Details

sample132.0ms

Algorithm

intervals

Results

45.0ms	98×	body	1280	valid
16.0ms	42×	body	640	valid
14.0ms	32×	body	10240	exit
10.0ms	168×	body	80	nan
7.0ms	33×	body	320	valid
7.0ms	146×	body	80	valid
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

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: 24.7b

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)))

rewrite65.0ms

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))
48.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series497.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(pow x (/ 1.0 n))
160.0ms	(pow (+ x 1.0) (/ 1.0 n))
280.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify73.0ms

Algorithm

egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 2 (48.0ms)

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

prune331.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 18.3b

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)))

rewrite173.0ms

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:

6.0ms	(pow (+ x 1.0) (/ 1.0 n))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
52.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series993.0ms

Counts

4 → 12

Calls

4 calls:

153.0ms	(pow (+ x 1.0) (/ 1.0 n))
278.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
281.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 2 (44.0ms)

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

prune764.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.3b

localize29.0ms

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))

rewrite295.0ms

Algorithm

rewrite-expression-head

Rules

866×	`unpow-prod-down`
552×	`prod-diff`
453×	`*-un-lft-identity`
395×	`add-sqr-sqrt`
382×	`cube-prod`
291×	`add-cube-cbrt`
222×	`sqr-pow`
82×	`difference-of-squares`
65×	`distribute-lft-out`
43×	`cube-mult` `unpow3`
38×	`fma-neg`
19×	`distribute-lft-out--`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`difference-cubes` `pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 764

Calls

4 calls:

5.0ms	(pow (+ x 1.0) (/ 1.0 n))
51.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
49.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
134.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))

series1.2s

Counts

4 → 12

Calls

4 calls:

158.0ms	(pow (+ x 1.0) (/ 1.0 n))
290.0ms	(- (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)))
425.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))

simplify301.0ms

Algorithm

egg-herbie

Counts

776 → 776

Iterations

Useful iterations: 2 (143.0ms)

Iter	Nodes	Cost
0	1298	17503
1	4218	12139
2	5001	12138

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 18.2b

localize32.0ms

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))))

rewrite668.0ms

Algorithm

rewrite-expression-head

Rules

1576×	`unpow-prod-down`
992×	`prod-diff`
765×	`*-un-lft-identity`
756×	`cube-prod`
679×	`add-sqr-sqrt`
495×	`add-cube-cbrt`
445×	`log-prod`
442×	`exp-sum`
395×	`sqr-pow`
146×	`difference-of-squares`
108×	`distribute-lft-out`
85×	`cube-mult` `unpow3`
82×	`log-pow`
81×	`exp-prod`
38×	`fma-neg`
32×	`distribute-lft-out--`
10×	`add-log-exp`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `sub-neg` `add-cbrt-cube` `log1p-expm1-u`
3×	`flip3--` `diff-log` `flip--`
2×	`difference-cubes`
1×	`log-div` `exp-diff` `rem-log-exp`

Counts

4 → 1272

Calls

4 calls:

50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
50.0ms	(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
132.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))
317.0ms	(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:

284.0ms	(- (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)))
422.0ms	(- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))
415.0ms	(log (exp (- (pow (pow (+ x 1.0) (/ 1.0 n)) 3) (pow (pow x (/ 1.0 n)) 3))))

simplify418.0ms

Algorithm

egg-herbie

Counts

1284 → 1284

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1662	30758
1	4365	20686
2	5001	20686

prune1.8s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 18.2b

regimes240.0ms

Accuracy

84.6% (1.2b remaining)

Error of 22.2b against oracle of 21.0b and baseline of 29.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	39
1	45	39

end0.0ms

sample4.2s

Algorithm

intervals

Results

1.4s	3155×	body	1280	valid
554.0ms	1216×	body	10240	exit
543.0ms	1561×	body	640	valid
291.0ms	635×	body	1280	nan
256.0ms	4871×	body	80	valid
212.0ms	654×	body	640	nan
195.0ms	5223×	body	80	nan
188.0ms	864×	body	320	valid
67.0ms	362×	body	320	nan
61.0ms	443×	body	160	valid
22.0ms	208×	body	160	nan