Details

Time bar (total: 13.1s)

sample184.0ms

Algorithm
intervals
Results
71.0ms109×body1280valid
23.0ms46×body640valid
18.0ms165×body80valid
13.0ms163×body80nan
12.0ms21×body1280nan
9.0ms27×body320valid
7.0ms16×body640nan
5.0ms49×body80overflowed
4.0ms14×body320nan
3.0ms14×body160valid
2.0ms10×body160nan

simplify36.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.9b

localize9.0ms

Local error

Found 3 expressions with local error:

1.0b
(pow x (/ 1.0 n))
1.5b
(pow (+ x 1.0) (/ 1.0 n))
2.1b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite72.0ms

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))
54.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series457.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(pow x (/ 1.0 n))
140.0ms
(pow (+ x 1.0) (/ 1.0 n))
263.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify70.0ms

Algorithm
egg-herbie
Counts
158 → 158
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
06542164
121641642
250021637

prune336.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b
(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
1.0b
(pow x (/ 1.0 n))
1.5b
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
2.8b
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
32×*-un-lft-identity
30×add-sqr-sqrt add-cube-cbrt
27×times-frac
14×pow1 unpow-prod-down
12×pow-pow
9×add-exp-log
7×pow1/3 prod-diff
6×add-log-exp
4×cbrt-prod expm1-log1p-u pow-exp add-cbrt-cube log1p-expm1-u sqr-pow
3×pow-to-exp div-inv
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus fma-neg diff-log prod-exp flip-- distribute-lft-out
Counts
4 → 121
Calls
4 calls:
10.0ms
(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
2.0ms
(pow x (/ 1.0 n))
6.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
24.0ms
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series1.6s

Counts
4 → 12
Calls
4 calls:
359.0ms
(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
54.0ms
(pow x (/ 1.0 n))
310.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
836.0ms
(- (* (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify78.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
08431331
131611206
250011191

prune484.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.5b

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow x (/ 1.0 n))
1.5b
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
1.5b
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
3.1b
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
28×*-un-lft-identity
27×pow-unpow
24×add-sqr-sqrt add-cube-cbrt
18×times-frac
17×unpow-prod-down
7×pow1 add-exp-log prod-diff
6×add-log-exp
4×cbrt-prod expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u sqr-pow
3×pow-to-exp pow-exp
2×div-inv distribute-lft-out
1×sub-neg flip3-- fma-neg pow1/3 diff-log flip--
Counts
4 → 103
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
6.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
5.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
21.0ms
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

series1.3s

Counts
4 → 12
Calls
4 calls:
55.0ms
(pow x (/ 1.0 n))
319.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
152.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
727.0ms
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify79.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
07371057
12864955
25001945

prune434.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(pow x (/ 1.0 n))
1.5b
(pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
1.5b
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
3.1b
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
17×add-sqr-sqrt add-cube-cbrt unpow-prod-down
15×pow-unpow
9×times-frac
7×pow1 add-exp-log prod-diff
6×add-log-exp
4×cbrt-prod expm1-log1p-u pow-pow add-cbrt-cube log1p-expm1-u sqr-pow
3×pow-to-exp pow-exp
2×distribute-lft-out
1×sub-neg flip3-- fma-neg pow1/3 diff-log flip-- div-inv
Counts
4 → 91
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
6.0ms
(pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
5.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
24.0ms
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))) (pow x (/ 1.0 n)))

series1.7s

Counts
4 → 12
Calls
4 calls:
61.0ms
(pow x (/ 1.0 n))
450.0ms
(pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
152.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
1.1s
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n)))) (cbrt (/ 1.0 n)))) (pow x (/ 1.0 n)))

simplify95.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08971500
140391375
250011344

prune437.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.5b

regimes271.0ms

Accuracy

80.6% (1.6b remaining)

Error of 22.4b against oracle of 20.8b and baseline of 28.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06272
16272

end0.0ms

sample5.3s

Algorithm
intervals
Results
1.9s3091×body1280valid
753.0ms1579×body640valid
522.0ms4775×body80valid
411.0ms5152×body80nan
384.0ms600×body1280nan
294.0ms651×body640nan
289.0ms871×body320valid
128.0ms1281×body80overflowed
107.0ms487×body160valid
99.0ms331×body320nan
40.0ms216×body160nan