Details

Time bar (total: 31.7s)

sample205.0ms

Algorithm
intervals
Results
72.0ms36×body2560valid
71.0ms80×body1280valid
25.0ms38×body640valid
6.0ms28×body320valid
6.0ms102×body80valid
4.0ms86×body80nan
2.0ms17×body160valid

simplify3.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
313915
433815
598615
6405915
done500015

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.0b

localize15.0ms

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))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
375.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
223.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
377.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
469.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
319.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
292.0ms
(pow (+ 1.0 (/ i n)) n)
490.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.0s

Counts
293 → 293
Iterations

Useful iterations: done (2.0s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.5b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
0.1b
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 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
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite792.0ms

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 add-log-exp
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×unpow-prod-down cbrt-unprod
3×distribute-rgt-in distribute-lft-in sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 186
Calls
4 calls:
36.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
377.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
25.0ms
(* (pow i 2) (log 1.0))
343.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series879.0ms

Counts
4 → 12
Calls
4 calls:
62.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
338.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
217.0ms
(* (pow i 2) (log 1.0))
262.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.6s

Counts
198 → 198
Iterations

Useful iterations: 2 (620.0ms)

IterNodesCost
03386829
19026613
233866123
done50006123

prune1.1s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 7.9b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite3.4s

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 frac-times unpow-prod-down rec-exp 1-exp *-commutative 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 → 129
Calls
4 calls:
1.9s
(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
616.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
926.0ms
(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
26.0ms
(* (pow i 2) (log 1.0))

series927.0ms

Counts
4 → 12
Calls
4 calls:
293.0ms
(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
170.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
268.0ms
(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
195.0ms
(* (pow i 2) (log 1.0))

simplify2.1s

Counts
141 → 141
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02404476
16164220
224833407
done50013389

prune459.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
3.3b
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.0b
(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 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))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×associate-*l*
23×add-exp-log
20×add-cbrt-cube
18×add-cube-cbrt *-un-lft-identity
12×pow1
10×prod-exp
9×times-frac add-log-exp
8×associate-*r* cbrt-unprod
7×associate-*l/
6×log-prod
5×unswap-sqr
4×unpow-prod-down pow-prod-down
3×distribute-rgt-in flip3-- distribute-lft-in sum-log *-commutative flip--
2×cbrt-undiv frac-times associate-*r/ div-exp unpow2 sqr-pow
1×+-commutative pow-to-exp associate-+r+ flip3-+ pow-exp log-pow flip-+ div-inv
Counts
4 → 104
Calls
4 calls:
21.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
435.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
628.0ms
(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 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))

series599.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
150.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
229.0ms
(* (/ 100.0 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
169.0ms
(* (pow i 2) (log 1.0))

simplify1.5s

Counts
116 → 116
Iterations

Useful iterations: done (1.5s)

IterNodesCost
02193108
15943005
224682555
done50022551

prune359.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 7.9b

regimes256.0ms

Accuracy

58.1% (10.3b remaining)

Error of 18.8b against oracle of 8.5b and baseline of 33.1b

bsearch258.0ms

Steps
ItersRangePoint
11
0.12160444842987421
4.529904795396554e+32
0.5476118163719529
6
-11.923248480236845
-0.7718806003288846
-0.8489635077384908

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04190
15690
done5690

end0.0ms

sample6.5s

Algorithm
intervals
Results
2.3s2469×body1280valid
2.3s1038×body2560valid
915.0ms1572×body640valid
228.0ms860×body320valid
174.0ms3059×body80valid
129.0ms2212×body80nan
56.0ms425×body160valid
25.0ms6×body5120valid