Details

Time bar (total: 12.5s)

sample156.0ms

Algorithm
intervals
Results
58.0ms30×body2560valid
58.0ms78×body1280valid
16.0ms53×body640valid
5.0ms25×body320valid
4.0ms98×body80valid
2.0ms56×body80nan
1.0ms12×body160valid

simplify43.0ms

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: 42.8b

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite650.0ms

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:
245.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
136.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
237.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.4s

Counts
4 → 12
Calls
4 calls:
512.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
259.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
224.0ms
(pow (+ 1.0 (/ i n)) n)
368.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify62.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune859.0ms

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))

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))
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))

series609.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(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)))
135.0ms
(* (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))

simplify113.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07313120
136262891
250022891

prune720.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.3b

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)
10.3b
(/ (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))

rewrite24.0ms

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:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
12.0ms
(* (* 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))

series574.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
219.0ms
(* (* 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)
148.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms
(* (pow i 2) (log 1.0))

simplify60.0ms

Algorithm
egg-herbie
Counts
110 → 110
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04101281
118001088
250011081

prune380.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
1.6b
(* (* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) n)
10.9b
(* (pow i 2) (log 1.0))
12.0b
(/ (* (* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) n) i)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity
12×pow1 associate-*l*
10×associate-*r* prod-exp
8×cbrt-unprod
6×log-prod
5×unswap-sqr
4×distribute-rgt-in expm1-log1p-u unpow-prod-down distribute-lft-in pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv times-frac div-exp associate-/r* *-commutative
2×fma-udef unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 103
Calls
4 calls:
3.0ms
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
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)))))) n)
7.0ms
(* (pow i 2) (log 1.0))
7.0ms
(/ (* (* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) n) i)

series656.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))))
169.0ms
(* (* 100.0 (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))) n)
145.0ms
(* (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)))))) n) i)

simplify86.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
04511424
125041162
250031159

prune310.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

regimes328.0ms

Accuracy

55.6% (9.8b remaining)

Error of 21.0b against oracle of 11.1b and baseline of 33.3b

bsearch637.0ms

Steps
ItersRangePoint
8
2.2112458842293344e-05
0.01694346711308432
0.0006093521534695529
8
7.60401498810488e-233
2.248873935831e-229
8.587016406998776e-230
9
7.333478328566493e-293
2.09185199160616e-287
2.6939372834177335e-290
9
-30.29444851407267
-2.830682320409962e-08
-0.14141811154607586

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06561
16561

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s2495×body1280valid
1.8s949×body2560valid
485.0ms1592×body640valid
150.0ms876×body320valid
135.0ms3055×body80valid
82.0ms2313×body80nan
47.0ms447×body160valid
23.0ms7×body5120valid