Details

Time bar (total: 38.5s)

sample159.0ms

Algorithm
intervals
Results
61.0ms84×body1280valid
61.0ms30×body2560valid
13.0ms42×body640valid
5.0ms28×body320valid
4.0ms93×body80valid
2.0ms56×body80nan
2.0ms19×body160valid

simplify2.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25915
314115
433715
599315
6391415
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
2.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.7b
(pow (+ 1.0 (/ i n)) n)
11.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite656.0ms

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:
250.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
137.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
237.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
369.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
220.0ms
(pow (+ 1.0 (/ i n)) n)
361.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.6s

Counts
333 → 333
Iterations

Useful iterations: done (1.6s)

IterNodesCost
04797415
113026800
239566406
done50016382

prune849.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 23.6b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
0.1b
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
2.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.7b
(pow (+ 1.0 (/ i n)) n)

rewrite757.0ms

Algorithm
rewrite-expression-head
Rules
1689×times-frac
1113×add-sqr-sqrt
854×*-un-lft-identity
678×add-cube-cbrt
330×associate-*r*
246×difference-of-squares
102×unpow-prod-down
87×sqr-pow
82×distribute-lft-out--
80×div-inv
59×add-exp-log
34×add-cbrt-cube
32×div-exp
25×associate-/l*
24×prod-diff
16×cbrt-undiv
13×associate-/r*
9×prod-exp
8×fma-neg
7×pow1 unswap-sqr
6×add-log-exp
5×cbrt-unprod distribute-lft-out
4×expm1-log1p-u rec-exp 1-exp log1p-expm1-u
3×pow-unpow associate-*l*
2×div-sub associate-/r/
1×pow-to-exp sub-neg flip3-- pow-pow frac-2neg diff-log associate-*r/ pow-prod-down pow-exp clear-num *-commutative flip-- associate-/l/
Counts
4 → 826
Calls
4 calls:
311.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
198.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
156.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
382.0ms
(* 100.0 (/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n)))
345.0ms
(/ (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) (/ 1 n))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.6s

Counts
838 → 838
Iterations

Useful iterations: done (1.6s)

IterNodesCost
0109022954
1322019509
done500019436

prune1.7s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.1b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
0.2b
(/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
10.8b
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
11.4b
(* (pow i 2) (log 1.0))

rewrite128.0ms

Algorithm
rewrite-expression-head
Rules
846×times-frac
428×add-sqr-sqrt
399×*-un-lft-identity
397×add-cube-cbrt
178×associate-*r*
65×add-exp-log
57×div-inv
38×add-cbrt-cube
33×div-exp
17×cbrt-undiv
16×associate-/r* associate-/l*
12×prod-exp
11×associate-*l* unswap-sqr
7×pow1
6×log-prod cbrt-unprod
4×expm1-log1p-u unpow-prod-down rec-exp 1-exp log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in div-sub associate-/l/
2×frac-2neg clear-num associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp flip3-- associate-*r/ pow-prod-down pow-exp log-pow flip--
Counts
4 → 500
Calls
4 calls:
63.0ms
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
18.0ms
(/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
7.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
7.0ms
(* (pow i 2) (log 1.0))

series675.0ms

Counts
4 → 12
Calls
4 calls:
205.0ms
(* 100.0 (/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n)))
188.0ms
(/ (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) (/ 1 n))
140.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
142.0ms
(* (pow i 2) (log 1.0))

simplify943.0ms

Counts
512 → 512
Iterations

Useful iterations: done (913.0ms)

IterNodesCost
072221187
1212219296
done500019100

prune1.5s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 12.0b

localize26.0ms

Local error

Found 4 expressions with local error:

2.4b
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
3.3b
(/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
6.8b
(/ (/ 1 (* (cbrt i) (cbrt i))) (/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))))
11.4b
(* (pow i 2) (log 1.0))

rewrite653.0ms

Algorithm
rewrite-expression-head
Rules
9420×times-frac
3549×add-sqr-sqrt
3543×add-cube-cbrt *-un-lft-identity
1074×cbrt-prod
620×div-inv
319×associate-/r*
302×add-exp-log
228×div-exp
70×add-cbrt-cube
58×cbrt-undiv
34×rec-exp 1-exp
30×prod-exp
23×associate-/l*
10×associate-/r/
8×associate-*l*
6×log-prod cbrt-unprod
5×pow1
4×expm1-log1p-u unpow-prod-down associate-*r* log1p-expm1-u associate-/l/ add-log-exp unswap-sqr
3×distribute-rgt-in frac-2neg distribute-lft-in clear-num
2×unpow2 sqr-pow
1×pow-to-exp flip3-- div-sub pow-exp log-pow *-commutative flip--
Counts
4 → 2854
Calls
4 calls:
7.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
16.0ms
(/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
100.0ms
(/ (/ 1 (* (cbrt i) (cbrt i))) (/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))))
7.0ms
(* (pow i 2) (log 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
168.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))
891.0ms
(/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i)))
211.0ms
(/ (/ 1 (* (cbrt i) (cbrt i))) (/ (/ 1 n) (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (cbrt i))))
136.0ms
(* (pow i 2) (log 1.0))

simplify1.4s

Counts
2866 → 2866
Iterations

Useful iterations: 0 (412.0ms)

IterNodesCost
03717196169
done5000196169

prune14.5s

Pruning

21 alts after pruning (21 fresh and 0 done)

Merged error: 12.0b

regimes320.0ms

Accuracy

52.8% (10.7b remaining)

Error of 21.6b against oracle of 10.9b and baseline of 33.6b

bsearch266.0ms

Steps
ItersRangePoint
9
1.0228685403935474e+157
1.3784090053042305e+164
2.1606840039657686e+162
11
9.874627991469258e-44
2.917990337929379e-18
2.882168870282429e-18
4
-1.7961213486546931e-06
-1.1893147564346013e-06
-1.7771586426478155e-06

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
065193
180193
done80193

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s957×body2560valid
1.6s2440×body1280valid
439.0ms1599×body640valid
131.0ms862×body320valid
123.0ms3094×body80valid
69.0ms2261×body80nan
44.0ms472×body160valid
30.0ms9×body5120valid