Details

Time bar (total: 15.9s)

sample198.0ms

Algorithm
intervals
Results
83.0ms89×body1280valid
64.0ms29×body2560valid
22.0ms50×body640valid
7.0ms89×body80valid
5.0ms20×body320valid
4.0ms62×body80nan
2.0ms12×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

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite615.0ms

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:
231.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
128.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
226.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
379.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
258.0ms
(- (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))

simplify69.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune853.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.5b

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)))
10.6b
(* (pow i 2) (log 1.0))
20.5b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite41.0ms

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)))))
22.0ms
(* 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))

series659.0ms

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)))))
225.0ms
(* 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)))
141.0ms
(* (pow i 2) (log 1.0))
196.0ms
(/ (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

prune727.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 9.1b

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)))))
4.2b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
10.6b
(* (pow i 2) (log 1.0))
14.0b
(* (/ 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)))

rewrite53.0ms

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)))))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
7.0ms
(* (pow i 2) (log 1.0))
28.0ms
(* (/ 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)))

series631.0ms

Counts
4 → 12
Calls
4 calls:
102.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
161.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n))
146.0ms
(* (pow i 2) (log 1.0))
222.0ms
(* (/ 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)))

simplify126.0ms

Algorithm
egg-herbie
Counts
227 → 227
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09673894
149243474
250013474

prune733.0ms

Pruning

14 alts after pruning (13 fresh and 1 done)

Merged error: 9.1b

localize22.0ms

Local error

Found 4 expressions with local error:

10.6b
(* (pow i 2) (log 1.0))
16.8b
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
16.8b
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
16.8b
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
198×times-frac
132×cbrt-prod
120×add-sqr-sqrt
114×add-cube-cbrt *-un-lft-identity
12×div-inv
9×add-exp-log
8×associate-*l*
6×log-prod add-cbrt-cube
5×pow1
4×expm1-log1p-u unpow-prod-down associate-*r* log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in cbrt-div distribute-lft-in pow1/3 prod-exp associate-/r/
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow *-commutative cbrt-unprod
Counts
4 → 201
Calls
4 calls:
7.0ms
(* (pow i 2) (log 1.0))
4.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
4.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
5.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))

series2.5s

Counts
4 → 12
Calls
4 calls:
142.0ms
(* (pow i 2) (log 1.0))
783.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
804.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))
804.0ms
(cbrt (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ 1 n)))

simplify93.0ms

Algorithm
egg-herbie
Counts
213 → 213
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05745094
121034913
250014759

prune710.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 9.1b

regimes214.0ms

Accuracy

48% (11.5b remaining)

Error of 22.4b against oracle of 10.9b and baseline of 33.1b

bsearch386.0ms

Steps
ItersRangePoint
8
7.108389521057788e-152
9.857230472394243e-149
7.185948283350093e-152
9
-4.622874842024395e-243
-4.995401923428486e-252
-3.9974032830534776e-251
9
-5.979882189147821e+84
-8.548989080955097e+79
-2.7155205583837284e+82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06052
16052

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.2s2461×body1280valid
2.0s956×body2560valid
691.0ms1617×body640valid
232.0ms3076×body80valid
222.0ms835×body320valid
121.0ms2193×body80nan
73.0ms433×body160valid
20.0ms6×body5120valid