Details

Time bar (total: 12.8s)

sample149.0ms

Algorithm
intervals
Results
58.0ms33×body2560valid
51.0ms75×body1280valid
14.0ms53×body640valid
4.0ms28×body320valid
4.0ms104×body80valid
2.0ms69×body80nan
1.0ms11×body160valid

simplify39.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017
done50017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b
(pow (+ 1.0 (/ i n)) n)
10.6b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite963.0ms

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:
350.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
227.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
30.0ms
(pow (+ 1.0 (/ i n)) n)
339.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
380.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
239.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)
363.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify61.0ms

Counts
333 → 333
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013193734
150023446
done50023446

prune804.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 24.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b
(pow (+ 1.0 (/ i n)) n)

rewrite856.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
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-*l* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv
Counts
4 → 139
Calls
4 calls:
360.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
295.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
179.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
373.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
162.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
250.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
228.0ms
(pow (+ 1.0 (/ i n)) n)

simplify86.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06551376
132011082
250011080
done50011080

prune320.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.5 (pow i 2) (* (log 1.0) n))
0.1b
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
13.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
14.1b
(* (pow i 2) (log 1.0))

rewrite48.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
10×pow1
9×times-frac associate-*l*
8×prod-exp
7×associate-*r*
6×log-prod cbrt-unprod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* associate-/l*
2×cbrt-undiv div-exp *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ associate-*l/ pow-exp clear-num log-pow fma-udef div-inv
Counts
4 → 98
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
28.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
13.0ms
(* (pow i 2) (log 1.0))

series572.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
219.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
142.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
146.0ms
(* (pow i 2) (log 1.0))

simplify55.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
04111287
117261088
250021081
done50021081

prune339.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.3b
(/ (fma i 1.0 (- (* (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n))) (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
14.1b
(* (pow i 2) (log 1.0))
30.7b
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))
30.7b
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
11×add-exp-log
9×times-frac
8×associate-*l* add-cbrt-cube
7×pow1
6×log-prod sqrt-prod
4×expm1-log1p-u unpow-prod-down associate-*r* log1p-expm1-u add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in prod-exp associate-/r* associate-/l*
2×rem-sqrt-square sqrt-pow1 pow1/2 unpow2 sqr-pow
1×cbrt-undiv pow-to-exp frac-2neg div-exp pow-exp clear-num log-pow *-commutative cbrt-unprod div-inv
Counts
4 → 95
Calls
4 calls:
5.0ms
(/ (fma i 1.0 (- (* (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n))) (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
13.0ms
(* (pow i 2) (log 1.0))
1.0ms
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))
2.0ms
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))

series598.0ms

Counts
4 → 12
Calls
4 calls:
149.0ms
(/ (fma i 1.0 (- (* (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n))) (sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms
(* (pow i 2) (log 1.0))
152.0ms
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))
151.0ms
(sqrt (fma 0.5 (pow i 2) (* (log 1.0) n)))

simplify47.0ms

Counts
107 → 107
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03261292
111801119
250021100
done50021100

prune378.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.0b

regimes140.0ms

Accuracy

48.6% (11.7b remaining)

Error of 22.9b against oracle of 11.1b and baseline of 34.0b

bsearch255.0ms

Steps
ItersRangePoint
8
1.5934329611832436e-130
4.113531426965663e-127
1.6134148830388508e-130
8
-7.622341151832115e-247
-6.506148429240512e-251
-9.519350012649904e-251
6
-4.3436177944509636e+95
-5.9618745358935405e+94
-7.766937677453618e+94

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05156
15156
done5156

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.9s1020×body2560valid
1.7s2402×body1280valid
459.0ms1647×body640valid
140.0ms884×body320valid
128.0ms3072×body80valid
69.0ms2291×body80nan
42.0ms438×body160valid
18.0ms5×body5120valid