Details

sample134.0ms

Algorithm

intervals

Results

38.0ms	83×	body	1280	valid
19.0ms	55×	body	640	valid
19.0ms	26×	body	10240	exit
9.0ms	171×	body	80	valid
8.0ms	19×	body	1280	nan
5.0ms	18×	body	640	nan
5.0ms	144×	body	80	nan
5.0ms	25×	body	320	valid
3.0ms	13×	body	320	nan
1.0ms	11×	body	160	valid
0.0ms	2×	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: 30.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite116.0ms

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))
10.0ms	(pow (+ x 1.0) (/ 1.0 n))
95.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series487.0ms

Counts

3 → 9

Calls

3 calls:

57.0ms	(pow x (/ 1.0 n))
150.0ms	(pow (+ x 1.0) (/ 1.0 n))
279.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify64.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (47.0ms)

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

prune327.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 22.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(pow x (/ 1.0 n))
1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite300.0ms

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))
12.0ms	(pow (+ x 1.0) (/ 1.0 n))
177.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
94.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series786.0ms

Counts

4 → 12

Calls

4 calls:

62.0ms	(pow x (/ 1.0 n))
147.0ms	(pow (+ x 1.0) (/ 1.0 n))
290.0ms	(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
287.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify79.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (49.0ms)

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

prune529.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.5b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite573.0ms

Algorithm

rewrite-expression-head

Rules

256×	`unpow-prod-down`
224×	`prod-diff`
222×	`*-un-lft-identity`
182×	`add-sqr-sqrt`
134×	`add-cube-cbrt`
128×	`log-prod`
122×	`sqrt-prod`
116×	`exp-sum`
86×	`sqr-pow`
36×	`log-pow` `difference-of-squares`
34×	`distribute-lft-out`
32×	`sqrt-pow1`
30×	`exp-prod`
16×	`fma-neg`
12×	`distribute-lft-out--`
8×	`pow1` `add-log-exp`
6×	`add-exp-log`
4×	`expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `flip3--` `pow1/2` `exp-diff` `sqrt-div` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 366

Calls

4 calls:

91.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
91.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
183.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
183.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.5s

Counts

4 → 12

Calls

4 calls:

293.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
290.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
471.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))
468.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify107.0ms

Algorithm

egg-herbie

Counts

378 → 378

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	711	8170
1	1720	6498
2	5001	5684

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.5b	(pow (+ x 1.0) (/ 1.0 n))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

rewrite393.0ms

Algorithm

rewrite-expression-head

Rules

198×	`unpow-prod-down`
178×	`*-un-lft-identity`
168×	`prod-diff`
145×	`add-sqr-sqrt`
109×	`add-cube-cbrt`
66×	`sqr-pow`
64×	`log-prod`
61×	`sqrt-prod`
58×	`exp-sum`
27×	`distribute-lft-out` `difference-of-squares`
18×	`log-pow`
16×	`sqrt-pow1` `fma-neg`
15×	`exp-prod`
13×	`pow-unpow`
9×	`times-frac` `distribute-lft-out--`
8×	`add-log-exp`
7×	`pow1`
6×	`add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg`
2×	`flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `log-div` `pow-pow` `pow1/2` `exp-diff` `sqrt-div` `rem-log-exp` `pow-exp` `div-inv`

Counts

4 → 303

Calls

4 calls:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
91.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
180.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

series1.2s

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
472.0ms	(log (sqrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify91.0ms

Algorithm

egg-herbie

Counts

315 → 315

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	840	6096
1	2235	4738
2	5002	4336

prune804.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.4b

regimes228.0ms

Accuracy

84.4% (1.3b remaining)

Error of 23.1b against oracle of 21.8b and baseline of 30.2b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	58
1	51	58

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3129×	body	1280	valid
575.0ms	1680×	body	640	valid
420.0ms	1075×	body	10240	exit
290.0ms	663×	body	1280	nan
250.0ms	4723×	body	80	valid
207.0ms	654×	body	640	nan
188.0ms	5045×	body	80	nan
185.0ms	847×	body	320	valid
63.0ms	343×	body	320	nan
60.0ms	446×	body	160	valid
20.0ms	185×	body	160	nan