Details

Time bar (total: 29.0s)

sample194.0ms

Algorithm
intervals
Results
78.0ms37×body2560valid
69.0ms87×body1280valid
15.0ms46×body640valid
5.0ms88×body80valid
5.0ms26×body320valid
3.0ms61×body80nan
2.0ms13×body160valid

simplify4.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.4b
(pow (+ 1.0 (/ i n)) n)
11.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

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:
519.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
259.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
32.0ms
(pow (+ 1.0 (/ i n)) n)
563.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
483.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
346.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
291.0ms
(pow (+ 1.0 (/ i n)) n)
458.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.3s

Counts
333 → 333
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 21.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.6b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
4.4b
(pow (+ 1.0 (/ i n)) n)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv
Counts
4 → 139
Calls
4 calls:
481.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
413.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
273.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
484.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
185.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
303.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
282.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.7s

Counts
151 → 151
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02662849
16422487
218012130
done50012066

prune369.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 9.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* i i) (- 0.5 (* 0.5 (log 1.0))))
0.0b
(* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
0.1b
(* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n)
8.4b
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-exp-log add-cbrt-cube
24×add-cube-cbrt *-un-lft-identity
19×times-frac associate-*r*
16×pow1
10×prod-exp cbrt-unprod
7×pow-prod-down
6×prod-diff
5×distribute-rgt-in distribute-lft-in associate-*l*
4×expm1-log1p-u associate-*r/ log1p-expm1-u add-log-exp
3×cbrt-undiv div-exp associate-/r* *-commutative associate-/l* unswap-sqr
2×sub-neg div-inv
1×flip3-- frac-2neg associate-*l/ clear-num flip--
Counts
4 → 119
Calls
4 calls:
31.0ms
(* (* i i) (- 0.5 (* 0.5 (log 1.0))))
14.0ms
(* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
38.0ms
(* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n)
11.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series927.0ms

Counts
4 → 12
Calls
4 calls:
282.0ms
(* (* i i) (- 0.5 (* 0.5 (log 1.0))))
194.0ms
(* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i))
254.0ms
(* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n)
198.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify1.2s

Counts
131 → 131
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02203344
15523287
218132812
done50012780

prune498.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 9.7b

localize43.0ms

Local error

Found 4 expressions with local error:

4.9b
(cbrt (* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n))
8.4b
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
8.4b
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
8.4b
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

rewrite58.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×times-frac
10×add-exp-log add-cbrt-cube
9×associate-/r* associate-/l*
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv frac-2neg div-exp clear-num div-inv
1×cbrt-prod cbrt-div pow1/3 associate-*r/ associate-*l/
Counts
4 → 99
Calls
4 calls:
22.0ms
(cbrt (* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n))
7.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
8.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
16.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

series1.7s

Counts
4 → 12
Calls
4 calls:
1.2s
(cbrt (* (* 100.0 (/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)) n))
178.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
176.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)
196.0ms
(/ (fma 1.0 i (fma n (log 1.0) (* (* i i) (- 0.5 (* 0.5 (log 1.0)))))) i)

simplify1.6s

Counts
111 → 111
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01363331
13003287
28773007
332872976
done50002940

prune480.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.7b

regimes240.0ms

Accuracy

50.4% (12.7b remaining)

Error of 21.6b against oracle of 9.0b and baseline of 34.5b

bsearch641.0ms

Steps
ItersRangePoint
10
4.6613578248599036e+256
1.2994524770628015e+268
1.6745382427765641e+263
10
1.5413302547539786e+215
3.373628491110601e+225
7.312595874998128e+224
8
1.2456778793859182e-05
0.01071774990460724
0.010271927589648086
7
3.438634446226003e-14
3.2324718487672696e-12
3.5115451043342654e-14
6
2.0778191396362455e-54
1.8656011488683937e-53
1.8395426177605914e-53
9
-3.362342865993284e+21
-574862664789267.1
-587178759827394.1

simplify11.0ms

Iterations

Useful iterations: 1 (7.0ms)

IterNodesCost
075310
196271
done96271

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.1s2532×body1280valid
2.0s953×body2560valid
794.0ms1601×body640valid
219.0ms3033×body80valid
164.0ms862×body320valid
121.0ms2249×body80nan
58.0ms493×body160valid
55.0ms7×body5120valid