Details

sample158.0ms

Algorithm

intervals

Results

56.0ms	118×	body	1280	valid
23.0ms	34×	body	10240	exit
14.0ms	22×	body	1280	nan
13.0ms	45×	body	640	valid
9.0ms	154×	body	80	valid
8.0ms	20×	body	640	nan
6.0ms	166×	body	80	nan
4.0ms	19×	body	320	valid
2.0ms	14×	body	160	valid
2.0ms	8×	body	320	nan
0.0ms	5×	body	160	nan

simplify34.0ms

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: 31.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite121.0ms

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:

4.0ms	(pow x (/ 1.0 n))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series455.0ms

Counts

3 → 9

Calls

3 calls:

60.0ms	(pow x (/ 1.0 n))
258.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
137.0ms	(pow (+ x 1.0) (/ 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

prune340.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.4b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite315.0ms

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:

4.0ms	(pow x (/ 1.0 n))
186.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
98.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series736.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(pow x (/ 1.0 n))
268.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
269.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
140.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify84.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (50.0ms)

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

prune530.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.1b

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

128×	`log-prod`
122×	`cbrt-prod`
116×	`*-un-lft-identity` `exp-sum`
112×	`unpow-prod-down` `prod-diff`
84×	`add-sqr-sqrt` `add-cube-cbrt`
32×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac`
16×	`distribute-lft-out`
8×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `log-pow` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `sub-neg` `log-div` `cbrt-div` `pow-pow` `exp-diff` `pow1/3` `rem-log-exp` `pow-exp` `div-inv`

Counts

4 → 214

Calls

4 calls:

84.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
87.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.2s

Counts

4 → 12

Calls

4 calls:

445.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
442.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
141.0ms	(pow (+ x 1.0) (/ 1.0 n))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify77.0ms

Algorithm

egg-herbie

Counts

226 → 226

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	680	4636
1	1733	3996
2	5002	3348

prune737.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 22.0b

localize18.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.4b	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))

rewrite226.0ms

Algorithm

rewrite-expression-head

Rules

126×	`unpow-prod-down`
125×	`*-un-lft-identity`
112×	`prod-diff`
96×	`add-sqr-sqrt`
84×	`add-cube-cbrt`
64×	`log-prod`
61×	`cbrt-prod`
58×	`exp-sum`
39×	`sqr-pow`
26×	`pow-unpow`
18×	`times-frac` `distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-out--`
2×	`pow-to-exp` `sub-neg` `pow-pow` `pow-exp` `log-pow` `div-inv`
1×	`log-div` `cbrt-div` `flip3--` `exp-diff` `pow1/3` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 227

Calls

4 calls:

97.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
89.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))
11.0ms	(pow (+ x 1.0) (/ 1.0 n))

series1.0s

Counts

4 → 12

Calls

4 calls:

277.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
448.0ms	(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
148.0ms	(pow (+ x 1.0) (/ 1.0 n))
143.0ms	(pow (+ x 1.0) (/ 1.0 n))

simplify93.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	794	4325
1	2158	3487
2	5002	3084

prune712.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.0b

regimes291.0ms

Accuracy

81.1% (1.7b remaining)

Error of 22.1b against oracle of 20.4b and baseline of 29.2b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	24
1	43	24

end0.0ms

sample4.4s

Algorithm

intervals

Results

1.4s	3151×	body	1280	valid
577.0ms	1640×	body	640	valid
508.0ms	1186×	body	10240	exit
291.0ms	627×	body	1280	nan
265.0ms	4753×	body	80	valid
221.0ms	645×	body	640	nan
197.0ms	5039×	body	80	nan
188.0ms	833×	body	320	valid
73.0ms	368×	body	320	nan
60.0ms	426×	body	160	valid
20.0ms	174×	body	160	nan