Details

Time bar (total: 28.3s)

sample207.0ms

Algorithm
intervals
Results
78.0ms36×body2560valid
75.0ms80×body1280valid
17.0ms38×body640valid
6.0ms102×body80valid
6.0ms28×body320valid
4.0ms86×body80nan
3.0ms17×body160valid

simplify4.4s

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: 45.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.3b
(pow (+ 1.0 (/ i n)) n)
11.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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:
462.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
272.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
26.0ms
(pow (+ 1.0 (/ i n)) n)
434.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.5s

Counts
4 → 12
Calls
4 calls:
445.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
343.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
251.0ms
(pow (+ 1.0 (/ i n)) n)
504.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.3s

Counts
333 → 333
Iterations

Useful iterations: done (2.3s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune1.1s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize30.0ms

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)))
10.1b
(* (pow i 2) (log 1.0))
18.9b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

rewrite124.0ms

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)))
57.0ms
(* 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)))
24.0ms
(* (pow i 2) (log 1.0))
34.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

series813.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
282.0ms
(* 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)))
226.0ms
(* (pow i 2) (log 1.0))
250.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ i n))

simplify1.5s

Counts
201 → 201
Iterations

Useful iterations: done (1.5s)

IterNodesCost
03296419
18256201
229905750
done50005741

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 7.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
3.3b
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.1b
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
10.1b
(* (pow i 2) (log 1.0))

rewrite225.0ms

Algorithm
rewrite-expression-head
Rules
65×add-exp-log
38×add-cbrt-cube
37×prod-exp
27×add-sqr-sqrt associate-*l*
21×pow1
19×add-cube-cbrt *-un-lft-identity cbrt-unprod
12×associate-*l/
10×pow-prod-down
9×times-frac associate-*r/ associate-*r*
8×div-exp
6×log-prod
5×flip3-- flip-- unswap-sqr
4×cbrt-undiv expm1-log1p-u frac-times unpow-prod-down rec-exp 1-exp *-commutative log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in
2×unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow div-inv
Counts
4 → 137
Calls
4 calls:
115.0ms
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
20.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
65.0ms
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
19.0ms
(* (pow i 2) (log 1.0))

series933.0ms

Counts
4 → 12
Calls
4 calls:
298.0ms
(* 100.0 (* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
197.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
215.0ms
(* (/ 1 i) (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))
222.0ms
(* (pow i 2) (log 1.0))

simplify2.2s

Counts
149 → 149
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02464394
16204114
223173360
done50003346

prune659.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 7.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
3.3b
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
10.0b
(* (/ 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)))) n))
10.1b
(* (pow i 2) (log 1.0))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
24×associate-*l*
23×add-exp-log
20×add-cbrt-cube
18×add-cube-cbrt *-un-lft-identity
12×pow1
10×prod-exp
9×times-frac
8×associate-*r* cbrt-unprod
7×associate-*l/
6×log-prod
5×unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×distribute-rgt-in flip3-- distribute-lft-in *-commutative flip--
2×cbrt-undiv frac-times associate-*r/ div-exp unpow2 sqr-pow
1×pow-to-exp pow-exp log-pow fma-udef div-inv
Counts
4 → 107
Calls
4 calls:
1.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
35.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
66.0ms
(* (/ 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)))) n))
23.0ms
(* (pow i 2) (log 1.0))

series759.0ms

Counts
4 → 12
Calls
4 calls:
64.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
195.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
312.0ms
(* (/ 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)))) n))
187.0ms
(* (pow i 2) (log 1.0))

simplify1.7s

Counts
119 → 119
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02112930
15202829
220032408
done50002395

prune462.0ms

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 7.8b

regimes251.0ms

Accuracy

58.2% (10.3b remaining)

Error of 18.8b against oracle of 8.5b and baseline of 33.1b

bsearch249.0ms

Steps
ItersRangePoint
11
0.12160444842987421
4.529904795396554e+32
0.5476118163719529
6
-11.923248480236845
-0.7718806003288846
-0.8489635077384908

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03665
14865
done4865

end0.0ms

sample6.2s

Algorithm
intervals
Results
2.6s2469×body1280valid
2.1s1038×body2560valid
542.0ms1572×body640valid
228.0ms860×body320valid
179.0ms3059×body80valid
121.0ms2212×body80nan
51.0ms425×body160valid
24.0ms6×body5120valid