Details

Time bar (total: 26.4s)

sample265.0ms

Algorithm
intervals
Results
95.0ms31×body2560valid
89.0ms69×body1280valid
28.0ms57×body640valid
8.0ms96×body80valid
8.0ms26×body320valid
7.0ms1×body5120valid
5.0ms74×body80nan
2.0ms11×body160valid

simplify1.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314415
436415
5157815
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.9b
(pow (+ 1.0 (/ i n)) n)
10.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.6s

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:
538.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
340.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
38.0ms
(pow (+ 1.0 (/ i n)) n)
652.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.8s

Counts
4 → 12
Calls
4 calls:
572.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
373.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
345.0ms
(pow (+ 1.0 (/ i n)) n)
514.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify997.0ms

Counts
333 → 333
Iterations

Useful iterations: done (978.0ms)

IterNodesCost
04797415
115206929
done50016480

prune1.6s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 22.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.3b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.9b
(pow (+ 1.0 (/ i n)) n)

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
340×times-frac
330×add-sqr-sqrt
230×*-un-lft-identity
162×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
48×unpow-prod-down
33×sqr-pow
30×add-cbrt-cube
28×distribute-lft-out--
24×prod-diff
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×fma-neg unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num *-commutative
Counts
4 → 350
Calls
4 calls:
496.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
582.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
338.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms
(pow (+ 1.0 (/ i n)) n)

series1.6s

Counts
4 → 12
Calls
4 calls:
459.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
519.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
344.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
268.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.0s

Counts
362 → 362
Iterations

Useful iterations: done (1.0s)

IterNodesCost
05098413
117837478
done50006553

prune1.1s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 11.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
4.7b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
12.2b
(* (/ 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)))
12.8b
(* (pow i 2) (log 1.0))

rewrite117.0ms

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 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
23.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
65.0ms
(* (/ 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)))
15.0ms
(* (pow i 2) (log 1.0))

series761.0ms

Counts
4 → 12
Calls
4 calls:
58.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
219.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
275.0ms
(* (/ 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)))
210.0ms
(* (pow i 2) (log 1.0))

simplify717.0ms

Counts
230 → 230
Iterations

Useful iterations: done (707.0ms)

IterNodesCost
03707821
111747432
done50006547

prune1.0s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.3b

localize27.0ms

Local error

Found 4 expressions with local error:

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)))) n) i))
4.5b
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
12.0b
(/ (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)
12.8b
(* (pow i 2) (log 1.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-exp-log
22×add-cbrt-cube
16×add-cube-cbrt *-un-lft-identity
14×associate-*r* associate-*l*
9×pow1 prod-exp
7×cbrt-unprod
6×log-prod times-frac unswap-sqr
4×cbrt-undiv expm1-log1p-u unpow-prod-down div-exp associate-*l/ log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/r* *-commutative
2×flip3-- pow-prod-down flip-- div-inv associate-/l/ unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-exp clear-num log-pow associate-/l*
Counts
4 → 112
Calls
4 calls:
28.0ms
(* 100.0 (/ (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i))
18.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
17.0ms
(/ (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)
15.0ms
(* (pow i 2) (log 1.0))

series996.0ms

Counts
4 → 12
Calls
4 calls:
220.0ms
(* 100.0 (/ (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i))
148.0ms
(* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n)
463.0ms
(/ (* (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) n) i)
164.0ms
(* (pow i 2) (log 1.0))

simplify1.6s

Counts
124 → 124
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02083199
15403118
231322626
done50002611

prune426.0ms

Pruning

18 alts after pruning (16 fresh and 2 done)

Merged error: 11.3b

regimes321.0ms

Accuracy

42.3% (12.6b remaining)

Error of 23.5b against oracle of 10.9b and baseline of 32.7b

bsearch372.0ms

Steps
ItersRangePoint
9
1.4677799112160757e-106
1.1702822108249084e-100
1.4887262418381814e-106
9
-3.387992976769487e-240
-2.0488175508739457e-248
-3.040807945417772e-242
8
-3.3100924427793195e+98
-7.40491600406347e+94
-2.2600474911734306e+95

simplify8.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
050157
164157
done64157

end0.0ms

sample6.7s

Algorithm
intervals
Results
2.6s2451×body1280valid
2.2s1008×body2560valid
693.0ms1652×body640valid
275.0ms2950×body80valid
220.0ms862×body320valid
136.0ms2281×body80nan
58.0ms424×body160valid
29.0ms6×body5120valid