Details

Time bar (total: 22.7s)

sample160.0ms

Algorithm
intervals
Results
62.0ms30×body2560valid
51.0ms75×body1280valid
14.0ms48×body640valid
6.0ms84×body80nan
5.0ms107×body80valid
4.0ms1×body5120valid
4.0ms23×body320valid
1.0ms15×body160valid

simplify2.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25915
314115
433715
599315
6391415
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite639.0ms

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:
238.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
132.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)
234.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts
4 → 12
Calls
4 calls:
596.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
277.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
234.0ms
(pow (+ 1.0 (/ i n)) n)
370.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.4s

Counts
333 → 333
Iterations

Useful iterations: done (1.4s)

IterNodesCost
04797415
113026800
239566406
done50016382

prune857.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
0.9b
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite705.0ms

Algorithm
rewrite-expression-head
Rules
431×sqrt-prod
330×prod-diff
302×*-un-lft-identity
272×distribute-rgt-in distribute-lft-in
234×add-sqr-sqrt
220×add-cube-cbrt
134×unpow-prod-down
39×distribute-lft-out
35×sqr-pow
19×associate-*l*
18×add-exp-log
16×add-cbrt-cube
15×times-frac
11×pow1 fma-neg
8×difference-of-squares
6×pow-unpow associate-*r/ prod-exp cbrt-unprod add-log-exp
5×sub-neg
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow-prod-down flip--
2×cbrt-undiv frac-times pow-to-exp pow-pow div-exp pow-exp distribute-lft-out--
1×diff-log associate-*r* associate-*l/ *-commutative div-inv
Counts
4 → 458
Calls
4 calls:
510.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
139.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
616.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))))
318.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
219.0ms
(pow (+ 1.0 (/ i n)) n)
221.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.4s

Counts
470 → 470
Iterations

Useful iterations: done (1.3s)

IterNodesCost
058225673
1146621377
2348116139
done500016119

prune581.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 19.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) (/ (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))) i)))
0.9b
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite825.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
74×*-un-lft-identity
66×add-sqr-sqrt prod-diff
52×add-cube-cbrt
38×unpow-prod-down
20×add-exp-log
18×add-cbrt-cube
11×pow1 fma-neg sqr-pow
9×distribute-lft-out
8×prod-exp cbrt-unprod difference-of-squares
6×pow-unpow associate-*r/ add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*l* pow-prod-down
2×cbrt-undiv frac-times pow-to-exp pow-pow flip3-+ div-exp associate-*l/ pow-exp flip-+ distribute-lft-out--
1×sub-neg flip3-- diff-log associate-*r* *-commutative flip--
Counts
4 → 170
Calls
4 calls:
651.0ms
(* 100.0 (* (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) (/ (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))) i)))
143.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
12.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.4s

Counts
4 → 12
Calls
4 calls:
653.0ms
(* 100.0 (* (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) (/ (* n (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))) i)))
318.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
233.0ms
(pow (+ 1.0 (/ i n)) n)
230.0ms
(pow (+ 1.0 (/ i n)) n)

simplify809.0ms

Counts
182 → 182
Iterations

Useful iterations: done (803.0ms)

IterNodesCost
02725151
16504197
220402964
done50002960

prune448.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 19.0b

localize27.0ms

Local error

Found 4 expressions with local error:

7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite47.0ms

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:
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series924.0ms

Counts
4 → 12
Calls
4 calls:
232.0ms
(pow (+ 1.0 (/ i n)) n)
225.0ms
(pow (+ 1.0 (/ i n)) n)
235.0ms
(pow (+ 1.0 (/ i n)) n)
231.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.5s

Counts
92 → 92
Iterations

Useful iterations: done (1.5s)

IterNodesCost
0551008
1113936
2235900
3569892
41576872
done5001856

prune388.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 18.6b

regimes148.0ms

Accuracy

47.1% (11.4b remaining)

Error of 32.9b against oracle of 21.5b and baseline of 43.1b

bsearch450.0ms

Steps
ItersRangePoint
7
1.8763976102611505e-155
6.193957419652655e-154
5.52097250963737e-155
6
1.428658578821738e-291
1.1241352939529096e-290
1.4472641457797862e-291
8
-542359391.39979
-925426.909356872
-934893.9033682138
5
-2.350670412092924e+26
-9.509086209243448e+25
-1.0288882388677418e+26
7
-9.598097109554337e+63
-7.474441928331378e+61
-5.658742524400702e+63
6
-4.85405993564138e+85
-5.838951595693273e+84
-6.3031952158969e+84

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
050170
160170
done60170

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s954×body2560valid
1.8s2510×body1280valid
479.0ms1657×body640valid
149.0ms866×body320valid
139.0ms3029×body80valid
74.0ms2286×body80nan
43.0ms423×body160valid
21.0ms6×body5120valid