Details

Time bar (total: 18.9s)

sample245.0ms

Algorithm
intervals
Results
52.0ms77×body1280nan
52.0ms110×body1280valid
32.0ms74×body640nan
27.0ms48×body10240exit
24.0ms73×body640valid
11.0ms40×body320nan
11.0ms234×body80nan
7.0ms32×body320valid
5.0ms104×body80valid
2.0ms14×body160nan
1.0ms11×body160valid

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1346
2806
32366
48686
550016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 35.1b

localize8.0ms

Local error

Found 1 expressions with local error:

2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
10×unpow-prod-down
9×difference-of-squares
8×*-un-lft-identity
6×sqr-pow
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 24
Calls
1 calls:
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series271.0ms

Counts
1 → 3
Calls
1 calls:
271.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify74.0ms

Algorithm
egg-herbie
Counts
27 → 27
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0222326
1594313
22745307
35003307

prune83.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 22.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
40×unpow-prod-down
36×difference-of-squares
33×*-un-lft-identity
24×sqr-pow
15×cbrt-prod
12×distribute-lft-out--
10×add-log-exp
5×add-cube-cbrt
4×pow1 add-exp-log flip3-- add-cbrt-cube flip-- distribute-lft-out
3×sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 97
Calls
4 calls:
9.0ms
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.4s

Counts
4 → 12
Calls
4 calls:
566.0ms
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
272.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
271.0ms
(- (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)))

simplify121.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (25.0ms)

IterNodesCost
03621439
19731385
243991363
350011363

prune418.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 22.2b

localize28.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
46×add-sqr-sqrt
30×unpow-prod-down difference-of-squares
23×*-un-lft-identity
19×sqr-pow
10×add-log-exp
7×distribute-lft-out--
5×add-cube-cbrt
4×pow1 add-exp-log cbrt-prod add-cbrt-cube
3×sub-neg flip3-- diff-log sqrt-prod flip-- distribute-lft-out
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 87
Calls
4 calls:
10.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
10.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
11.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

series3.7s

Counts
4 → 12
Calls
4 calls:
2.7s
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
283.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
277.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
440.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n)))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
05641424
116931352
250011335

prune555.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b
(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
38×difference-of-squares
37×unpow-prod-down
27×sqrt-prod
23×*-un-lft-identity
21×sqr-pow
10×add-log-exp
7×distribute-lft-out--
5×add-cube-cbrt
4×pow1 add-exp-log cbrt-prod add-cbrt-cube
3×sub-neg flip3-- diff-log flip-- distribute-lft-out
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 95
Calls
4 calls:
10.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
19.0ms
(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

series3.8s

Counts
4 → 12
Calls
4 calls:
2.7s
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow (sqrt x) (/ 1.0 n))))
276.0ms
(- (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)))
468.0ms
(- (sqrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (pow (sqrt (sqrt x)) (/ 1.0 n)))

simplify61.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
06601712
120681634
250011631

prune671.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.2b

regimes273.0ms

Accuracy

81.9% (2.0b remaining)

Error of 24.0b against oracle of 22.1b and baseline of 33.0b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07280
17480
27480

end0.0ms

sample6.9s

Algorithm
intervals
Results
1.8s3923×body1280valid
1.4s2258×body1280nan
763.0ms1811×body640nan
637.0ms1446×body10240exit
603.0ms1792×body640valid
437.0ms918×body320nan
271.0ms6286×body80nan
195.0ms891×body320valid
159.0ms3191×body80valid
75.0ms478×body160nan
64.0ms466×body160valid