Details

sample149.0ms

Algorithm

intervals

Results

52.0ms	123×	body	1280	valid
19.0ms	40×	body	10240	exit
16.0ms	53×	body	640	valid
9.0ms	26×	body	1280	nan
8.0ms	150×	body	80	valid
8.0ms	24×	body	640	nan
7.0ms	199×	body	80	nan
5.0ms	26×	body	320	valid
2.0ms	9×	body	320	nan
2.0ms	12×	body	160	valid
1.0ms	7×	body	160	nan

simplify39.0ms

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: 30.4b

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

70×	`unpow-prod-down`
67×	`*-un-lft-identity`
56×	`prod-diff`
54×	`add-sqr-sqrt`
42×	`add-cube-cbrt`
23×	`sqr-pow`
13×	`pow-unpow`
10×	`distribute-lft-out`
9×	`times-frac` `difference-of-squares`
8×	`fma-neg`
4×	`add-log-exp`
3×	`pow1` `add-exp-log` `distribute-lft-out--`
2×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `diff-log` `pow-exp` `flip--` `div-inv`

Counts

2 → 120

Calls

2 calls:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series418.0ms

Counts

2 → 6

Calls

2 calls:

148.0ms	(pow (+ x 1.0) (/ 1.0 n))
270.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify58.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	542	2011
1	1694	1489
2	5001	1488

prune250.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.7b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (+ x 1.0) (/ 1.0 n))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite296.0ms

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:

10.0ms	(pow (+ x 1.0) (/ 1.0 n))
90.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
92.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series993.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(pow (+ x 1.0) (/ 1.0 n))
281.0ms	(- (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)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify84.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (42.0ms)

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

prune761.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.7b

localize20.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

264×	`unpow-prod-down`
224×	`*-un-lft-identity` `prod-diff`
180×	`add-sqr-sqrt`
132×	`add-cube-cbrt`
88×	`sqr-pow`
36×	`distribute-lft-out` `difference-of-squares`
32×	`fma-neg`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 360

Calls

4 calls:

88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
88.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
89.0ms	(- (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)))

series1.1s

Counts

4 → 12

Calls

4 calls:

275.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
286.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
280.0ms	(- (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)))

simplify91.0ms

Algorithm

egg-herbie

Counts

372 → 372

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	413	7360
1	1182	5280
2	5002	5264

prune941.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.7b

localize25.0ms

Local error

Found 4 expressions with local error:

1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.7b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.0b	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

rewrite380.0ms

Algorithm

rewrite-expression-head

Rules

270×	`unpow-prod-down`
245×	`prod-diff`
233×	`*-un-lft-identity`
199×	`add-sqr-sqrt`
146×	`add-cube-cbrt`
92×	`sqr-pow`
73×	`sqrt-prod`
39×	`difference-of-squares`
35×	`fma-neg` `distribute-lft-out`
12×	`add-log-exp`
10×	`distribute-lft-out--`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

4 → 385

Calls

4 calls:

87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
87.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
98.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

series1.2s

Counts

4 → 12

Calls

4 calls:

280.0ms	(- (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)))
282.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
401.0ms	(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))

simplify128.0ms

Algorithm

egg-herbie

Counts

397 → 397

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	765	8539
1	2199	5995
2	5002	5954

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 20.7b

regimes394.0ms

Accuracy

84.1% (1.3b remaining)

Error of 22.7b against oracle of 21.4b and baseline of 29.8b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	67	112
1	67	112

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3146×	body	1280	valid
536.0ms	1612×	body	640	valid
505.0ms	1184×	body	10240	exit
285.0ms	632×	body	1280	nan
245.0ms	4730×	body	80	valid
215.0ms	660×	body	640	nan
189.0ms	867×	body	320	valid
184.0ms	5206×	body	80	nan
65.0ms	354×	body	320	nan
56.0ms	432×	body	160	valid
17.0ms	166×	body	160	nan