Details

Time bar (total: 11.9s)

sample168.0ms

Algorithm
intervals
Results
74.0ms36×body2560valid
53.0ms80×body1280valid
16.0ms52×body640valid
6.0ms34×body320valid
4.0ms77×body80valid
2.0ms55×body80nan
2.0ms15×body160valid

simplify40.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 47.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite83.0ms

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:
33.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
10.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.0ms
(pow (+ 1.0 (/ i n)) n)
16.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
348.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
235.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
199.0ms
(pow (+ 1.0 (/ i n)) n)
346.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify60.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (27.0ms)

IterNodesCost
013193734
150023446

prune843.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 21.5b

localize15.0ms

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)))
12.8b
(* (pow i 2) (log 1.0))
19.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite32.0ms

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)))))
13.0ms
(* 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))

series623.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
211.0ms
(* 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)))
129.0ms
(* (pow i 2) (log 1.0))
189.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify115.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (18.0ms)

IterNodesCost
07343209
137502968
250012968

prune730.0ms

Filtered
198 candidates to 152 candidates (76.8%)
Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.0b

localize14.0ms

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)
12.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite18.0ms

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))

series580.0ms

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)))))
208.0ms
(* (* 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)
134.0ms
(* (pow i 2) (log 1.0))

simplify59.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04131370
118881165
250021158

prune372.0ms

Filtered
110 candidates to 74 candidates (67.3%)
Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 11.0b

localize20.0ms

Local error

Found 4 expressions with local error:

12.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
12.8b
(* (pow i 2) (log 1.0))
12.8b
(* (pow i 2) (log 1.0))
12.8b
(* (pow i 2) (log 1.0))

rewrite26.0ms

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

series551.0ms

Counts
4 → 12
Calls
4 calls:
138.0ms
(/ (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))
139.0ms
(* (pow i 2) (log 1.0))
135.0ms
(* (pow i 2) (log 1.0))

simplify38.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
02381134
18681013
25001998

prune581.0ms

Filtered
149 candidates to 97 candidates (65.1%)
Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 11.0b

regimes196.0ms

Accuracy

63.6% (6.5b remaining)

Error of 17.6b against oracle of 11.1b and baseline of 29.0b

bsearch220.0ms

Steps
ItersRangePoint
7
2.8959938237950545e+203
1.5617903206865062e+205
1.5471622621860444e+204
8
4.036504835668646e-26
2.5947478503916157e-23
2.5704520336039343e-23
7
-2.2963680336716634e-10
-5.6669034693225635e-12
-2.2717441078324636e-10

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04938
14938

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.1s2891×body1280valid
1.9s987×body2560valid
559.0ms1745×body640valid
168.0ms918×body320valid
121.0ms2492×body80valid
77.0ms2140×body80nan
48.0ms437×body160valid
30.0ms8×body5120valid