Details

Time bar (total: 31.1s)

sample233.0ms

Algorithm
intervals
Results
78.0ms70×body1280valid
71.0ms27×body2560valid
29.0ms47×body320valid
23.0ms47×body640valid
8.0ms103×body80valid
5.0ms69×body80nan
3.0ms15×body160valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
313915
433815
598615
6405915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.7b
(pow (+ 1.0 (/ i n)) n)
7.7b
(/ (- (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:
463.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
270.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms
(pow (+ 1.0 (/ i n)) n)
457.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
484.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
305.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
290.0ms
(pow (+ 1.0 (/ i n)) n)
507.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.1s

Counts
293 → 293
Iterations

Useful iterations: done (2.1s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune1.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 17.8b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.0b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.7b
(pow (+ 1.0 (/ i n)) n)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num *-commutative distribute-lft-out
Counts
4 → 310
Calls
4 calls:
422.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
528.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
222.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
33.0ms
(pow (+ 1.0 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
400.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
465.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
290.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
285.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.5s

Counts
322 → 322
Iterations

Useful iterations: done (2.5s)

IterNodesCost
04677463
113956375
236765965
done50005949

prune821.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.8b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
2.3b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
11.9b
(* (pow i 2) (log 1.0))
11.9b
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite928.0ms

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
9×add-log-exp
7×pow1 cbrt-unprod
6×log-prod
4×unpow-prod-down
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative frac-times pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 215
Calls
4 calls:
40.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
374.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
28.0ms
(* (pow i 2) (log 1.0))
473.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series682.0ms

Counts
4 → 12
Calls
4 calls:
60.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
176.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
200.0ms
(* (pow i 2) (log 1.0))
246.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify1.6s

Counts
227 → 227
Iterations

Useful iterations: 2 (745.0ms)

IterNodesCost
03798307
110887654
235336960
done50006960

prune865.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 9.8b

localize28.0ms

Local error

Found 4 expressions with local error:

11.9b
(* (pow i 2) (log 1.0))
19.3b
(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
19.3b
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
19.3b
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

rewrite380.0ms

Algorithm
rewrite-expression-head
Rules
66×times-frac
50×add-sqr-sqrt
46×cbrt-prod
44×add-cube-cbrt *-un-lft-identity
9×add-exp-log
8×associate-*l*
6×log-prod add-cbrt-cube
5×pow1 cbrt-div
4×unpow-prod-down associate-*r* associate-*l/ div-inv add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in pow1/3 prod-exp
2×flip3-- flip-- unpow2 sqr-pow
1×pow-to-exp pow-exp associate-/r/ log-pow *-commutative cbrt-unprod
Counts
4 → 109
Calls
4 calls:
15.0ms
(* (pow i 2) (log 1.0))
64.0ms
(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
145.0ms
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
152.0ms
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

series2.6s

Counts
4 → 12
Calls
4 calls:
166.0ms
(* (pow i 2) (log 1.0))
823.0ms
(cbrt (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))
808.0ms
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
812.0ms
(cbrt (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

simplify1.1s

Counts
121 → 121
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03284947
16694626
217514392
done50003719

prune586.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.8b

regimes257.0ms

Accuracy

54.9% (11.5b remaining)

Error of 20.1b against oracle of 8.7b and baseline of 34.1b

bsearch320.0ms

Steps
ItersRangePoint
7
2.2669604678046256e+182
1.3827742542902607e+184
1.353418716849569e+183
6
6.338470633040872e+46
3.8306613581281646e+47
6.433403710498658e+46
10
-7465.585501010854
-4.353488769003373e-11
-0.09568466101685805

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
048142
167142
done67142

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.2s978×body2560valid
2.0s2443×body1280valid
676.0ms1612×body640valid
228.0ms3081×body80valid
209.0ms910×body320valid
95.0ms2245×body80nan
53.0ms433×body160valid
37.0ms10×body5120valid