Details

Time bar (total: 19.9s)

sample152.0ms

Algorithm
intervals
Results
61.0ms30×body2560valid
49.0ms75×body1280valid
14.0ms48×body640valid
4.0ms107×body80valid
4.0ms1×body5120valid
4.0ms23×body320valid
3.0ms84×body80nan
1.0ms15×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25915
314115
433715
599415
6397915
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))

rewrite611.0ms

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:
228.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
127.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
227.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
371.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
209.0ms
(pow (+ 1.0 (/ i n)) n)
350.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify575.0ms

Counts
333 → 333
Iterations

Useful iterations: done (559.0ms)

IterNodesCost
04797415
113026800
done50006712

prune862.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite794.0ms

Algorithm
rewrite-expression-head
Rules
107×sqrt-prod
94×*-un-lft-identity
74×add-sqr-sqrt
66×prod-diff
60×add-cube-cbrt
38×unpow-prod-down
19×associate-*l*
18×add-exp-log
16×add-cbrt-cube
15×times-frac distribute-lft-out
11×pow1 fma-neg sqr-pow
8×difference-of-squares
6×pow-unpow prod-exp cbrt-unprod add-log-exp
5×associate-*l/
4×expm1-log1p-u log1p-expm1-u
3×flip3-- pow-prod-down flip--
2×cbrt-undiv frac-times pow-to-exp pow-pow associate-*r/ div-exp pow-exp distribute-lft-out--
1×sub-neg diff-log associate-*r* *-commutative div-inv
Counts
4 → 186
Calls
4 calls:
628.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) n))
133.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
14.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.3s

Counts
4 → 12
Calls
4 calls:
592.0ms
(* (/ (+ (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) i) (* (- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0)) n))
304.0ms
(- (sqrt (pow (+ 1.0 (/ i n)) n)) (sqrt 1.0))
220.0ms
(pow (+ 1.0 (/ i n)) n)
215.0ms
(pow (+ 1.0 (/ i n)) n)

simplify804.0ms

Counts
198 → 198
Iterations

Useful iterations: done (797.0ms)

IterNodesCost
02705563
16334179
220833275
done50003271

prune482.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 19.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* n (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.1b
(* 100.0 (/ (* n (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.8b
(pow (+ 1.0 (/ i n)) n)

rewrite529.0ms

Algorithm
rewrite-expression-head
Rules
81×*-un-lft-identity
72×prod-diff
69×add-sqr-sqrt
55×add-cube-cbrt
46×unpow-prod-down
26×distribute-rgt-in distribute-lft-in
16×add-exp-log
15×add-cbrt-cube
14×associate-*r*
13×sqr-pow
11×distribute-lft-out
9×pow1
8×fma-neg
6×associate-*l* add-log-exp difference-of-squares
5×prod-exp cbrt-unprod
4×expm1-log1p-u log1p-expm1-u
3×sub-neg pow-unpow times-frac associate-*r/
2×cbrt-undiv flip3-- div-exp pow-prod-down *-commutative flip-- distribute-lft-out-- unswap-sqr
1×pow-to-exp pow-pow diff-log pow-exp div-inv
Counts
4 → 177
Calls
4 calls:
222.0ms
(* n (- (pow (+ 1.0 (/ i n)) n) 1.0))
158.0ms
(* 100.0 (/ (* n (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
128.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series751.0ms

Counts
4 → 12
Calls
4 calls:
105.0ms
(* n (- (pow (+ 1.0 (/ i n)) n) 1.0))
162.0ms
(* 100.0 (/ (* n (- (pow (+ 1.0 (/ i n)) n) 1.0)) i))
260.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
224.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.3s

Counts
189 → 189
Iterations

Useful iterations: done (1.3s)

IterNodesCost
03814877
19403971
238993287
done50013277

prune364.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 6.6b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i))
4.3b
(* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
12.1b
(* (pow i 2) (log 1.0))
12.5b
(/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
25×add-exp-log
22×add-cbrt-cube
18×add-cube-cbrt *-un-lft-identity
14×associate-*r* associate-*l*
9×pow1 distribute-rgt-in distribute-lft-in prod-exp
7×cbrt-unprod
6×log-prod times-frac prod-diff unswap-sqr
5×associate-*r/
4×cbrt-undiv expm1-log1p-u unpow-prod-down div-exp log1p-expm1-u add-log-exp
3×associate-/r* *-commutative
2×sub-neg flip3-- pow-prod-down associate--l+ flip-- fma-udef div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg pow-exp clear-num log-pow associate-/l*
Counts
4 → 124
Calls
4 calls:
10.0ms
(* 100.0 (/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i))
8.0ms
(* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
6.0ms
(* (pow i 2) (log 1.0))
8.0ms
(/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)

series693.0ms

Counts
4 → 12
Calls
4 calls:
206.0ms
(* 100.0 (/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i))
153.0ms
(* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))))
146.0ms
(* (pow i 2) (log 1.0))
188.0ms
(/ (* n (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0))))) i)

simplify1.2s

Counts
136 → 136
Iterations

Useful iterations: 2 (540.0ms)

IterNodesCost
02373653
15703572
224602990
done50012990

prune375.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.6b

regimes255.0ms

Accuracy

48% (12.7b remaining)

Error of 22.3b against oracle of 9.6b and baseline of 34.0b

bsearch710.0ms

Steps
ItersRangePoint
9
2.5671232099758783e-108
2.1919214055018434e-100
6.744970164018845e-102
9
2.385744712109479e-299
1.428658578821738e-291
2.4424949821184467e-299
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

simplify12.0ms

Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
096297
1120297
done120297

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s954×body2560valid
1.7s2510×body1280valid
464.0ms1657×body640valid
143.0ms866×body320valid
124.0ms3029×body80valid
71.0ms2286×body80nan
42.0ms423×body160valid
21.0ms6×body5120valid