Details

Time bar (total: 2.5m)

sample35.3s

Algorithm
intervals
Results
55.0ms74×body1280valid
50.0ms22×body2560valid
17.0ms39×body640valid
7.0ms113×body80valid
6.0ms26×body320valid
4.0ms94×body80nan
2.0ms17×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 37.8b

Counts
2 → 1

localize9.0ms

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)
6.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
9.7b
(pow (+ 1.0 (/ i n)) n)

rewrite76.0ms

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:
28.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
6.0ms
(pow (+ 1.0 (/ i n)) n)

series181.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
34.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
55.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))
30.0ms
(pow (+ 1.0 (/ i n)) n)

simplify60.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
012263285
150013166

prune573.0ms

Filtered
293 candidates to 223 candidates (23.9%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New2858293
Fresh000
Picked101
Done000
Total2868294

Merged error: 18.7b

Counts
294 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

1.8b
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0)))
6.7b
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
9.7b
(pow (+ 1.0 (/ i n)) (* 2 n))
9.7b
(pow (+ 1.0 (/ i n)) n)

rewrite79.0ms

Algorithm
rewrite-expression-head
Rules
717×times-frac
524×*-un-lft-identity
294×add-sqr-sqrt add-cube-cbrt
115×distribute-lft-out
38×div-inv
29×associate-/r/
22×associate-/l*
18×add-exp-log
16×add-cbrt-cube
15×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv unpow-prod-down div-exp add-log-exp
6×pow1 div-sub
4×pow-unpow
2×neg-sub0 pow-to-exp associate-+r- pow-pow unsub-neg pow-exp sum-log sqr-pow
1×+-commutative frac-2neg neg-log clear-num associate-/l/
Counts
4 → 394
Calls
4 calls:
10.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0)))
28.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
6.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
6.0ms
(pow (+ 1.0 (/ i n)) n)

series556.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0)))
466.0ms
(/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (neg (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
31.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
25.0ms
(pow (+ 1.0 (/ i n)) n)

simplify124.0ms

Algorithm
egg-herbie
Counts
406 → 406
Iterations

Useful iterations: 1 (38.0ms)

IterNodesCost
0186410059
150019637

prune1.4s

Filtered
406 candidates to 251 candidates (38.2%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New4015406
Fresh257
Picked101
Done000
Total40410414

Merged error: 18.6b

Counts
414 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

6.7b
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (neg (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
9.7b
(pow (+ 1.0 (/ i n)) (* 2 n))
9.7b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
9.7b
(pow (+ 1.0 (/ i n)) n)

rewrite203.0ms

Algorithm
rewrite-expression-head
Rules
3405×times-frac
2121×*-un-lft-identity
1275×add-sqr-sqrt add-cube-cbrt
423×distribute-lft-out
150×div-inv
141×associate-/r/
78×associate-/l*
70×flip3-+ flip-+
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
9×div-sub
7×pow1
5×pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp sqr-pow
1×neg-sub0 associate-+r- frac-2neg unsub-neg clear-num associate-/l/
Counts
4 → 1182
Calls
4 calls:
61.0ms
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (neg (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
6.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
8.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
6.0ms
(pow (+ 1.0 (/ i n)) n)

series4.1s

Counts
4 → 12
Calls
4 calls:
4.1s
(/ (/ (/ (+ (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (neg (* (* 1.0 1.0) (* 1.0 1.0)))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))
29.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
26.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
25.0ms
(pow (+ 1.0 (/ i n)) n)

simplify467.0ms

Algorithm
egg-herbie
Counts
1194 → 1194
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
0500154232

prune17.6s

Filtered
1194 candidates to 690 candidates (42.2%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New118681194
Fresh279
Picked101
Done000
Total1189151204

Merged error: 18.6b

Counts
1204 → 15

localize26.0ms

Local error

Found 4 expressions with local error:

9.7b
(pow (+ 1.0 (/ i n)) n)
9.7b
(pow (+ 1.0 (/ i n)) (* 2 n))
9.7b
(pow (+ 1.0 (/ i n)) (* 2 n))
9.7b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
16×unpow-prod-down
9×add-sqr-sqrt add-cube-cbrt
8×pow1 add-exp-log
6×pow-unpow
4×pow-to-exp pow-pow pow-exp add-cbrt-cube distribute-lft-out add-log-exp sqr-pow
Counts
4 → 66
Calls
4 calls:
6.0ms
(pow (+ 1.0 (/ i n)) n)
6.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
6.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
6.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))

series104.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(pow (+ 1.0 (/ i n)) n)
26.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
25.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
27.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))

simplify130.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 3 (123.0ms)

IterNodesCost
0245501
11105460
24301447
35001431

prune259.0ms

Filtered
78 candidates to 59 candidates (24.4%)
Pruning

15 alts after pruning (15 fresh and 0 done)

PrunedKeptTotal
New74478
Fresh31114
Picked101
Done000
Total781593

Merged error: 17.8b

Counts
93 → 15

regimes473.0ms

bsearch1.4m

Steps
ItersRangePoint
8
91.72138886812158
759511.670651485
277.8895279531163
9
-6.311257326365898
-1.1685001080762325e-05
-0.005628518052809723

simplify4.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
087136
190136
290136

end0.0ms

sample5.4s

Algorithm
intervals
Results

Profiling

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