Details

Time bar (total: 30.1s)

sample230.0ms

Algorithm
intervals
Results
83.0ms36×body2560valid
78.0ms80×body1280valid
25.0ms38×body640valid
7.0ms28×body320valid
7.0ms102×body80valid
5.0ms86×body80nan
3.0ms17×body160valid

simplify6.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
14015
217915
3121215
done500015

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b
(pow (+ 1.0 (/ i n)) n)
11.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.5s

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:
547.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
294.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
34.0ms
(pow (+ 1.0 (/ i n)) n)
574.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts
4 → 12
Calls
4 calls:
561.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
362.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
335.0ms
(pow (+ 1.0 (/ i n)) n)
572.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify933.0ms

Counts
333 → 333
Iterations

Useful iterations: done (914.0ms)

IterNodesCost
04797415
done50006760

prune1.4s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.2b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (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)))
10.1b
(* (pow i 2) (log 1.0))
18.9b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite126.0ms

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
53.0ms
(* 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)))
26.0ms
(* (pow i 2) (log 1.0))
37.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series783.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
276.0ms
(* 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)))
209.0ms
(* (pow i 2) (log 1.0))
240.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify680.0ms

Counts
201 → 201
Iterations

Useful iterations: done (672.0ms)

IterNodesCost
03296419
done50016180

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 10.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
3.3b
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.1b
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
10.1b
(* (pow i 2) (log 1.0))

rewrite590.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
38×add-cbrt-cube
37×prod-exp
27×add-sqr-sqrt associate-*l*
21×pow1
19×add-cube-cbrt *-un-lft-identity cbrt-unprod
12×associate-*l/
10×pow-prod-down
9×times-frac associate-*r/ associate-*r*
8×div-exp
6×log-prod
5×flip3-- flip-- unswap-sqr
4×cbrt-undiv expm1-log1p-u frac-times unpow-prod-down rec-exp 1-exp *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 137
Calls
4 calls:
487.0ms
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
28.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
52.0ms
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
15.0ms
(* (pow i 2) (log 1.0))

series988.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
203.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
275.0ms
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
217.0ms
(* (pow i 2) (log 1.0))

simplify3.2s

Counts
149 → 149
Iterations

Useful iterations: done (3.2s)

IterNodesCost
02464394
143534079
done50004077

prune594.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.5b

localize20.0ms

Local error

Found 4 expressions with local error:

0.3b
(* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
3.3b
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
9.6b
(/ (* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
10.1b
(* (pow i 2) (log 1.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
25×add-exp-log
22×add-sqr-sqrt add-cbrt-cube
14×add-cube-cbrt *-un-lft-identity associate-*l*
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod associate-*l/
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down associate-*r/ pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in flip3-- distribute-lft-in times-frac div-exp associate-/r* *-commutative flip--
2×associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow div-inv associate-/l*
Counts
4 → 107
Calls
4 calls:
30.0ms
(* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
19.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
40.0ms
(/ (* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
16.0ms
(* (pow i 2) (log 1.0))

series742.0ms

Counts
4 → 12
Calls
4 calls:
174.0ms
(* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) 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)))) n)
238.0ms
(/ (* 100.0 (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) i)
174.0ms
(* (pow i 2) (log 1.0))

simplify1.8s

Counts
119 → 119
Iterations

Useful iterations: done (1.8s)

IterNodesCost
02043097
143693000
done50002998

prune424.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.5b

regimes238.0ms

Accuracy

55.3% (9.9b remaining)

Error of 20.7b against oracle of 10.8b and baseline of 33.0b

bsearch265.0ms

Steps
ItersRangePoint
11
0.12160444842987421
4.529904795396554e+32
0.5476118163719529
6
-11.923248480236845
-0.7718806003288846
-1.746254556247626

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03889
14889
done4889

end0.0ms

sample6.0s

Algorithm
intervals
Results
2.5s1038×body2560valid
2.0s2469×body1280valid
545.0ms1572×body640valid
199.0ms860×body320valid
194.0ms3059×body80valid
124.0ms2212×body80nan
52.0ms425×body160valid
24.0ms6×body5120valid