Details

Time bar (total: 33.6s)

sample215.0ms

Algorithm
intervals
Results
74.0ms70×body1280valid
69.0ms27×body2560valid
22.0ms47×body640valid
13.0ms47×body320valid
7.0ms103×body80valid
4.0ms69×body80nan
3.0ms15×body160valid

simplify4.3s

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: 41.6b

localize17.0ms

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))

rewrite1.3s

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:
429.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
526.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
564.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
337.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
273.0ms
(pow (+ 1.0 (/ i n)) n)
510.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.2s

Counts
333 → 333
Iterations

Useful iterations: done (2.2s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.2s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 17.8b

localize21.0ms

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)

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
340×times-frac
330×add-sqr-sqrt
230×*-un-lft-identity
162×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
48×unpow-prod-down
33×sqr-pow
30×add-cbrt-cube
28×distribute-lft-out--
24×prod-diff
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×fma-neg unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
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
Counts
4 → 350
Calls
4 calls:
573.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
485.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
308.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms
(pow (+ 1.0 (/ i n)) n)

series1.8s

Counts
4 → 12
Calls
4 calls:
687.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
461.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
356.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
269.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.6s

Counts
362 → 362
Iterations

Useful iterations: done (2.6s)

IterNodesCost
05098413
114857047
238466493
done50016429

prune887.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 9.8b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

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
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×frac-times pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 218
Calls
4 calls:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
25.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
13.0ms
(* (pow i 2) (log 1.0))
55.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series655.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
184.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
175.0ms
(* (pow i 2) (log 1.0))
248.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify1.5s

Counts
230 → 230
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03707821
110117158
230696509
done50006506

prune909.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 9.8b

localize27.0ms

Local error

Found 4 expressions with local error:

11.9b
(* (/ 100.0 i) (* (* (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))))
19.3b
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
19.3b
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
19.3b
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
143×associate-*l/
114×cbrt-div
82×frac-times
57×flip3-- flip--
42×associate-*r/
25×add-exp-log
17×add-cbrt-cube
13×pow1 associate-*l*
12×prod-exp cbrt-unprod
11×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
9×times-frac
6×pow-prod-down
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv cbrt-prod pow1/3 div-exp
1×associate-*r* *-commutative div-inv
Counts
4 → 131
Calls
4 calls:
297.0ms
(* (/ 100.0 i) (* (* (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))))
11.0ms
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
11.0ms
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
9.0ms
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

series3.5s

Counts
4 → 12
Calls
4 calls:
292.0ms
(* (/ 100.0 i) (* (* (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))) (cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))))
1.1s
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
1.1s
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
1.0s
(cbrt (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

simplify1.2s

Counts
143 → 143
Iterations

Useful iterations: done (1.2s)

IterNodesCost
030013923
179913413
2237610381
done50009785

prune820.0ms

Pruning

16 alts after pruning (15 fresh and 1 done)

Merged error: 9.8b

regimes283.0ms

Accuracy

51.4% (12.7b remaining)

Error of 21.2b against oracle of 8.5b and baseline of 34.6b

bsearch507.0ms

Steps
ItersRangePoint
7
2.2669604678046256e+182
1.3827742542902607e+184
1.353418716849569e+183
6
6.338470633040872e+46
3.8306613581281646e+47
6.433403710498658e+46
1
2.3857838936282895e-182
2.530195443784478e-182
2.4218867811673365e-182
7
8.139263728298644e-233
9.809081465533469e-231
4.636828096634822e-231
10
-7465.585501010854
-4.353488769003373e-11
-0.09568466101685805

simplify8.0ms

Iterations

Useful iterations: 1 (5.0ms)

IterNodesCost
059196
173195
done73195

end0.0ms

sample6.1s

Algorithm
intervals
Results
2.3s2443×body1280valid
2.0s978×body2560valid
623.0ms1612×body640valid
365.0ms433×body160valid
238.0ms910×body320valid
161.0ms3081×body80valid
121.0ms2245×body80nan
37.0ms10×body5120valid