Details

Time bar (total: 11.6s)

sample160.0ms

Algorithm
intervals
Results
61.0ms31×body2560valid
57.0ms87×body1280valid
17.0ms57×body640valid
5.0ms35×body320valid
3.0ms71×body80valid
3.0ms67×body80nan
2.0ms17×body160valid

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: 43.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
9.5b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite84.0ms

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:
31.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
9.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
372.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
216.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify61.0ms

Algorithm
egg-herbie
Counts
293 → 293
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
012263285
150013166

prune781.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
0.2b
(* 0.5 (pow i 2))
11.6b
(* (pow i 2) (log 1.0))
17.7b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
111×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
56×associate-*r*
28×add-exp-log
22×add-cbrt-cube
14×associate-*l*
13×associate-/r*
11×unswap-sqr
9×prod-exp div-inv
8×unpow-prod-down
7×pow1
6×cbrt-undiv log-prod div-exp
5×cbrt-unprod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num log-pow flip--
Counts
4 → 200
Calls
4 calls:
19.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
5.0ms
(* 0.5 (pow i 2))
6.0ms
(* (pow i 2) (log 1.0))
13.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series566.0ms

Counts
4 → 12
Calls
4 calls:
211.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
25.0ms
(* 0.5 (pow i 2))
137.0ms
(* (pow i 2) (log 1.0))
192.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify148.0ms

Algorithm
egg-herbie
Counts
212 → 212
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09073537
148563275
250013275

prune702.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 10.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
0.2b
(* 0.5 (pow i 2))
10.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b
(* (pow i 2) (log 1.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×associate-*r*
12×associate-*l*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ associate-*l/ clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
11.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
6.0ms
(* 0.5 (pow i 2))
15.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms
(* (pow i 2) (log 1.0))

series530.0ms

Counts
4 → 12
Calls
4 calls:
216.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
31.0ms
(* 0.5 (pow i 2))
138.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
145.0ms
(* (pow i 2) (log 1.0))

simplify81.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05251450
126211228
250011228

prune371.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 10.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
0.2b
(* 0.5 (pow i 2))
10.8b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.6b
(* (pow i 2) (log 1.0))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
14×associate-*l*
13×associate-*r*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ associate-*l/ clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
11.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
5.0ms
(* 0.5 (pow i 2))
14.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
6.0ms
(* (pow i 2) (log 1.0))

series529.0ms

Counts
4 → 12
Calls
4 calls:
215.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
31.0ms
(* 0.5 (pow i 2))
138.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
145.0ms
(* (pow i 2) (log 1.0))

simplify75.0ms

Algorithm
egg-herbie
Counts
124 → 124
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
05181449
124681227
250011223

prune327.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 10.3b

regimes191.0ms

Accuracy

67.2% (5.7b remaining)

Error of 16.6b against oracle of 10.9b and baseline of 28.3b

bsearch219.0ms

Steps
ItersRangePoint
10
1.3206356360948104e-13
0.22405535791780642
0.006616225279936071
9
-1.0159879302621945e-12
-1.9136020858029802e-21
-9.902418589881058e-13

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04522
14522

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.1s2950×body1280valid
1.9s1023×body2560valid
549.0ms1779×body640valid
149.0ms881×body320valid
109.0ms2327×body80valid
82.0ms2318×body80nan
52.0ms437×body160valid
32.0ms9×body5120valid