Details

Time bar (total: 21.7s)

sample179.0ms

Algorithm
intervals
Results
68.0ms88×body1280valid
63.0ms31×body2560valid
16.0ms52×body640valid
5.0ms1×body5120valid
4.0ms30×body320valid
4.0ms86×body80valid
3.0ms80×body80nan
2.0ms17×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 43.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.2b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite892.0ms

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:
327.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
192.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
335.0ms
(/ (- (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)))
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.8s

Counts
333 → 333
Iterations

Useful iterations: done (1.7s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune873.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 18.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
0.1b
(* 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)))
9.4b
(* (pow i 2) (log 1.0))
18.6b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite78.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 189
Calls
4 calls:
0.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
37.0ms
(* 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)))
13.0ms
(* (pow i 2) (log 1.0))
20.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series619.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
218.0ms
(* 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)))
154.0ms
(* (pow i 2) (log 1.0))
198.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.1s

Counts
201 → 201
Iterations

Useful iterations: done (1.1s)

IterNodesCost
03296419
18256201
229905750
done50005741

prune948.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 7.4b

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))
0.1b
(* (* 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)
9.0b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.4b
(* (pow i 2) (log 1.0))

rewrite91.0ms

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:
21.0ms
(* 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))
36.0ms
(* (* 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)
16.0ms
(/ (- (fma 1.0 i (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))

series662.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* 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))
213.0ms
(* (* 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)
147.0ms
(/ (- (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))

simplify1.0s

Counts
137 → 137
Iterations

Useful iterations: done (995.0ms)

IterNodesCost
02243707
15363615
217913106
done50003071

prune422.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

localize21.0ms

Local error

Found 4 expressions with local error:

9.0b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
9.4b
(* (pow i 2) (log 1.0))
9.4b
(* (pow i 2) (log 1.0))
9.4b
(* (pow i 2) (log 1.0))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
27×add-cube-cbrt *-un-lft-identity
24×associate-*l*
21×add-exp-log
18×log-prod
12×unpow-prod-down associate-*r* add-cbrt-cube unswap-sqr
9×distribute-rgt-in distribute-lft-in times-frac prod-exp
7×pow1
6×unpow2 sqr-pow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-exp associate-/r* log-pow *-commutative cbrt-unprod associate-/l*
2×associate-/l/
1×cbrt-undiv flip3-- frac-2neg div-sub div-exp clear-num flip-- div-inv
Counts
4 → 140
Calls
4 calls:
15.0ms
(/ (- (fma 1.0 i (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))
13.0ms
(* (pow i 2) (log 1.0))
16.0ms
(* (pow i 2) (log 1.0))

series566.0ms

Counts
4 → 12
Calls
4 calls:
133.0ms
(/ (- (fma 1.0 i (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))
144.0ms
(* (pow i 2) (log 1.0))
143.0ms
(* (pow i 2) (log 1.0))

simplify2.2s

Counts
152 → 152
Iterations

Useful iterations: done (2.2s)

IterNodesCost
01382322
12952227
29141986
340981972
done50001969

prune610.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 7.4b

regimes159.0ms

Accuracy

48.6% (12.8b remaining)

Error of 21.0b against oracle of 8.2b and baseline of 33.1b

bsearch218.0ms

Steps
ItersRangePoint
10
1.4247645541724984e-187
3.537376337853017e-175
3.089742171439268e-181
6
5.2254629500859e-285
6.442889750848156e-284
5.321174585513156e-285
7
-344.8786496099632
-2.176521556311946
-2.3466525277232653

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
041104
151104
done51104

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.9s1043×body2560valid
1.8s2494×body1280valid
441.0ms1569×body640valid
130.0ms793×body320valid
127.0ms3021×body80valid
72.0ms2273×body80nan
49.0ms470×body160valid
20.0ms5×body5120valid