Details

Time bar (total: 13.2s)

sample191.0ms

Algorithm
intervals
Results
79.0ms42×body2560valid
61.0ms71×body1280valid
16.0ms48×body640valid
7.0ms92×body80valid
6.0ms30×body320valid
4.0ms1×body5120valid
3.0ms63×body80nan
2.0ms13×body160valid

simplify45.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 46.4b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
13.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite658.0ms

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:
246.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
138.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)
239.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms
(- (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))

simplify70.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
013193734
150023446

prune844.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 25.8b

localize17.0ms

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)))
11.4b
(* (pow i 2) (log 1.0))
21.9b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite45.0ms

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)))))
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))
9.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series658.0ms

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)))))
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)))
140.0ms
(* (pow i 2) (log 1.0))
202.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify130.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (21.0ms)

IterNodesCost
07343209
137502968
250012968

prune748.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize17.0ms

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)))))
2.7b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
11.2b
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
11.4b
(* (pow i 2) (log 1.0))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
127×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
53×add-exp-log
48×associate-*r*
32×add-cbrt-cube
23×div-exp
21×associate-*l*
13×prod-exp associate-/r*
12×cbrt-undiv unswap-sqr
10×div-inv
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×frac-times pow-to-exp frac-2neg associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow fma-udef
Counts
4 → 215
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)))))
6.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
33.0ms
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
8.0ms
(* (pow i 2) (log 1.0))

series616.0ms

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)))))
153.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
218.0ms
(* (/ 100.0 i) (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
146.0ms
(* (pow i 2) (log 1.0))

simplify61.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
09683888
150013477

prune740.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 11.6b

localize22.0ms

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)))))
2.6b
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
11.2b
(* (/ 100.0 i) (* 1 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)))
11.4b
(* (pow i 2) (log 1.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
44×add-exp-log
29×add-cbrt-cube
26×add-sqr-sqrt prod-exp
24×associate-*l*
18×add-cube-cbrt *-un-lft-identity
16×pow1
14×cbrt-unprod
9×times-frac
8×associate-*r*
7×pow-prod-down
6×log-prod
5×div-exp unswap-sqr
4×expm1-log1p-u unpow-prod-down 1-exp log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in *-commutative
2×unpow2 sqr-pow
1×pow-to-exp associate-*l/ pow-exp log-pow fma-udef div-inv
Counts
4 → 110
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)))))
3.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
22.0ms
(* (/ 100.0 i) (* 1 (* (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))

series791.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
339.0ms
(* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)
214.0ms
(* (/ 100.0 i) (* 1 (* (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) n)))
142.0ms
(* (pow i 2) (log 1.0))

simplify79.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
05221554
125971266
250011263

prune318.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 11.6b

regimes216.0ms

Accuracy

51.7% (10.6b remaining)

Error of 21.6b against oracle of 11.0b and baseline of 33.0b

bsearch317.0ms

Steps
ItersRangePoint
5
2.6930000565052037e+265
9.367091293497255e+265
5.663291218810887e+265
7
1.0575510317571654e+51
1.2501576144527626e+53
1.2243718320891224e+53
5
4.8244160186105205e-08
1.574218364489979e-07
1.5425208996765195e-07
7
-0.012567608813020674
-0.0006597345534036075
-0.003897370925930358

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07561
17561

end0.0ms

sample5.3s

Algorithm
intervals
Results
2.0s1015×body2560valid
1.9s2485×body1280valid
543.0ms1585×body640valid
223.0ms3032×body80valid
192.0ms903×body320valid
120.0ms2180×body80nan
63.0ms434×body160valid
15.0ms4×body5120valid