Details

Time bar (total: 54.2s)

sample231.0ms

Algorithm
intervals
Results
89.0ms74×body1280valid
70.0ms24×body2560valid
26.0ms53×body640valid
8.0ms27×body320valid
8.0ms104×body80valid
4.0ms58×body80nan
4.0ms18×body160valid

simplify3.5s

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

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (- (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:
389.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
294.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms
(pow (+ 1.0 (/ i n)) n)
420.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
486.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
329.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
287.0ms
(pow (+ 1.0 (/ i n)) n)
514.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.4s

Counts
293 → 293
Iterations

Useful iterations: done (2.4s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (- (pow (/ i n) n) 1.0) (/ i n))
0.1b
(* 100.0 (/ (- (pow (/ i n) n) 1.0) (/ i n)))
1.7b
(- (pow (/ i n) n) 1.0)
6.1b
(pow (/ i n) n)

rewrite377.0ms

Algorithm
rewrite-expression-head
Rules
401×times-frac
393×add-sqr-sqrt
216×*-un-lft-identity
160×add-cube-cbrt
112×difference-of-squares
109×associate-*r*
69×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
21×add-exp-log
20×div-inv
18×add-cbrt-cube
13×associate-/r*
8×associate-/l*
7×pow1 div-exp
6×cbrt-undiv add-log-exp
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- pow-exp associate-/r/ flip-- associate-/l/
1×pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down clear-num *-commutative
Counts
4 → 319
Calls
4 calls:
106.0ms
(/ (- (pow (/ i n) n) 1.0) (/ i n))
187.0ms
(* 100.0 (/ (- (pow (/ i n) n) 1.0) (/ i n)))
52.0ms
(- (pow (/ i n) n) 1.0)
9.0ms
(pow (/ i n) n)

series513.0ms

Counts
4 → 12
Calls
4 calls:
189.0ms
(/ (- (pow (/ i n) n) 1.0) (/ i n))
170.0ms
(* 100.0 (/ (- (pow (/ i n) n) 1.0) (/ i n)))
94.0ms
(- (pow (/ i n) n) 1.0)
59.0ms
(pow (/ i n) n)

simplify820.0ms

Counts
331 → 331
Iterations

Useful iterations: done (807.0ms)

IterNodesCost
05536805
115666436
done50016208

prune1.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 16.9b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))
7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite868.0ms

Algorithm
rewrite-expression-head
Rules
1005×times-frac
550×*-un-lft-identity
492×add-sqr-sqrt
378×add-cube-cbrt
171×difference-of-squares
86×distribute-lft-out
65×unpow-prod-down
59×sqr-pow
46×div-inv
30×associate-/l*
29×associate-/r/
18×add-exp-log
16×add-cbrt-cube
14×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv div-exp
6×pow1 add-log-exp
4×pow-unpow
2×pow-to-exp pow-pow div-sub pow-exp
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- associate-/l/
Counts
4 → 503
Calls
4 calls:
205.0ms
(- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
18.0ms
(pow (+ 1.0 (/ i n)) n)
576.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series3.5s

Counts
4 → 12
Calls
4 calls:
390.0ms
(- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))
297.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
270.0ms
(pow (+ 1.0 (/ i n)) n)
2.5s
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.7s

Counts
515 → 515
Iterations

Useful iterations: done (1.6s)

IterNodesCost
087025488
1256224435
done500023520

prune2.2s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.9b

localize32.0ms

Local error

Found 4 expressions with local error:

7.1b
(pow (+ 1.0 (/ i n)) (* 2 n))
7.1b
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
7.1b
(pow (+ 1.0 (/ i n)) n)
8.4b
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
2805×times-frac
1519×*-un-lft-identity
1093×add-sqr-sqrt add-cube-cbrt
213×distribute-lft-out
141×associate-/r/
138×div-inv
70×flip3-+ flip-+
66×associate-/l*
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
13×associate-/r*
12×unpow-prod-down
7×pow1
5×pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow div-sub pow-exp sqr-pow
1×frac-2neg clear-num associate-/l/
Counts
4 → 1012
Calls
4 calls:
28.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
28.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
26.0ms
(pow (+ 1.0 (/ i n)) n)
976.0ms
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series19.0s

Counts
4 → 12
Calls
4 calls:
223.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
220.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
219.0ms
(pow (+ 1.0 (/ i n)) n)
18.4s
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (+ (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.9s

Counts
1024 → 1024
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0164387135
1474280060
done500179480

prune4.5s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 16.9b

regimes202.0ms

Accuracy

47.3% (13.5b remaining)

Error of 30.1b against oracle of 16.6b and baseline of 42.3b

bsearch844.0ms

Steps
ItersRangePoint
8
1.1212535610288124e+173
2.4125232853227754e+177
2.1280471197997414e+177
9
8.666561730544872e-18
1.507024095617085e-11
9.089128901802148e-18
6
4.924640387312937e-45
6.021187163235515e-44
3.6825165457393707e-44
9
1.0780503446373146e-112
5.256007885959504e-104
2.053192934454679e-111
10
-7.877897683081498e-299
5.372664985270084e-304
-2.4372743425058e-310

simplify19.0ms

Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
0136388
1202388
done202388

end0.0ms

sample5.4s

Algorithm
intervals
Results
2.2s2456×body1280valid
1.8s957×body2560valid
516.0ms1652×body640valid
174.0ms3034×body80valid
173.0ms811×body320valid
84.0ms2209×body80nan
51.0ms452×body160valid
41.0ms12×body5120valid