Details

Time bar (total: 18.6s)

sample155.0ms

Algorithm
intervals
Results
60.0ms30×body2560valid
52.0ms75×body1280valid
14.0ms48×body640valid
5.0ms107×body80valid
4.0ms1×body5120valid
4.0ms23×body320valid
3.0ms84×body80nan
1.0ms15×body160valid

simplify2.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25915
314115
434415
5104615
6437615
done500015

prune2.0ms

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))

rewrite666.0ms

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:
247.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
138.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)
244.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
381.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
216.0ms
(pow (+ 1.0 (/ i n)) n)
363.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify427.0ms

Counts
333 → 333
Iterations

Useful iterations: done (415.0ms)

IterNodesCost
04797415
113316800
done50006771

prune917.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite585.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*l*
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-*r* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*r/ pow-exp flip-- div-inv
Counts
4 → 139
Calls
4 calls:
180.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
247.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
140.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
13.0ms
(pow (+ 1.0 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
399.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
373.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
266.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.2s

Counts
151 → 151
Iterations

Useful iterations: 2 (395.0ms)

IterNodesCost
02522834
16342497
225032114
done50002114

prune325.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.2b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
0.1b
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.5b
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.1b
(* (pow i 2) (log 1.0))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*l/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 125
Calls
4 calls:
12.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
14.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
10.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms
(* (pow i 2) (log 1.0))

series679.0ms

Counts
4 → 12
Calls
4 calls:
190.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
212.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
135.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
141.0ms
(* (pow i 2) (log 1.0))

simplify725.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (166.0ms)

IterNodesCost
02203686
15393611
221823106
done50003106

prune435.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
0.1b
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
11.5b
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.1b
(* (pow i 2) (log 1.0))

rewrite45.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*l/ pow-exp clear-num log-pow flip--
Counts
4 → 125
Calls
4 calls:
11.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
16.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
7.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms
(* (pow i 2) (log 1.0))

series645.0ms

Counts
4 → 12
Calls
4 calls:
154.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
210.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
140.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
141.0ms
(* (pow i 2) (log 1.0))

simplify843.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (187.0ms)

IterNodesCost
02243707
15533615
224633112
done50003112

prune393.0ms

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 8.2b

regimes220.0ms

Accuracy

46.1% (12.2b remaining)

Error of 23.6b against oracle of 11.4b and baseline of 34.0b

bsearch574.0ms

Steps
ItersRangePoint
7
1.8763976102611505e-155
6.193957419652655e-154
6.2539521969327255e-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
-1.0912719332224593e+26
7
-9.598097109554337e+63
-7.474441928331378e+61
-3.317476088456595e+63
6
-4.85405993564138e+85
-5.838951595693273e+84
-4.0369911640829986e+85
7
-2.854726066546375e+174
-4.469800189377323e+172
-1.0029723224091834e+174

simplify5.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
058201
171201
done71201

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s954×body2560valid
1.8s2510×body1280valid
479.0ms1657×body640valid
145.0ms866×body320valid
132.0ms3029×body80valid
74.0ms2286×body80nan
43.0ms423×body160valid
21.0ms6×body5120valid