- (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)))
20.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
13.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

276.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
393.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify133.0ms

Algorithm

egg-herbie

Counts

395 → 395

Iterations

Useful iterations: 2 (62.0ms)

Iter	Nodes	Cost
0	944	8470
1	2502	5917
2	5001	5278

prune1.2s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.8b

regimes236.0ms

Accuracy

82.1% (1.5b remaining)

Error of 22.8b against oracle of 21.4b and baseline of 29.7b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	54
1	60	54

end0.0ms

sample4.0s

Algorithm

intervals

Results

1.4s	3200×	body	1280	valid
518.0ms	1546×	body	640	valid
430.0ms	1113×	body	10240	exit
294.0ms	595×	body	1280	nan
244.0ms	4679×	body	80	valid
202.0ms	926×	body	320	valid
198.0ms	601×	body	640	nan
187.0ms	5039×	body	80	nan
75.0ms	385×	body	320	nan
57.0ms	429×	body	160	valid
21.0ms	188×	body	160	nan