Details

Time bar (total: 14.2s)

sample210.0ms

Algorithm
intervals
Results
75.0ms35×body2560valid
69.0ms79×body1280valid
32.0ms68×body640valid
8.0ms32×body320valid
8.0ms87×body80valid
4.0ms72×body80nan
2.0ms11×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.8b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.9b
(pow (+ 1.0 (/ i n)) n)
11.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite654.0ms

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:
243.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
135.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
240.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
386.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
224.0ms
(pow (+ 1.0 (/ i n)) n)
370.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
013193734
150023446

prune893.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 26.1b

localize21.0ms

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)))))
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)))
11.1b
(* (pow i 2) (log 1.0))
19.0b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite41.0ms

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 i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
19.0ms
(* 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))

series674.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
226.0ms
(* 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)))
149.0ms
(* (pow i 2) (log 1.0))
201.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify124.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07343215
136832968
250012968

prune788.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 14.2b

localize18.0ms

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)))))
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))
10.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.1b
(* (pow i 2) (log 1.0))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
11×associate-*l*
10×pow1
9×times-frac
8×prod-exp
6×log-prod cbrt-unprod
5×associate-*r*
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/l*
2×cbrt-undiv div-exp *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ associate-*l/ pow-exp clear-num log-pow fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
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))
2.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
7.0ms
(* (pow i 2) (log 1.0))

series629.0ms

Counts
4 → 12
Calls
4 calls:
109.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
224.0ms
(* 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))
151.0ms
(/ (fma i 1.0 (- (fma 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))

simplify62.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04061369
117341164
250031157

prune399.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 14.2b

localize22.0ms

Local error

Found 4 expressions with local error:

10.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.1b
(* (pow i 2) (log 1.0))
11.1b
(* (pow i 2) (log 1.0))
11.1b
(* (pow i 2) (log 1.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
24×associate-*l*
21×add-exp-log
18×log-prod
12×unpow-prod-down associate-*r* add-cbrt-cube unswap-sqr
9×distribute-rgt-in distribute-lft-in times-frac prod-exp
7×pow1
6×unpow2 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-exp associate-/r* log-pow *-commutative cbrt-unprod associate-/l*
1×cbrt-undiv frac-2neg div-exp clear-num div-inv
Counts
4 → 137
Calls
4 calls:
2.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
11.0ms
(* (pow i 2) (log 1.0))
7.0ms
(* (pow i 2) (log 1.0))
7.0ms
(* (pow i 2) (log 1.0))

series774.0ms

Counts
4 → 12
Calls
4 calls:
336.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
147.0ms
(* (pow i 2) (log 1.0))
141.0ms
(* (pow i 2) (log 1.0))
151.0ms
(* (pow i 2) (log 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
02381134
18681013
25001998

prune593.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 14.2b

regimes265.0ms

Accuracy

66.1% (6.1b remaining)

Error of 17.3b against oracle of 11.2b and baseline of 29.2b

bsearch251.0ms

Steps
ItersRangePoint
9
1.3261300952414648e-20
8.815605325869767e-16
8.746094629864195e-16
8
-1.1902930357079885e-07
-1.3081950593114417e-10
-1.1787990607175087e-07

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04630
14630

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.6s2947×body1280valid
2.1s989×body2560valid
773.0ms1773×body640valid
233.0ms853×body320valid
191.0ms2425×body80valid
130.0ms2296×body80nan
76.0ms434×body160valid
43.0ms11×body5120valid