Details

Time bar (total: 13.1s)

sample191.0ms

Algorithm
intervals
Results
75.0ms33×body2560valid
64.0ms75×body1280valid
18.0ms53×body640valid
8.0ms104×body80valid
5.0ms28×body320valid
3.0ms69×body80nan
1.0ms11×body160valid

simplify41.0ms

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))

rewrite877.0ms

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:
317.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
203.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
320.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
352.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
241.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
231.0ms
(pow (+ 1.0 (/ i n)) n)
344.0ms
(/ (- (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

prune794.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 24.0b

localize9.0ms

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)

rewrite1.2s

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:
515.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
460.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
183.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
370.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
157.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
261.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
264.0ms
(pow (+ 1.0 (/ i n)) n)

simplify83.0ms

Counts
151 → 151
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
06551376
132011082
250011080
done50011080

prune319.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.0b

localize20.0ms

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))

rewrite46.0ms

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))
25.0ms
(* (* 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))

series575.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
218.0ms
(* (* 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)
146.0ms
(/ (fma i 1.0 (- (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))

simplify60.0ms

Counts
110 → 110
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
04101281
118001088
250011081
done50011081

prune339.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
0.1b
(* (* 100.0 (/ (fma i 1.0 (- (+ (* 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 (- (+ (* 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))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×associate-*r*
12×associate-*l*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp
1×frac-2neg associate-*r/ associate-*l/ clear-num log-pow div-inv
Counts
4 → 117
Calls
4 calls:
14.0ms
(* 0.5 (pow i 2))
25.0ms
(* (* 100.0 (/ (fma i 1.0 (- (+ (* 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 (- (+ (* 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))

series537.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* 0.5 (pow i 2))
217.0ms
(* (* 100.0 (/ (fma i 1.0 (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
147.0ms
(/ (fma i 1.0 (- (+ (* 0.5 (pow i 2)) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
140.0ms
(* (pow i 2) (log 1.0))

simplify66.0ms

Counts
129 → 129
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
04751400
121051165
250021139
done50021139

prune356.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 13.0b

regimes149.0ms

Accuracy

49.5% (11.7b remaining)

Error of 22.9b against oracle of 11.1b and baseline of 34.4b

bsearch265.0ms

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
05244
15244
done5244

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.9s1020×body2560valid
1.7s2402×body1280valid
455.0ms1647×body640valid
142.0ms884×body320valid
128.0ms3072×body80valid
67.0ms2291×body80nan
42.0ms438×body160valid
18.0ms5×body5120valid