Details

Time bar (total: 12.8s)

sample162.0ms

Algorithm
intervals
Results
66.0ms36×body2560valid
54.0ms72×body1280valid
13.0ms46×body640valid
5.0ms114×body80valid
4.0ms1×body5120valid
3.0ms22×body320valid
2.0ms75×body80nan
2.0ms18×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
11.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite564.0ms

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:
229.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
106.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
201.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
364.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify63.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012263285
150023166

prune993.0ms

Filtered
293 candidates to 223 candidates (76.1%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.3b

localize15.0ms

Local error

Found 4 expressions with local error:

2.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)

rewrite139.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
15×add-sqr-sqrt
13×unpow-prod-down
10×add-cube-cbrt
9×pow-unpow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube sqr-pow
3×pow-to-exp pow-pow pow-exp distribute-lft-out difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 70
Calls
4 calls:
104.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series881.0ms

Counts
4 → 12
Calls
4 calls:
256.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms
(pow (+ 1.0 (/ i n)) n)
206.0ms
(pow (+ 1.0 (/ i n)) n)
207.0ms
(pow (+ 1.0 (/ i n)) n)

simplify65.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (59.0ms)

IterNodesCost
0192470
1556461
22075455
35001449

prune284.0ms

Filtered
82 candidates to 60 candidates (73.2%)
Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 22.3b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b
(cbrt (+ 1.0 (/ i n)))
4.7b
(cbrt (+ 1.0 (/ i n)))
6.1b
(pow (+ 1.0 (/ i n)) n)
6.1b
(pow (+ 1.0 (/ i n)) n)

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
10×add-sqr-sqrt add-cube-cbrt
8×cbrt-prod unpow-prod-down
6×pow1 add-exp-log pow-unpow
4×cbrt-div add-cbrt-cube distribute-lft-out add-log-exp
2×pow-to-exp pow-pow flip3-+ pow1/3 pow-exp flip-+ sqr-pow
Counts
4 → 64
Calls
4 calls:
5.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series905.0ms

Counts
4 → 12
Calls
4 calls:
246.0ms
(cbrt (+ 1.0 (/ i n)))
240.0ms
(cbrt (+ 1.0 (/ i n)))
211.0ms
(pow (+ 1.0 (/ i n)) n)
209.0ms
(pow (+ 1.0 (/ i n)) n)

simplify60.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 3 (54.0ms)

IterNodesCost
0179432
1542410
22102398
35001390

prune361.0ms

Filtered
76 candidates to 58 candidates (76.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 22.3b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
2.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)
11.7b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite407.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×times-frac
28×*-un-lft-identity
22×add-cube-cbrt
19×add-exp-log
18×add-cbrt-cube
13×associate-/r*
7×pow1 associate-*r*
6×cbrt-undiv unpow-prod-down div-exp add-log-exp difference-of-squares
4×associate-*r/
3×sub-neg pow-unpow flip3-- associate-*l* prod-exp flip-- cbrt-unprod div-inv sqr-pow
2×distribute-rgt-in distribute-lft-in associate-/l/ distribute-lft-out--
1×pow-to-exp pow-pow frac-2neg diff-log pow-prod-down pow-exp clear-num associate-/r/ *-commutative distribute-lft-out associate-/l* unswap-sqr
Counts
4 → 110
Calls
4 calls:
195.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
103.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
94.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
264.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
257.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)
380.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify75.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06511023
13174917
25001912

prune250.0ms

Filtered
122 candidates to 90 candidates (73.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.7b

regimes237.0ms

Accuracy

52.7% (11.3b remaining)

Error of 30.5b against oracle of 19.3b and baseline of 43.1b

bsearch117.0ms

Steps
ItersRangePoint
6
2.289162948056721e-13
9.558161037350472e-13
9.412915699220923e-13
4
-0.041603525395973645
-0.02085603301560968
-0.04063035479082508

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06252
16252

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s957×body2560valid
1.8s2539×body1280valid
467.0ms1636×body640valid
140.0ms850×body320valid
132.0ms3037×body80valid
70.0ms2255×body80nan
43.0ms428×body160valid
30.0ms8×body5120valid