Details

Time bar (total: 13.6s)

sample171.0ms

Algorithm
intervals
Results
66.0ms36×body2560valid
64.0ms89×body1280valid
14.0ms44×body640valid
5.0ms34×body320valid
5.0ms76×body80nan
3.0ms83×body80valid
1.0ms14×body160valid

simplify40.0ms

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: 46.9b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
11.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite728.0ms

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:
241.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
149.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
22.0ms
(pow (+ 1.0 (/ i n)) n)
294.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
370.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
254.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)
355.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune902.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 25.2b

localize20.0ms

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)))
9.9b
(* (pow i 2) (log 1.0))
19.1b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite40.0ms

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))
20.0ms
(* 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))

series630.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
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)))
143.0ms
(* (pow i 2) (log 1.0))
200.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify118.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07313120
136262891
250022891

prune744.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.5b

localize21.0ms

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))
9.4b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
9.9b
(* (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 0.5 (pow i 2) (* (log 1.0) 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))
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))

series571.0ms

Counts
4 → 12
Calls
4 calls:
63.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
220.0ms
(* 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)
147.0ms
(* (pow i 2) (log 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04041286
115711087
250021080

prune378.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 12.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt i)
6.7b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
9.3b
(* (/ 100.0 (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) n)))
9.9b
(* (pow i 2) (log 1.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
341×times-frac
264×add-sqr-sqrt
168×add-cube-cbrt *-un-lft-identity
85×cbrt-prod
75×associate-*r*
56×add-exp-log
45×associate-*l*
30×unpow-prod-down
29×add-cbrt-cube
28×unswap-sqr
24×div-exp
22×associate-/r*
15×prod-exp
12×cbrt-undiv
10×div-inv
9×unpow2 sqr-pow
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u pow-to-exp pow-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative
1×frac-times frac-2neg pow1/3 associate-*r/ pow-prod-down associate-*l/ clear-num log-pow
Counts
4 → 321
Calls
4 calls:
1.0ms
(cbrt i)
9.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
72.0ms
(* (/ 100.0 (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) n)))
7.0ms
(* (pow i 2) (log 1.0))

series806.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt i)
231.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ (cbrt i) n))
245.0ms
(* (/ 100.0 (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) n)))
147.0ms
(* (pow i 2) (log 1.0))

simplify100.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
015366872
150016520

prune1.5s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 12.5b

regimes411.0ms

Accuracy

55.7% (10.0b remaining)

Error of 21.3b against oracle of 11.4b and baseline of 33.9b

bsearch210.0ms

Steps
ItersRangePoint
9
3.233625039177592e-11
0.003342748024832997
0.0030890666332557444
9
-40603.17280191813
-0.00667476531596465
-0.31883140503528035

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04430
14430

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s978×body2560valid
1.8s2479×body1280valid
467.0ms1638×body640valid
139.0ms844×body320valid
138.0ms3088×body80valid
75.0ms2284×body80nan
45.0ms449×body160valid
16.0ms5×body5120valid