Details

Time bar (total: 49.5s)

sample155.0ms

Algorithm
intervals
Results
57.0ms81×body1280valid
52.0ms26×body2560valid
17.0ms56×body640valid
5.0ms33×body320valid
4.0ms93×body80valid
3.0ms88×body80nan
1.0ms12×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite906.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 281
Calls
4 calls:
423.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
155.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
294.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
342.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
230.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
194.0ms
(pow (+ 1.0 (/ i n)) n)
315.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify58.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012263285
150023166

prune781.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.6b

localize8.0ms

Local error

Found 3 expressions with local error:

1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite322.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
24×add-sqr-sqrt
23×*-un-lft-identity
19×add-cube-cbrt
16×add-exp-log
15×add-cbrt-cube
13×associate-/r*
6×cbrt-undiv div-exp
5×unpow-prod-down add-log-exp
4×pow1
3×pow-unpow div-inv difference-of-squares
2×flip3-- associate-*r/ prod-exp flip-- cbrt-unprod associate-/l/ sqr-pow
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log pow-exp clear-num associate-/r/ distribute-lft-out associate-/l* distribute-lft-out--
Counts
3 → 82
Calls
3 calls:
156.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
146.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series787.0ms

Counts
3 → 9
Calls
3 calls:
238.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
202.0ms
(pow (+ 1.0 (/ i n)) n)
346.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0572795
12705711
25001706

prune222.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize23.0ms

Local error

Found 4 expressions with local error:

6.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.3b
(pow (+ 1.0 (/ i n)) n)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
4569×times-frac
3397×add-sqr-sqrt
1975×*-un-lft-identity
1549×add-cube-cbrt
1356×unpow-prod-down
1344×difference-of-squares
1008×cube-prod
843×sqr-pow
210×distribute-lft-out--
145×div-inv
129×associate-/l*
42×difference-cubes
29×associate-/r/
19×add-exp-log
16×add-cbrt-cube
14×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv div-exp
7×pow1 pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out
2×div-sub
1×frac-2neg clear-num associate-/l/
Counts
4 → 1892
Calls
4 calls:
20.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
17.0ms
(pow (+ 1.0 (/ i n)) n)
17.0ms
(pow (+ 1.0 (/ i n)) n)
941.0ms
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

series7.4s

Counts
4 → 12
Calls
4 calls:
254.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
233.0ms
(pow (+ 1.0 (/ i n)) n)
202.0ms
(pow (+ 1.0 (/ i n)) n)
6.7s
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

simplify659.0ms

Algorithm
egg-herbie
Counts
1904 → 1904
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
0500179107

prune5.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 17.5b

localize21.0ms

Local error

Found 4 expressions with local error:

6.3b
(pow (+ 1.0 (/ i n)) n)
6.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.3b
(pow (+ 1.0 (/ i n)) (* 2 n))
11.6b
(- (/ (/ (pow (pow (+ 1.0 (/ i n)) n) 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)) (/ (/ (pow 1.0 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)))

rewrite15.4s

Algorithm
rewrite-expression-head
Rules
2154×times-frac
1628×add-sqr-sqrt
846×*-un-lft-identity
404×add-cube-cbrt
316×unpow-prod-down
260×cube-prod
209×distribute-lft-out-- difference-of-squares
107×sqr-pow
70×div-inv
62×associate-/r/
47×distribute-rgt-out--
30×flip3-+ flip-+
7×pow1 add-exp-log
6×add-log-exp
5×pow-unpow
4×add-cbrt-cube
3×pow-to-exp pow-pow pow-exp distribute-lft-out
1×sub-neg flip3-- diff-log frac-sub flip-- sub-div
Counts
4 → 529
Calls
4 calls:
16.0ms
(pow (+ 1.0 (/ i n)) n)
17.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
17.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
15.3s
(- (/ (/ (pow (pow (+ 1.0 (/ i n)) n) 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)) (/ (/ (pow 1.0 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)))

series8.2s

Counts
4 → 12
Calls
4 calls:
184.0ms
(pow (+ 1.0 (/ i n)) n)
188.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
185.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
7.6s
(- (/ (/ (pow (pow (+ 1.0 (/ i n)) n) 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)) (/ (/ (pow 1.0 3) (+ (* 1.0 (+ 1.0 (pow (+ 1.0 (/ i n)) n))) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n)))

simplify226.0ms

Algorithm
egg-herbie
Counts
541 → 541
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
0176526117
1500225507

prune1.6s

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 14.9b

regimes226.0ms

Accuracy

54.3% (12.1b remaining)

Error of 28.6b against oracle of 16.5b and baseline of 42.9b

bsearch467.0ms

Steps
ItersRangePoint
8
1.537653969837454
6330.810310882262
1.5611070050253792
6
7.80304287794127e-202
5.2230152784006795e-201
4.88009604790167e-201
8
-6.252648529454302e-209
-4.5644137463814576e-212
-5.957104773494907e-209
8
-3.87394257886499e-12
-2.117072550125069e-15
-3.796684874032534e-12

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
099109
199109

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s1015×body2560valid
1.7s2487×body1280valid
441.0ms1605×body640valid
135.0ms849×body320valid
123.0ms3015×body80valid
65.0ms2238×body80nan
46.0ms469×body160valid
22.0ms6×body5120valid