Details

Time bar (total: 12.2s)

sample161.0ms

Algorithm
intervals
Results
66.0ms89×body1280valid
49.0ms25×body2560valid
22.0ms69×body640valid
4.0ms84×body80valid
3.0ms20×body320valid
3.0ms85×body80nan
1.0ms12×body160valid

simplify45.0ms

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: 46.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
9.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite89.0ms

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:
32.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
11.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.0ms
(pow (+ 1.0 (/ i n)) n)
18.0ms
(/ (- (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)))
252.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)
350.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify65.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150013446

prune852.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.4b

localize19.0ms

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))
16.1b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite34.0ms

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:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
14.0ms
(* 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)))
6.0ms
(* (pow i 2) (log 1.0))
6.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series650.0ms

Counts
4 → 12
Calls
4 calls:
96.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
217.0ms
(* 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)))
142.0ms
(* (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))

simplify117.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07343209
137502968
250012968

prune763.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.8b

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)))))
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))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
10×pow1
9×times-frac associate-*l*
8×prod-exp
7×associate-*r*
6×log-prod cbrt-unprod
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:
1.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
6.0ms
(* (* 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)
6.0ms
(* (pow i 2) (log 1.0))

series607.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
221.0ms
(* (* 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)
142.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms
(* (pow i 2) (log 1.0))

simplify72.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
04131370
118881165
250021158

prune387.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.8b

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))

rewrite27.0ms

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:
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)
6.0ms
(* (pow i 2) (log 1.0))
7.0ms
(* (pow i 2) (log 1.0))
7.0ms
(* (pow i 2) (log 1.0))

series565.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms
(* (pow i 2) (log 1.0))
143.0ms
(* (pow i 2) (log 1.0))
140.0ms
(* (pow i 2) (log 1.0))

simplify44.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
02381134
18681013
25001998

prune665.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 11.8b

regimes262.0ms

Accuracy

67.7% (5.8b remaining)

Error of 16.9b against oracle of 11.1b and baseline of 29.0b

bsearch229.0ms

Steps
ItersRangePoint
9
1.560051953962792e-13
3.9524390088012255e-07
3.902879756316096e-07
9
-6.956871504263554e-09
-9.165072888214816e-14
-6.8977356701701615e-09

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04838
14838

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.1s2889×body1280valid
2.0s1010×body2560valid
564.0ms1770×body640valid
161.0ms879×body320valid
121.0ms2459×body80valid
90.0ms2270×body80nan
48.0ms460×body160valid