Details

Time bar (total: 21.5s)

sample222.0ms

Algorithm
intervals
Results
85.0ms77×body1280valid
82.0ms35×body2560valid
18.0ms43×body640valid
7.0ms31×body320valid
6.0ms85×body80valid
3.0ms63×body80nan
2.0ms16×body160valid

simplify1.7s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize23.0ms

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)
8.5b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.3s

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:
430.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
371.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
40.0ms
(pow (+ 1.0 (/ i n)) n)
480.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts
4 → 12
Calls
4 calls:
534.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
307.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
299.0ms
(pow (+ 1.0 (/ i n)) n)
405.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify911.0ms

Counts
333 → 333
Iterations

Useful iterations: done (899.0ms)

IterNodesCost
04797415
115206929
done50016480

prune1.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 23.4b

localize27.0ms

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n)))
12.1b
(* (pow i 2) (log 1.0))
20.1b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite107.0ms

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 0.5 (pow i 2) (* (log 1.0) n))
52.0ms
(* 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)))
20.0ms
(* (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))

series820.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
260.0ms
(* 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)))
220.0ms
(* (pow i 2) (log 1.0))
261.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify564.0ms

Counts
201 → 201
Iterations

Useful iterations: done (554.0ms)

IterNodesCost
03286373
19426200
done50005731

prune1.0s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 11.7b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 0.5 (pow i 2) (* (log 1.0) n))
2.8b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
12.1b
(* (pow i 2) (log 1.0))
12.7b
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
127×add-sqr-sqrt
95×*-un-lft-identity
93×add-cube-cbrt
53×add-exp-log
48×associate-*r*
32×add-cbrt-cube
23×div-exp
21×associate-*l*
13×prod-exp associate-/r*
12×cbrt-undiv unswap-sqr
10×div-inv
7×pow1 cbrt-unprod
6×log-prod
4×expm1-log1p-u unpow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×frac-times pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- fma-udef
Counts
4 → 218
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
27.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
19.0ms
(* (pow i 2) (log 1.0))
53.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series718.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
156.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
200.0ms
(* (pow i 2) (log 1.0))
268.0ms
(* (/ 100.0 i) (/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify654.0ms

Counts
230 → 230
Iterations

Useful iterations: done (641.0ms)

IterNodesCost
03697775
111637377
done50016511

prune1.1s

Pruning

15 alts after pruning (14 fresh and 1 done)

Merged error: 11.7b

localize18.0ms

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
11.4b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.1b
(* (pow i 2) (log 1.0))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
20×add-exp-log
18×add-cube-cbrt *-un-lft-identity
17×add-cbrt-cube
11×associate-*l*
10×pow1
9×times-frac
8×prod-exp
6×log-prod cbrt-unprod
5×associate-*r*
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 associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ associate-*l/ pow-exp clear-num log-pow flip-- fma-udef div-inv
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
44.0ms
(* 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))
19.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
25.0ms
(* (pow i 2) (log 1.0))

series654.0ms

Counts
4 → 12
Calls
4 calls:
69.0ms
(fma 0.5 (pow i 2) (* (log 1.0) n))
226.0ms
(* 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))
162.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
196.0ms
(* (pow i 2) (log 1.0))

simplify1.2s

Counts
113 → 113
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02002682
14692615
221882246
done50012240

prune386.0ms

Pruning

15 alts after pruning (13 fresh and 2 done)

Merged error: 11.7b

regimes211.0ms

Accuracy

52.2% (10.6b remaining)

Error of 21.6b against oracle of 11.0b and baseline of 33.2b

bsearch404.0ms

Steps
ItersRangePoint
8
5.344653673325432e+100
5.6044378618353505e+103
5.534188978290048e+103
10
0.00038500758258708294
1371021975238077.5
1.1647242678127252
9
-13.304859898696009
-9.641814872486784e-07
-0.0035428999671728045

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
049103
161103
done61103

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.1s2478×body1280valid
2.0s936×body2560valid
983.0ms1611×body640valid
473.0ms3090×body80valid
247.0ms902×body320valid
99.0ms2341×body80nan
58.0ms465×body160valid
20.0ms5×body5120valid