Details

Time bar (total: 14.9s)

sample146.0ms

Algorithm
intervals
Results
61.0ms32×body2560valid
47.0ms75×body1280valid
10.0ms40×body640valid
5.0ms36×body320valid
5.0ms108×body80valid
3.0ms83×body80nan
2.0ms18×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite635.0ms

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:
259.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
118.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)
225.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
250.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)
349.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify67.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
012263285
150023166

prune835.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 22.8b

localize15.0ms

Local error

Found 4 expressions with local error:

2.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)

rewrite159.0ms

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:
119.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
13.0ms
(pow (+ 1.0 (/ i n)) n)
13.0ms
(pow (+ 1.0 (/ i n)) n)

series919.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
223.0ms
(pow (+ 1.0 (/ i n)) n)
216.0ms
(pow (+ 1.0 (/ i n)) n)
221.0ms
(pow (+ 1.0 (/ i n)) n)

simplify68.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 3 (61.0ms)

IterNodesCost
0192470
1556461
22075455
35001449

prune296.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 22.8b

localize19.0ms

Local error

Found 4 expressions with local error:

2.3b
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)

rewrite285.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
17×add-sqr-sqrt
13×unpow-prod-down
12×add-cube-cbrt
9×pow-unpow
8×pow1 log-pow
7×add-exp-log exp-prod
5×log-prod
4×add-cbrt-cube add-log-exp sqr-pow
3×pow-to-exp pow-pow pow-exp distribute-lft-out difference-of-squares
2×exp-sum
1×sub-neg log-div exp-diff rem-log-exp distribute-lft-out--
Counts
4 → 76
Calls
4 calls:
246.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
12.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) n)

series918.0ms

Counts
4 → 12
Calls
4 calls:
254.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
228.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(pow (+ 1.0 (/ i n)) n)
212.0ms
(pow (+ 1.0 (/ i n)) n)

simplify60.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 3 (53.0ms)

IterNodesCost
0195503
1566471
22078465
35002459

prune340.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 22.8b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n)))
2.3b
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
5.8b
(pow (+ 1.0 (/ i n)) (/ n 2))
5.8b
(pow (+ 1.0 (/ i n)) (/ n 2))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
27×*-un-lft-identity
26×pow-unpow
24×add-exp-log
22×add-cbrt-cube
21×add-cube-cbrt
18×times-frac
15×pow1
11×prod-exp cbrt-unprod
10×unpow-prod-down
7×associate-*r/
6×pow-prod-down add-log-exp difference-of-squares
5×associate-*l/
4×sqr-pow
3×flip3-- associate-*l* sqrt-prod flip--
2×cbrt-undiv frac-times pow-to-exp pow-pow div-exp pow-exp div-inv distribute-lft-out
1×sub-neg diff-log associate-*r* *-commutative distribute-lft-out--
Counts
4 → 105
Calls
4 calls:
1.2s
(* 100.0 (* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n)))
120.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
13.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
14.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

series1.4s

Counts
4 → 12
Calls
4 calls:
633.0ms
(* 100.0 (* (/ (+ (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) i) (* (- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0)) n)))
272.0ms
(- (pow (+ 1.0 (/ i n)) (/ n 2)) (sqrt 1.0))
221.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))
227.0ms
(pow (+ 1.0 (/ i n)) (/ n 2))

simplify70.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05771362
124091101
250011027

prune340.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 22.8b

regimes128.0ms

Accuracy

45.3% (11.8b remaining)

Error of 33.2b against oracle of 21.4b and baseline of 43.0b

bsearch869.0ms

Steps
ItersRangePoint
7
8.639792360287736e-11
7.241082556785e-09
7.147085067578077e-09
7
2.7499475250696328e-134
7.422960692703227e-133
2.8738884927185156e-134
6
8.896230187054732e-198
8.190807967914936e-197
8.057002382378186e-197
9
2.78333567540328e-277
5.2293129153053376e-272
1.6479702105467177e-275
7
-3.2963305767896758e-273
-9.078934504337964e-275
-1.1313305452296457e-274
10
-1530624.207495954
-2.4048977341445043e-11
-1.2132993654259578

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
096109
196109

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s2501×body1280valid
1.8s961×body2560valid
475.0ms1585×body640valid
152.0ms885×body320valid
140.0ms3123×body80valid
79.0ms2336×body80nan
48.0ms457×body160valid
14.0ms4×body5120valid