Details

Time bar (total: 14.0s)

sample156.0ms

Algorithm
intervals
Results
67.0ms34×body2560valid
45.0ms58×body1280valid
15.0ms54×body640valid
4.0ms99×body80valid
4.0ms24×body320valid
2.0ms76×body80nan
2.0ms20×body160valid
1.0ms32×body80overflowed

simplify41.0ms

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: 41.7b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite806.0ms

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:
332.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
151.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
289.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
343.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
229.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
196.0ms
(pow (+ 1.0 (/ i n)) n)
343.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify56.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
012263285
150023166

prune900.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.9b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.3b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
2.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)

rewrite824.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 310
Calls
4 calls:
287.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
343.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
156.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series997.0ms

Counts
4 → 12
Calls
4 calls:
262.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
324.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
224.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
187.0ms
(pow (+ 1.0 (/ i n)) n)

simplify66.0ms

Algorithm
egg-herbie
Counts
322 → 322
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
014853727
150023400

prune714.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.6b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
3.9b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
13.9b
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
15.1b
(* (pow i 2) (log 1.0))

rewrite556.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
136×add-sqr-sqrt
98×*-un-lft-identity
96×add-cube-cbrt
58×add-exp-log
56×associate-*r*
34×add-cbrt-cube
24×associate-*l*
23×div-exp
16×prod-exp unswap-sqr
13×associate-/r*
12×cbrt-undiv
10×div-inv
8×unpow-prod-down cbrt-unprod
7×pow1
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×frac-times flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ clear-num log-pow flip--
Counts
4 → 229
Calls
4 calls:
11.0ms
(* 0.5 (pow i 2))
251.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
269.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
13.0ms
(* (pow i 2) (log 1.0))

series473.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* 0.5 (pow i 2))
130.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
188.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
132.0ms
(* (pow i 2) (log 1.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
241 → 241
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
011334294
150013845

prune683.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.3b

localize24.0ms

Local error

Found 4 expressions with local error:

15.1b
(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
15.1b
(* (pow i 2) (log 1.0))
15.1b
(* (pow i 2) (log 1.0))
15.1b
(* (pow i 2) (log 1.0))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
38×add-sqr-sqrt
24×associate-*l*
20×add-cube-cbrt *-un-lft-identity
19×add-exp-log
18×log-prod
12×unpow-prod-down associate-*r* unswap-sqr
10×add-cbrt-cube
9×distribute-rgt-in distribute-lft-in prod-exp
7×pow1
6×unpow2 sqr-pow
4×add-log-exp
3×cbrt-prod pow-to-exp pow-exp log-pow *-commutative cbrt-unprod
2×cbrt-div
1×flip3-- pow1/3 flip--
Counts
4 → 115
Calls
4 calls:
64.0ms
(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
13.0ms
(* (pow i 2) (log 1.0))
13.0ms
(* (pow i 2) (log 1.0))
16.0ms
(* (pow i 2) (log 1.0))

series1.1s

Counts
4 → 12
Calls
4 calls:
653.0ms
(cbrt (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
140.0ms
(* (pow i 2) (log 1.0))
139.0ms
(* (pow i 2) (log 1.0))
137.0ms
(* (pow i 2) (log 1.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
127 → 127
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
03331006
11251895
25002873

prune466.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 12.3b

regimes188.0ms

Accuracy

50.7% (12.2b remaining)

Error of 24.2b against oracle of 12.0b and baseline of 36.8b

bsearch286.0ms

Steps
ItersRangePoint
11
611368.3395468491
2.887894694535045e+31
622281.33147616
8
-1.645476760304416e-16
-3.5128575905099626e-19
-1.6262601569927174e-16

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07371
17671
27671

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s2235×body1280valid
1.5s799×body2560valid
452.0ms1587×body640valid
139.0ms3349×body80valid
139.0ms818×body320valid
77.0ms2445×body80nan
46.0ms443×body160valid
41.0ms991×body80overflowed
23.0ms7×body5120valid