Details

Time bar (total: 28.0s)

sample195.0ms

Algorithm
intervals
Results
73.0ms82×body1280valid
56.0ms27×body2560valid
24.0ms57×body640valid
9.0ms35×body320valid
7.0ms106×body80valid
3.0ms63×body80nan
2.0ms15×body160valid

simplify4.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.2b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.7b
(pow (+ 1.0 (/ i n)) n)
9.9b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

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:
456.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
307.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
478.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.3s

Counts
4 → 12
Calls
4 calls:
423.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
297.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms
(pow (+ 1.0 (/ i n)) n)
373.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.2s

Counts
333 → 333
Iterations

Useful iterations: done (2.2s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.2b

localize19.0ms

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
11.1b
(* (pow i 2) (log 1.0))
19.0b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite90.0ms

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 associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 189
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
37.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
22.0ms
(* (pow i 2) (log 1.0))
22.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series779.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
259.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
184.0ms
(* (pow i 2) (log 1.0))
242.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.4s

Counts
201 → 201
Iterations

Useful iterations: done (1.4s)

IterNodesCost
03286373
18216158
229465713
done50005704

prune1.1s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 8.6b

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
10.5b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b
(* (pow i 2) (log 1.0))

rewrite125.0ms

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 associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ associate-*l/ pow-exp clear-num log-pow flip-- fma-udef div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
61.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
34.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
26.0ms
(* (pow i 2) (log 1.0))

series723.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
262.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
172.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
196.0ms
(* (pow i 2) (log 1.0))

simplify1.3s

Counts
113 → 113
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02022685
14612616
216032239
done50002145

prune511.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 8.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
0.2b
(/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
10.5b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.1b
(* (pow i 2) (log 1.0))

rewrite209.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
428×add-sqr-sqrt
399×*-un-lft-identity
397×add-cube-cbrt
178×associate-*r*
65×add-exp-log
57×div-inv
38×add-cbrt-cube
33×div-exp
17×cbrt-undiv
16×associate-/r* associate-/l*
12×prod-exp
11×associate-*l* unswap-sqr
7×pow1
6×log-prod cbrt-unprod
4×expm1-log1p-u unpow-prod-down rec-exp 1-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in div-sub associate-/l/
2×frac-2neg clear-num associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp flip3-- associate-*r/ pow-prod-down pow-exp log-pow flip--
Counts
4 → 500
Calls
4 calls:
97.0ms
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
33.0ms
(/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
17.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
16.0ms
(* (pow i 2) (log 1.0))

series884.0ms

Counts
4 → 12
Calls
4 calls:
278.0ms
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
232.0ms
(/ (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
155.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
218.0ms
(* (pow i 2) (log 1.0))

simplify1.9s

Counts
512 → 512
Iterations

Useful iterations: done (1.9s)

IterNodesCost
072221187
1196719296
2488518235
done500018232

prune1.5s

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 8.6b

regimes354.0ms

Accuracy

58.1% (10.6b remaining)

Error of 19.3b against oracle of 8.7b and baseline of 33.9b

bsearch652.0ms

Steps
ItersRangePoint
8
2.2645982852769956e+107
6.775003655927392e+110
3.8771146764698036e+110
11
5.295671684036253
1.0753369259707482e+28
5.738844998942818
10
-30895859.745759934
-0.00012163823945093722
-0.11981838180458737

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03781
14681
done4681

end0.0ms

sample5.9s

Algorithm
intervals
Results
2.1s1021×body2560valid
2.0s2400×body1280valid
570.0ms1650×body640valid
429.0ms2277×body80nan
224.0ms3079×body80valid
188.0ms866×body320valid
56.0ms459×body160valid
9.0ms3×body5120valid