Details

Time bar (total: 28.5s)

sample219.0ms

Algorithm
intervals
Results
83.0ms82×body1280valid
71.0ms29×body2560valid
23.0ms48×body640valid
8.0ms107×body80valid
7.0ms25×body320valid
4.0ms73×body80nan
2.0ms12×body160valid

simplify3.8s

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: 43.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.3b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

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:
412.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
223.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
35.0ms
(pow (+ 1.0 (/ i n)) n)
443.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
424.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
267.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
238.0ms
(pow (+ 1.0 (/ i n)) n)
701.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.9s

Counts
293 → 293
Iterations

Useful iterations: done (1.9s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 17.9b

localize27.0ms

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)))
11.9b
(* (pow i 2) (log 1.0))
18.2b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite837.0ms

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:
26.0ms
(* 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)))
15.0ms
(* (pow i 2) (log 1.0))
389.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series824.0ms

Counts
4 → 12
Calls
4 calls:
27.0ms
(* 0.5 (pow i 2))
271.0ms
(* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
210.0ms
(* (pow i 2) (log 1.0))
316.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.9s

Counts
212 → 212
Iterations

Useful iterations: 2 (883.0ms)

IterNodesCost
03456722
18786496
232056002
done50006002

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.5b

localize25.0ms

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))
11.2b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.9b
(* (pow i 2) (log 1.0))

rewrite665.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
14×associate-*l*
13×associate-*r*
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:
24.0ms
(* 0.5 (pow i 2))
267.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
345.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
23.0ms
(* (pow i 2) (log 1.0))

series654.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* 0.5 (pow i 2))
264.0ms
(* 100.0 (* (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
158.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
187.0ms
(* (pow i 2) (log 1.0))

simplify1.3s

Counts
124 → 124
Iterations

Useful iterations: done (1.3s)

IterNodesCost
02162789
15112708
217682292
done50011965

prune517.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.5b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.0b
(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
2.0b
(log (exp (* 0.5 (pow i 2))))
11.9b
(* (pow i 2) (log 1.0))

rewrite917.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
21×associate-*l*
19×times-frac
16×add-exp-log
13×add-cbrt-cube
9×log-prod
8×pow1
7×associate-*r*
6×unswap-sqr
5×prod-exp add-log-exp
4×unpow-prod-down log-pow
3×distribute-rgt-in distribute-lft-in associate-/r* cbrt-unprod associate-/l*
2×cbrt-undiv div-exp *-commutative div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp exp-prod flip3-- exp-to-pow frac-2neg div-sub rem-log-exp pow-prod-down associate-*l/ pow-exp clear-num flip--
Counts
4 → 110
Calls
4 calls:
430.0ms
(* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
456.0ms
(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
4.0ms
(log (exp (* 0.5 (pow i 2))))
22.0ms
(* (pow i 2) (log 1.0))

series695.0ms

Counts
4 → 12
Calls
4 calls:
229.0ms
(* (/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
182.0ms
(/ (- (+ (* 1.0 i) (+ (log (exp (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
30.0ms
(log (exp (* 0.5 (pow i 2))))
254.0ms
(* (pow i 2) (log 1.0))

simplify1.1s

Counts
122 → 122
Iterations

Useful iterations: done (1.1s)

IterNodesCost
01993116
14512869
215012534
done50002153

prune678.0ms

Pruning

20 alts after pruning (19 fresh and 1 done)

Merged error: 7.5b

regimes357.0ms

Accuracy

57% (10.9b remaining)

Error of 19.2b against oracle of 8.3b and baseline of 33.7b

bsearch296.0ms

Steps
ItersRangePoint
11
0.0033763382367094055
5.206713059748268e+29
0.10387405912847383
5
-2.921513544512531
-0.7794201341187467
-0.9131486383075667

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03867
15267
done5267

end0.0ms

sample6.9s

Algorithm
intervals
Results
2.5s2473×body1280valid
2.3s961×body2560valid
682.0ms1602×body640valid
555.0ms3083×body80valid
193.0ms822×body320valid
145.0ms2281×body80nan
99.0ms429×body160valid
38.0ms8×body5120valid