Details

Time bar (total: 29.9s)

sample250.0ms

Algorithm
intervals
Results
94.0ms31×body2560valid
83.0ms76×body1280valid
23.0ms44×body640valid
9.0ms115×body80valid
8.0ms30×body320valid
5.0ms82×body80nan
2.0ms12×body160valid

simplify737.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.9b

localize12.0ms

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)
7.5b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
320×times-frac
289×add-sqr-sqrt
198×*-un-lft-identity
140×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
32×unpow-prod-down
29×sqr-pow
28×distribute-lft-out--
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
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 distribute-lft-out
Counts
4 → 281
Calls
4 calls:
491.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
210.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
406.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.6s

Counts
4 → 12
Calls
4 calls:
470.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
371.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
275.0ms
(pow (+ 1.0 (/ i n)) n)
455.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify596.0ms

Counts
293 → 293

prune1.1s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 19.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite958.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
31×times-frac
28×*-un-lft-identity
22×add-cube-cbrt
19×add-exp-log
18×add-cbrt-cube
13×associate-/r*
7×pow1 associate-*r*
6×cbrt-undiv unpow-prod-down div-exp add-log-exp difference-of-squares
4×associate-*r/
3×sub-neg pow-unpow flip3-- associate-*l* prod-exp flip-- cbrt-unprod div-inv sqr-pow
2×distribute-rgt-in distribute-lft-in associate-/l/ distribute-lft-out--
1×pow-to-exp pow-pow frac-2neg diff-log pow-prod-down pow-exp clear-num associate-/r/ *-commutative distribute-lft-out associate-/l* unswap-sqr
Counts
4 → 110
Calls
4 calls:
435.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
260.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
31.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
423.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
373.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
334.0ms
(pow (+ 1.0 (/ i n)) n)
564.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify1.2s

Counts
122 → 122

prune478.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 16.9b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
0.0b
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
1.5b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.5b
(pow (+ 1.0 (/ i n)) n)

rewrite3.3s

Algorithm
rewrite-expression-head
Rules
59×add-exp-log
34×add-cbrt-cube
33×prod-exp
19×pow1 add-sqr-sqrt
18×*-un-lft-identity
17×cbrt-unprod
16×associate-*l*
14×add-cube-cbrt
10×associate-*l/
9×times-frac associate-*r/ pow-prod-down
8×div-exp
6×add-log-exp
5×unpow-prod-down flip3-- flip--
4×cbrt-undiv frac-times rec-exp 1-exp
3×pow-unpow difference-of-squares
2×associate-*r* *-commutative sqr-pow
1×pow-to-exp sub-neg pow-pow diff-log pow-exp div-inv distribute-lft-out distribute-lft-out--
Counts
4 → 109
Calls
4 calls:
954.0ms
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
2.1s
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
231.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
22.0ms
(pow (+ 1.0 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
442.0ms
(* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n))
459.0ms
(* 100.0 (* (/ 1 i) (* (- (pow (+ 1.0 (/ i n)) n) 1.0) n)))
322.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
267.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.1s

Counts
121 → 121

prune371.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
2.6b
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
12.8b
(* (pow i 2) (log 1.0))
13.0b
(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

rewrite2.7s

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 frac-times unpow-prod-down rec-exp 1-exp *-commutative 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 → 129
Calls
4 calls:
1.5s
(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
436.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
15.0ms
(* (pow i 2) (log 1.0))
746.0ms
(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

series951.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(* 100.0 (* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)))
176.0ms
(* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
221.0ms
(* (pow i 2) (log 1.0))
284.0ms
(* (/ 1 i) (* (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n))

simplify1.4s

Counts
141 → 141

prune498.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 6.4b

regimes240.0ms

Accuracy

54.3% (11.7b remaining)

Error of 20.1b against oracle of 8.4b and baseline of 34.0b

bsearch597.0ms

Steps
ItersRangePoint
9
0.1320695871758506
6055834.380950506
0.45420165919035843
7
1.0582870265166675e-163
1.7736093765111178e-161
1.0785590189517503e-163
7
2.6776797066476143e-214
1.89121651515583e-212
1.2804889042748375e-213
9
-1.3250394268561034e-11
-7.781475254185234e-18
-1.3103314113916408e-11

simplify716.0ms

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.5s2363×body1280valid
2.3s990×body2560valid
632.0ms1602×body640valid
234.0ms914×body320valid
212.0ms2372×body80nan
200.0ms461×body160valid
184.0ms3144×body80valid
23.0ms5×body5120valid