Details

Time bar (total: 26.6s)

sample193.0ms

Algorithm
intervals
Results
67.0ms74×body1280valid
59.0ms22×body2560valid
30.0ms66×body640valid
7.0ms100×body80valid
5.0ms21×body320valid
3.0ms49×body80nan
2.0ms13×body160valid

simplify1.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.0b

localize28.0ms

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)
6.1b
(pow (+ 1.0 (/ i n)) n)
8.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.4s

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:
572.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
263.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
19.0ms
(pow (+ 1.0 (/ i n)) n)
514.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.2s

Counts
4 → 12
Calls
4 calls:
927.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
388.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
316.0ms
(pow (+ 1.0 (/ i n)) n)
542.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify992.0ms

Counts
333 → 333
Iterations

Useful iterations: done (975.0ms)

IterNodesCost
04797415
115206929
done50016480

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 19.3b

localize20.0ms

Local error

Found 4 expressions with local error:

5.2b
(cbrt (+ 1.0 (/ i n)))
5.2b
(cbrt (+ 1.0 (/ i n)))
5.2b
(cbrt (+ 1.0 (/ i n)))
8.0b
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

rewrite57.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
55×*-un-lft-identity
49×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
12×cbrt-prod
9×add-exp-log add-cbrt-cube
6×cbrt-div
5×div-inv
4×pow1 expm1-log1p-u log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ pow1/3 div-exp flip-+ distribute-lft-out associate-/l*
1×frac-2neg clear-num associate-/r/
Counts
4 → 120
Calls
4 calls:
25.0ms
(cbrt (+ 1.0 (/ i n)))
10.0ms
(cbrt (+ 1.0 (/ i n)))
8.0ms
(cbrt (+ 1.0 (/ i n)))
9.0ms
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

series1.9s

Counts
4 → 12
Calls
4 calls:
301.0ms
(cbrt (+ 1.0 (/ i n)))
297.0ms
(cbrt (+ 1.0 (/ i n)))
299.0ms
(cbrt (+ 1.0 (/ i n)))
1.0s
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

simplify1.2s

Counts
132 → 132
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02414542
15994442
227784189
done50004162

prune651.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.4b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
0.0b
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.1b
(pow (+ 1.0 (/ i n)) n)

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*l*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*r* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*l/ *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*r/ pow-exp flip-- div-inv
Counts
4 → 139
Calls
4 calls:
469.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
335.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
246.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
28.0ms
(pow (+ 1.0 (/ i n)) n)

series1.5s

Counts
4 → 12
Calls
4 calls:
461.0ms
(* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n)
463.0ms
(* 100.0 (* (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i) n))
336.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
268.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.7s

Counts
151 → 151
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02522834
16772542
226042162
done50042110

prune468.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.7b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
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) n))
11.7b
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
12.4b
(* (pow i 2) (log 1.0))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×associate-*l*
22×add-cbrt-cube
19×times-frac
12×pow1
10×prod-exp
8×associate-*r* 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-*l/ div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp flip3-- frac-2neg div-sub associate-*r/ pow-exp clear-num log-pow flip--
Counts
4 → 125
Calls
4 calls:
24.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
31.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
23.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
16.0ms
(* (pow i 2) (log 1.0))

series837.0ms

Counts
4 → 12
Calls
4 calls:
234.0ms
(* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n)
247.0ms
(* 100.0 (* (/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i) n))
199.0ms
(/ (- (fma 1.0 i (fma 0.5 (* i i) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
158.0ms
(* (pow i 2) (log 1.0))

simplify1.6s

Counts
137 → 137
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02203686
15433611
225653112
done50013100

prune520.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 8.7b

regimes241.0ms

Accuracy

56.6% (10.8b remaining)

Error of 19.4b against oracle of 8.6b and baseline of 33.4b

bsearch343.0ms

Steps
ItersRangePoint
8
3162079221.758062
63527163486164.19
3222196569.8044276
6
-1.263328474033804e-18
-8.622232208669777e-20
-1.2371314562791146e-18

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
03595
14566
done4566

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.4s2439×body1280valid
2.1s977×body2560valid
990.0ms1632×body640valid
250.0ms3056×body80valid
178.0ms807×body320valid
113.0ms2361×body80nan
100.0ms483×body160valid
48.0ms12×body5120valid