Details

Time bar (total: 52.9s)

sample179.0ms

Algorithm
intervals
Results
67.0ms74×body1280valid
57.0ms24×body2560valid
20.0ms53×body640valid
7.0ms104×body80valid
6.0ms27×body320valid
3.0ms58×body80nan
3.0ms18×body160valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.6b

localize11.0ms

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))

rewrite1.2s

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:
418.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
271.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms
(pow (+ 1.0 (/ i n)) n)
445.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts
4 → 12
Calls
4 calls:
571.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
322.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
279.0ms
(pow (+ 1.0 (/ i n)) n)
771.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.6s

Counts
333 → 333
Iterations

Useful iterations: done (2.6s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.2b

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))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
1005×times-frac
558×*-un-lft-identity
496×add-sqr-sqrt
382×add-cube-cbrt
171×difference-of-squares
88×distribute-lft-out
73×unpow-prod-down
61×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 fma-neg div-exp prod-diff
6×pow1 add-log-exp
4×expm1-log1p-u pow-unpow log1p-expm1-u
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 → 527
Calls
4 calls:
250.0ms
(- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))
25.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
26.0ms
(pow (+ 1.0 (/ i n)) n)
616.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series3.6s

Counts
4 → 12
Calls
4 calls:
348.0ms
(- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0))
294.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
275.0ms
(pow (+ 1.0 (/ i n)) n)
2.7s
(/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 n)) (* 1.0 1.0)) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.7s

Counts
539 → 539
Iterations

Useful iterations: done (1.7s)

IterNodesCost
088725894
1260524811
done500023853

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize48.0ms

Local error

Found 4 expressions with local error:

7.1b
(pow (+ 1.0 (/ i n)) n)
7.1b
(pow (+ 1.0 (/ i n)) n)
7.1b
(pow (+ 1.0 (/ i n)) n)
7.1b
(pow (+ 1.0 (/ i n)) n)

rewrite132.0ms

Algorithm
rewrite-expression-head
Rules
20×*-un-lft-identity
16×unpow-prod-down
12×add-sqr-sqrt add-cube-cbrt pow-unpow
8×pow1 add-exp-log
4×expm1-log1p-u pow-to-exp pow-pow pow-exp add-cbrt-cube log1p-expm1-u distribute-lft-out add-log-exp sqr-pow
Counts
4 → 80
Calls
4 calls:
30.0ms
(pow (+ 1.0 (/ i n)) n)
30.0ms
(pow (+ 1.0 (/ i n)) n)
39.0ms
(pow (+ 1.0 (/ i n)) n)
30.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
293.0ms
(pow (+ 1.0 (/ i n)) n)
305.0ms
(pow (+ 1.0 (/ i n)) n)
296.0ms
(pow (+ 1.0 (/ i n)) n)
273.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.8s

Counts
92 → 92
Iterations

Useful iterations: done (1.8s)

IterNodesCost
0551008
1113936
2236900
3617892
41717872
done5000856

prune451.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

localize35.0ms

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))) (fma 1.0 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite857.0ms

Algorithm
rewrite-expression-head
Rules
2517×times-frac
1379×*-un-lft-identity
1009×add-sqr-sqrt add-cube-cbrt
185×distribute-lft-out
130×div-inv
58×associate-/l*
29×associate-/r/
28×add-exp-log
25×add-cbrt-cube
15×cbrt-undiv div-exp
14×flip3-+ flip-+
13×associate-/r*
12×unpow-prod-down
7×pow1
5×pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow div-sub pow-exp sqr-pow
1×frac-2neg clear-num associate-/l/
Counts
4 → 908
Calls
4 calls:
19.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
34.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
24.0ms
(pow (+ 1.0 (/ i n)) n)
670.0ms
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (fma 1.0 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series16.8s

Counts
4 → 12
Calls
4 calls:
222.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
218.0ms
(pow (+ 1.0 (/ i n)) (* 2 (* 2 n)))
217.0ms
(pow (+ 1.0 (/ i n)) n)
16.1s
(/ (/ (/ (- (pow (+ 1.0 (/ i n)) (* 2 (* 2 n))) (* 1.0 (pow 1.0 3))) (fma 1.0 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))) (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.6s

Counts
920 → 920
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0147275199
1421469945
done500068060

prune3.8s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.2b

regimes161.0ms

Accuracy

48.5% (11.9b remaining)

Error of 31.3b against oracle of 19.4b and baseline of 42.5b

bsearch783.0ms

Steps
ItersRangePoint
10
84517967325.35463
1.9680762236544087e+23
85896130569.3759
10
1.761934526793414e-195
2.1477908055279466e-185
1.7898866790545242e-195
9
-1.5161657059709947e-251
-2.6825235325208276e-257
-6.20217558039948e-257
6
-5.2146422133700853e-08
-7.850775522833093e-09
-3.143171245412234e-08

simplify9.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
066208
183208
done83208

end0.0ms

sample5.7s

Algorithm
intervals
Results
2.0s957×body2560valid
1.8s2456×body1280valid
576.0ms1652×body640valid
438.0ms3034×body80valid
145.0ms811×body320valid
126.0ms2209×body80nan
108.0ms452×body160valid
41.0ms12×body5120valid