Details

Time bar (total: 32.0s)

sample241.0ms

Algorithm
intervals
Results
87.0ms27×body2560valid
82.0ms82×body1280valid
26.0ms57×body640valid
9.0ms35×body320valid
8.0ms106×body80valid
4.0ms63×body80nan
3.0ms15×body160valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
313915
433815
598615
6405915
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.8b

localize26.0ms

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))

rewrite1.2s

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:
557.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
244.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
388.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts
4 → 12
Calls
4 calls:
526.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
378.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
297.0ms
(pow (+ 1.0 (/ i n)) n)
604.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.6s

Counts
293 → 293
Iterations

Useful iterations: done (2.5s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune1.2s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.2b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
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)))
11.1b
(* (pow i 2) (log 1.0))
19.0b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite878.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
111×add-sqr-sqrt
90×add-cube-cbrt *-un-lft-identity
56×associate-*r*
28×add-exp-log
22×add-cbrt-cube
14×associate-*l*
13×associate-/r*
11×unswap-sqr
9×prod-exp div-inv
8×unpow-prod-down
7×pow1
6×cbrt-undiv log-prod div-exp
5×cbrt-unprod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in *-commutative associate-/l*
2×pow-to-exp pow-exp associate-/r/ associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num log-pow flip--
Counts
4 → 200
Calls
4 calls:
23.0ms
(* 0.5 (pow i 2))
445.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
28.0ms
(* (pow i 2) (log 1.0))
364.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series921.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(* 0.5 (pow i 2))
333.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
255.0ms
(* (pow i 2) (log 1.0))
283.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.8s

Counts
212 → 212
Iterations

Useful iterations: 2 (931.0ms)

IterNodesCost
03456722
18786496
232056002
done50006002

prune1.1s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
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)
10.5b
(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite762.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×associate-*r*
12×associate-*l*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ associate-*l/ clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
12.0ms
(* 0.5 (pow i 2))
385.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
337.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
24.0ms
(* (pow i 2) (log 1.0))

series729.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* 0.5 (pow i 2))
254.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
185.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
257.0ms
(* (pow i 2) (log 1.0))

simplify1.1s

Counts
124 → 124
Iterations

Useful iterations: 2 (427.0ms)

IterNodesCost
02182792
15182709
218232293
done50012293

prune453.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 8.7b

localize22.0ms

Local error

Found 4 expressions with local error:

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) (/ 1 n)))
0.2b
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
10.5b
(/ (- (+ (* 1.0 i) (+ (* 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))

rewrite917.0ms

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×unpow-prod-down rec-exp 1-exp 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 → 492
Calls
4 calls:
327.0ms
(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
246.0ms
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
288.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
15.0ms
(* (pow i 2) (log 1.0))

series1.0s

Counts
4 → 12
Calls
4 calls:
225.0ms
(* 100.0 (/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
201.0ms
(/ (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
427.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
165.0ms
(* (pow i 2) (log 1.0))

simplify2.2s

Counts
504 → 504
Iterations

Useful iterations: 2 (1.2s)

IterNodesCost
071622321
1196420455
2497419340
done500119340

prune1.6s

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 8.6b

regimes451.0ms

Accuracy

58.1% (10.6b remaining)

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

bsearch449.0ms

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

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04285
15985
done5985

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.2s1021×body2560valid
2.1s2400×body1280valid
718.0ms1650×body640valid
540.0ms3079×body80valid
180.0ms866×body320valid
128.0ms2277×body80nan
60.0ms459×body160valid
10.0ms3×body5120valid