Details

Time bar (total: 12.8s)

sample157.0ms

Algorithm
intervals
Results
59.0ms78×body1280valid
58.0ms30×body2560valid
16.0ms53×body640valid
4.0ms25×body320valid
4.0ms98×body80valid
2.0ms56×body80nan
1.0ms12×body160valid

simplify46.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite630.0ms

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 321
Calls
4 calls:
236.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
132.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
231.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
360.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
210.0ms
(pow (+ 1.0 (/ i n)) n)
349.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify69.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013193734
150023446

prune856.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.6b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.5 (pow i 2) (* (log 1.0) n))
0.1b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
10.9b
(* (pow i 2) (log 1.0))
16.6b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow fma-udef
Counts
4 → 186
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
22.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
7.0ms
(* (pow i 2) (log 1.0))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series601.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
212.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
137.0ms
(* (pow i 2) (log 1.0))
195.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify119.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07313126
135652891
250022891

prune722.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
0.1b
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
10.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
10.9b
(* (pow i 2) (log 1.0))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
7.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
11.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
3.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
9.0ms
(* (pow i 2) (log 1.0))

series696.0ms

Counts
4 → 12
Calls
4 calls:
196.0ms
(* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n)
222.0ms
(* 100.0 (* (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i) n))
139.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
139.0ms
(* (pow i 2) (log 1.0))

simplify69.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
04761783
120111521
250011513

prune456.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt i)
1.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i))
9.3b
(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i)))
10.9b
(* (pow i 2) (log 1.0))

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
156×add-sqr-sqrt
121×times-frac
74×*-un-lft-identity
61×add-exp-log
59×add-cube-cbrt
50×cbrt-prod
45×associate-*l*
37×unswap-sqr
34×unpow-prod-down
26×associate-*r*
23×div-exp prod-exp
17×add-cbrt-cube
11×unpow2 sqr-pow
7×pow1 pow-to-exp pow-exp
6×rec-exp log-prod 1-exp associate-/r*
5×cbrt-undiv cbrt-unprod
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in div-inv associate-/l*
2×*-commutative
1×frac-times frac-2neg pow1/3 associate-*r/ pow-prod-down associate-*l/ clear-num log-pow
Counts
4 → 220
Calls
4 calls:
0.0ms
(cbrt i)
3.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i))
37.0ms
(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i)))
7.0ms
(* (pow i 2) (log 1.0))

series681.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(cbrt i)
176.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i))
180.0ms
(* (/ 1 (pow (cbrt i) 2)) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (cbrt i)))
149.0ms
(* (pow i 2) (log 1.0))

simplify135.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 2 (92.0ms)

IterNodesCost
09544194
144623729
250013641

prune830.0ms

Pruning

21 alts after pruning (20 fresh and 1 done)

Merged error: 11.3b

regimes378.0ms

Accuracy

53.6% (10.7b remaining)

Error of 21.8b against oracle of 11.1b and baseline of 34.1b

bsearch203.0ms

Steps
ItersRangePoint
8
2.2112458842293344e-05
0.01694346711308432
0.009080166023661082
9
-30.29444851407267
-2.830682320409962e-08
-0.14141811154607586

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05435
15435

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s2495×body1280valid
1.8s949×body2560valid
469.0ms1592×body640valid
149.0ms876×body320valid
129.0ms3055×body80valid
74.0ms2313×body80nan
45.0ms447×body160valid
24.0ms7×body5120valid