Details

sample131.0ms

Algorithm

intervals

Results

45.0ms	98×	body	1280	valid
19.0ms	42×	body	640	valid
14.0ms	32×	body	10240	exit
7.0ms	33×	body	320	valid
7.0ms	146×	body	80	valid
6.0ms	168×	body	80	nan
6.0ms	21×	body	640	nan
6.0ms	16×	body	1280	nan
2.0ms	13×	body	160	valid
2.0ms	9×	body	320	nan
1.0ms	8×	body	160	nan

simplify35.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	6
1	34	6
2	80	6
3	236	6
4	868	6
5	5001	6

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.7b

localize8.0ms

Local error

Found 3 expressions with local error:

0.7b	(pow x (/ 1.0 n))
1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
26×	`pow-unpow`
19×	`add-cube-cbrt`
18×	`times-frac`
17×	`unpow-prod-down`
9×	`difference-of-squares`
8×	`sqr-pow`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`add-cbrt-cube` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 79

Calls

3 calls:

2.0ms	(pow x (/ 1.0 n))
5.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series465.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(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)))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	476	639
1	1600	623
2	5001	609

prune233.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.1b

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

48×	`add-sqr-sqrt`
35×	`*-un-lft-identity`
34×	`unpow-prod-down`
27×	`difference-of-squares`
19×	`sqr-pow`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube` `distribute-lft-out`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 100

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
40.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
43.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series970.0ms

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)))
278.0ms	(- (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)))

simplify42.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	359	1142
1	1141	1101
2	5002	1078

prune414.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.1b

localize30.0ms

Local error

Found 4 expressions with local error:

1.2b	(pow (+ x 1.0) (/ 1.0 n))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))

rewrite205.0ms

Algorithm

rewrite-expression-head

Rules

132×	`unpow-prod-down`
116×	`add-sqr-sqrt`
82×	`difference-of-squares`
61×	`sqr-pow`
60×	`cube-prod`
58×	`*-un-lft-identity`
19×	`distribute-lft-out--`
13×	`pow-unpow`
12×	`add-cube-cbrt`
10×	`add-log-exp`
9×	`times-frac`
7×	`distribute-lft-out`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 166

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
106.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))

series1.1s

Counts

4 → 12

Calls

4 calls:

145.0ms	(pow (+ x 1.0) (/ 1.0 n))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
301.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
404.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))

simplify79.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	605	2386
1	1868	2340
2	5002	2323

prune742.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
1.6b	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))
1.6b	(log (exp (- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))))

rewrite478.0ms

Algorithm

rewrite-expression-head

Rules

236×	`unpow-prod-down`
190×	`add-sqr-sqrt`
146×	`difference-of-squares`
120×	`cube-prod`
108×	`sqr-pow`
82×	`log-pow`
81×	`exp-prod`
80×	`*-un-lft-identity`
32×	`distribute-lft-out--`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`add-exp-log` `sub-neg` `add-cbrt-cube`
3×	`flip3--` `diff-log` `flip--`
2×	`difference-cubes` `exp-sum`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 234

Calls

4 calls:

41.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
42.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
106.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))
272.0ms	(log (exp (- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))))

series1.4s

Counts

4 → 12

Calls

4 calls:

283.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
285.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
415.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))
405.0ms	(log (exp (- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))))

simplify84.0ms

Algorithm

egg-herbie

Counts

246 → 246

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	607	3120
1	1745	3047
2	5002	3027

prune910.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.1b

regimes232.0ms

Accuracy

85.1% (1.3b remaining)

Error of 21.9b against oracle of 20.6b and baseline of 29.0b

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	37
1	37	37

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3155×	body	1280	valid
535.0ms	1216×	body	10240	exit
534.0ms	1561×	body	640	valid
287.0ms	635×	body	1280	nan
255.0ms	4871×	body	80	valid
218.0ms	654×	body	640	nan
189.0ms	5223×	body	80	nan
187.0ms	864×	body	320	valid
67.0ms	362×	body	320	nan
64.0ms	443×	body	160	valid
23.0ms	208×	body	160	nan