Details

Time bar (total: 12.8s)

sample187.0ms

Algorithm
intervals
Results
69.0ms109×body1280valid
24.0ms46×body640valid
18.0ms165×body80valid
14.0ms163×body80nan
12.0ms21×body1280nan
12.0ms27×body320valid
7.0ms16×body640nan
5.0ms49×body80overflowed
4.0ms14×body320nan
3.0ms14×body160valid
2.0ms10×body160nan

simplify34.0ms

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: 30.9b

localize12.0ms

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)))

rewrite52.0ms

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))
6.0ms
(pow (+ x 1.0) (/ 1.0 n))
41.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series467.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(pow x (/ 1.0 n))
138.0ms
(pow (+ x 1.0) (/ 1.0 n))
272.0ms
(- (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)

IterNodesCost
0476639
11600623
25001609

prune252.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.1b

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)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
30×*-un-lft-identity
28×add-sqr-sqrt add-cube-cbrt
27×times-frac
14×pow1
12×pow-pow
11×unpow-prod-down
9×add-exp-log
7×pow1/3
6×add-log-exp
4×cbrt-prod pow-exp add-cbrt-cube
3×pow-to-exp div-inv sqr-pow
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 sub-neg flip3-- pow-plus diff-log prod-exp flip-- distribute-lft-out
Counts
4 → 105
Calls
4 calls:
9.0ms
(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))
19.0ms
(- (* (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:
354.0ms
(pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n))
61.0ms
(pow x (/ 1.0 n))
308.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
841.0ms
(- (* (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)))

simplify71.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
07321074
12678993
25001990

prune429.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.0b

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)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
27×pow-unpow
26×*-un-lft-identity
22×add-sqr-sqrt add-cube-cbrt
18×times-frac
14×unpow-prod-down
7×pow1 add-exp-log
6×add-log-exp
4×cbrt-prod pow-pow add-cbrt-cube
3×pow-to-exp pow-exp sqr-pow
2×div-inv distribute-lft-out
1×sub-neg flip3-- pow1/3 diff-log flip--
Counts
4 → 87
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)))
15.0ms
(- (* (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:
64.0ms
(pow x (/ 1.0 n))
311.0ms
(pow (cbrt (+ x 1.0)) (/ 1.0 n))
150.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
735.0ms
(- (* (pow (+ x 1.0) (* 2/3 (/ 1.0 n))) (pow (cbrt (+ x 1.0)) (/ 1.0 n))) (pow x (/ 1.0 n)))

simplify60.0ms

Algorithm
egg-herbie
Counts
99 → 99
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0635822
12384767
25001763

prune376.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.0b

localize25.0ms

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)))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
19×*-un-lft-identity
15×add-sqr-sqrt add-cube-cbrt pow-unpow
14×unpow-prod-down
9×times-frac
7×pow1 add-exp-log
6×add-log-exp
4×cbrt-prod pow-pow add-cbrt-cube
3×pow-to-exp pow-exp sqr-pow
2×distribute-lft-out
1×sub-neg flip3-- pow1/3 diff-log flip-- div-inv
Counts
4 → 75
Calls
4 calls:
2.0ms
(pow x (/ 1.0 n))
5.0ms
(pow (cbrt (+ x 1.0)) (* (cbrt (/ 1.0 n)) (cbrt (/ 1.0 n))))
5.0ms
(pow (+ x 1.0) (* 2/3 (/ 1.0 n)))
21.0ms
(- (* (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:
55.0ms
(pow x (/ 1.0 n))
447.0ms
(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)))

simplify80.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
07951193
135211115
250021113

prune368.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.0b

regimes210.0ms

Accuracy

81.3% (1.6b remaining)

Error of 22.1b against oracle of 20.5b and baseline of 28.9b

bsearch1.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05470
15470

end0.0ms

sample5.4s

Algorithm
intervals
Results
1.9s3091×body1280valid
773.0ms1579×body640valid
512.0ms4775×body80valid
401.0ms5152×body80nan
384.0ms600×body1280nan
299.0ms651×body640nan
293.0ms871×body320valid
132.0ms1281×body80overflowed
113.0ms487×body160valid
96.0ms331×body320nan
40.0ms216×body160nan