Details

sample110.0ms

Algorithm

intervals

Results

49.0ms	100×	body	1280	valid
12.0ms	37×	body	640	valid
9.0ms	164×	body	80	valid
6.0ms	161×	body	80	nan
6.0ms	25×	body	320	valid
4.0ms	75×	body	80	overflowed
4.0ms	8×	body	640	nan
2.0ms	2×	body	1280	nan
1.0ms	10×	body	160	valid
1.0ms	5×	body	320	nan
0.0ms	2×	body	160	nan

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: 24.8b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite67.0ms

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:

2.0ms	(pow x (/ 1.0 n))
8.0ms	(pow (+ x 1.0) (/ 1.0 n))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series452.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(pow x (/ 1.0 n))
138.0ms	(pow (+ x 1.0) (/ 1.0 n))
261.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify69.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune324.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow x (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

135×	`unpow-prod-down`
130×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
61×	`log-prod`
58×	`exp-sum`
45×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out` `difference-of-squares`
16×	`log-pow`
15×	`exp-prod`
8×	`fma-neg`
7×	`pow1`
6×	`add-exp-log` `distribute-lft-out--` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `div-inv`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 237

Calls

4 calls:

2.0ms	(pow x (/ 1.0 n))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
53.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
107.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

series734.0ms

Counts

4 → 12

Calls

4 calls:

59.0ms	(pow x (/ 1.0 n))
144.0ms	(pow (+ x 1.0) (/ 1.0 n))
266.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
264.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))

simplify83.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	835	3935
1	2477	2885
2	5001	2880

prune526.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 19.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ x 1.0) (/ 1.0 n))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

140×	`unpow-prod-down`
134×	`*-un-lft-identity`
112×	`prod-diff`
108×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
46×	`sqr-pow`
26×	`pow-unpow`
20×	`distribute-lft-out`
18×	`times-frac` `difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

4 → 240

Calls

4 calls:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
7.0ms	(pow (+ x 1.0) (/ 1.0 n))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
54.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series839.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(pow (+ x 1.0) (/ 1.0 n))
146.0ms	(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)))

simplify77.0ms

Algorithm

egg-herbie

Counts

252 → 252

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	542	4022
1	1694	2978
2	5001	2976

prune668.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.8b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.8b	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

162×	`*-un-lft-identity`
140×	`unpow-prod-down`
136×	`add-sqr-sqrt`
112×	`add-cube-cbrt` `prod-diff`
75×	`times-frac`
56×	`pow-unpow`
46×	`sqr-pow`
20×	`distribute-lft-out`
18×	`difference-of-squares`
16×	`fma-neg`
8×	`add-log-exp`
6×	`pow1` `add-exp-log` `distribute-lft-out--`
5×	`div-inv`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--`

Counts

4 → 270

Calls

4 calls:

10.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
6.0ms	(pow (+ x 1.0) (/ 1.0 n))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
55.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series861.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ (/ 1.0 n) 2))
152.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
278.0ms	(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify124.0ms

Algorithm

egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1195	4650
1	4018	3441
2	5001	3438

prune950.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 19.2b

regimes250.0ms

Accuracy

82.4% (1.5b remaining)

Error of 22.6b against oracle of 21.1b and baseline of 29.4b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	41
1	44	41

end0.0ms

sample3.5s

Algorithm

intervals

Results

1.4s	3131×	body	1280	valid
570.0ms	1610×	body	640	valid
267.0ms	4802×	body	80	valid
192.0ms	5101×	body	80	nan
184.0ms	815×	body	320	valid
136.0ms	2313×	body	80	overflowed
131.0ms	266×	body	640	nan
127.0ms	128×	body	1280	nan
65.0ms	470×	body	160	valid
39.0ms	162×	body	320	nan
12.0ms	95×	body	160	nan