Details

Time bar (total: 18.2s)

sample161.0ms

Algorithm
intervals
Results
63.0ms91×body1280valid
55.0ms31×body2560valid
13.0ms43×body640valid
6.0ms95×body80nan
4.0ms92×body80valid
4.0ms23×body320valid
2.0ms20×body160valid

simplify3.0s

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: 41.9b

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b
(pow (+ 1.0 (/ i n)) n)
9.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite677.0ms

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:
253.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
139.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)
247.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
391.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)
357.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify455.0ms

Counts
333 → 333
Iterations

Useful iterations: done (443.0ms)

IterNodesCost
04797415
113316800
done50006771

prune966.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.6b

localize10.0ms

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))
1.7b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.2b
(pow (+ 1.0 (/ i n)) n)

rewrite648.0ms

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:
256.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
231.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
142.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
389.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
163.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
218.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.4s

Counts
151 → 151
Iterations

Useful iterations: done (1.4s)

IterNodesCost
02662849
16682487
230002106
done50002102

prune368.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 10.3b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
0.3b
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
10.8b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b
(* (pow i 2) (log 1.0))

rewrite50.0ms

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:
12.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
16.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
7.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.0ms
(* (pow i 2) (log 1.0))

series663.0ms

Counts
4 → 12
Calls
4 calls:
157.0ms
(* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i))
221.0ms
(* (* 100.0 (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
136.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
148.0ms
(* (pow i 2) (log 1.0))

simplify914.0ms

Counts
137 → 137
Iterations

Useful iterations: 2 (191.0ms)

IterNodesCost
02243707
15533615
224633112
done50013112

prune471.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.3b

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))))
0.3b
(* (* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0))))) n)

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
9×pow1 add-exp-log add-sqr-sqrt add-cbrt-cube
7×add-cube-cbrt *-un-lft-identity
6×distribute-rgt-in distribute-lft-in associate-*r* prod-diff
4×associate-*r/ associate-*l* pow-prod-down prod-exp cbrt-unprod
2×expm1-log1p-u sub-neg flip3-- associate-*l/ associate--l+ *-commutative flip-- fma-udef log1p-expm1-u add-log-exp
1×unswap-sqr
Counts
2 → 56
Calls
2 calls:
8.0ms
(* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))))
12.0ms
(* (* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0))))) n)

series269.0ms

Counts
2 → 6
Calls
2 calls:
112.0ms
(* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0)))))
157.0ms
(* (* 100.0 (- (fma 0.5 i (+ (/ (* (log 1.0) n) i) 1.0)) (* 0.5 (* i (log 1.0))))) n)

simplify593.0ms

Counts
62 → 62
Iterations

Useful iterations: 2 (106.0ms)

IterNodesCost
01301831
13281808
214041540
done50001540

prune145.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.3b

regimes198.0ms

Accuracy

53.4% (10.8b remaining)

Error of 21.4b against oracle of 10.6b and baseline of 33.7b

bsearch190.0ms

Steps
ItersRangePoint
6
2.0126860685752985e-10
2.7764519059011607e-09
2.7217117903300314e-09
11
-1011077464093715.9
-1.3606912768451591e-05
-1.4961350298470049

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03781
14781
done4781

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s984×body2560valid
1.7s2487×body1280valid
471.0ms1595×body640valid
144.0ms857×body320valid
138.0ms3098×body80valid
72.0ms2196×body80nan
46.0ms446×body160valid
15.0ms4×body5120valid