Details

Time bar (total: 15.7s)

sample201.0ms

Algorithm
intervals
Results
60.0ms125×body1280valid
37.0ms64×body1280nan
21.0ms50×body640nan
19.0ms51×body10240exit
16.0ms51×body640valid
8.0ms184×body80nan
7.0ms28×body320nan
6.0ms117×body80valid
5.0ms23×body320valid
2.0ms14×body160nan
2.0ms11×body160valid

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.2b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (+ x 1.0) (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite32.0ms

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:
6.0ms
(pow (+ x 1.0) (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
15.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series501.0ms

Counts
3 → 9
Calls
3 calls:
149.0ms
(pow (+ x 1.0) (/ 1.0 n))
63.0ms
(pow x (/ 1.0 n))
289.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify72.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
06542164
121641642
250021637

prune343.0ms

Filtered
158 candidates to 95 candidates (60.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.9b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
208×unpow-prod-down
177×*-un-lft-identity
168×prod-diff
149×add-sqr-sqrt
101×add-cube-cbrt
72×sqr-pow
36×difference-of-squares
28×distribute-lft-out
24×fma-neg
15×cbrt-prod
12×distribute-lft-out--
10×add-log-exp
4×pow1 add-exp-log expm1-log1p-u flip3-- add-cbrt-cube flip-- log1p-expm1-u
3×sub-neg diff-log
2×cbrt-div
1×pow1/3
Counts
4 → 297
Calls
4 calls:
9.0ms
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
11.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series1.5s

Counts
4 → 12
Calls
4 calls:
585.0ms
(cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))
299.0ms
(- (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)))
292.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify91.0ms

Algorithm
egg-herbie
Counts
309 → 309
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05545996
115344421
250014401

prune755.0ms

Filtered
309 candidates to 157 candidates (50.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.6b
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
202×unpow-prod-down
177×*-un-lft-identity
168×prod-diff
137×add-sqr-sqrt
101×add-cube-cbrt
66×sqr-pow
31×distribute-lft-out
27×difference-of-squares
24×fma-neg
10×add-log-exp
9×distribute-lft-out--
6×cbrt-prod
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×sub-neg flip3-- diff-log flip--
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 288
Calls
4 calls:
9.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
11.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

series1.5s

Counts
4 → 12
Calls
4 calls:
582.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
292.0ms
(- (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)))
291.0ms
(- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))

simplify125.0ms

Algorithm
egg-herbie
Counts
300 → 300
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08376206
125274461
250024449

prune1.0s

Filtered
300 candidates to 148 candidates (49.3%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.8b

localize32.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
2.5b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
4.3b
(- (* (* (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

rewrite66.0ms

Algorithm
rewrite-expression-head
Rules
139×unpow-prod-down
124×*-un-lft-identity
119×prod-diff
95×add-sqr-sqrt
71×add-cube-cbrt
45×sqr-pow
22×distribute-lft-out
18×difference-of-squares
17×fma-neg
10×add-log-exp
6×cbrt-prod distribute-lft-out--
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×sub-neg flip3-- diff-log flip--
2×cbrt-div
1×flip3-+ pow1/3 flip-+
Counts
4 → 220
Calls
4 calls:
11.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
11.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
12.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
21.0ms
(- (* (* (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

series1.6s

Counts
4 → 12
Calls
4 calls:
567.0ms
(cbrt (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))))
287.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
485.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))
299.0ms
(- (* (* (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (cbrt (pow (+ x 1.0) (/ (/ 1.0 n) 2)))) (pow x (/ (/ 1.0 n) 2)))

simplify107.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07384753
124553345
250023148

prune900.0ms

Filtered
232 candidates to 118 candidates (50.9%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.8b

regimes307.0ms

Accuracy

80.4% (2.0b remaining)

Error of 24.0b against oracle of 21.9b and baseline of 32.3b

bsearch1.0ms

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06883
16883

end0.0ms

sample6.4s

Algorithm
intervals
Results
1.8s3865×body1280valid
1.2s2164×body1280nan
718.0ms1824×body640nan
622.0ms1449×body10240exit
588.0ms1754×body640valid
262.0ms6127×body80nan
217.0ms920×body320nan
198.0ms890×body320valid
154.0ms3154×body80valid
63.0ms445×body160nan
60.0ms432×body160valid