Details

Time bar (total: 22.0s)

sample169.0ms

Algorithm
intervals
Results
67.0ms35×body2560valid
59.0ms77×body1280valid
15.0ms51×body640valid
4.0ms1×body5120valid
4.0ms95×body80valid
3.0ms20×body320valid
2.0ms61×body80nan
1.0ms14×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25915
314115
433715
599415
6397915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
11.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite636.0ms

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:
238.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
133.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
233.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
361.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
249.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)
354.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify556.0ms

Counts
333 → 333
Iterations

Useful iterations: done (541.0ms)

IterNodesCost
04797415
113026800
done50006712

prune879.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 20.6b

localize13.0ms

Local error

Found 4 expressions with local error:

1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)
5.6b
(pow (+ 1.0 (/ i n)) n)
5.6b
(pow (+ 1.0 (/ i n)) n)

rewrite170.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
29×unpow-prod-down
26×add-cube-cbrt
24×prod-diff
9×pow-unpow
8×fma-neg sqr-pow
7×pow1 add-exp-log distribute-lft-out
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
130.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
14.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series892.0ms

Counts
4 → 12
Calls
4 calls:
250.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)
211.0ms
(pow (+ 1.0 (/ i n)) n)
216.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.9s

Counts
122 → 122
Iterations

Useful iterations: done (1.9s)

IterNodesCost
01291939
12671579
27641390
336781330
done50001322

prune345.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 20.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.5b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
1.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.6b
(pow (+ 1.0 (/ i n)) n)

rewrite630.0ms

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:
225.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
244.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
129.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
298.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
371.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
254.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.0s

Counts
362 → 362
Iterations

Useful iterations: 2 (996.0ms)

IterNodesCost
05098413
115587047
248286469
done50006469

prune715.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
2.8b
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
12.1b
(* (pow i 2) (log 1.0))
14.4b
(* (/ 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)))

rewrite62.0ms

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)))
10.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
7.0ms
(* (pow i 2) (log 1.0))
35.0ms
(* (/ 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)))

series732.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n)))
139.0ms
(/ (- (fma 1.0 i (fma 0.5 (pow i 2) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
332.0ms
(* (pow i 2) (log 1.0))
216.0ms
(* (/ 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)))

simplify1.4s

Counts
230 → 230
Iterations

Useful iterations: 2 (608.0ms)

IterNodesCost
03707821
110727158
235716515
done50006515

prune636.0ms

Pruning

19 alts after pruning (17 fresh and 2 done)

Merged error: 9.2b

regimes271.0ms

Accuracy

55.6% (10.0b remaining)

Error of 21.3b against oracle of 11.3b and baseline of 33.8b

bsearch635.0ms

Steps
ItersRangePoint
10
2.1223866484582205e-19
4.6630490365774907e-07
4.6153207705272044e-07
5
1.529952483106425e-220
4.28059771107976e-220
2.3133805028339562e-220
7
1.110810473879014e-279
1.8130708176709333e-278
6.7609796441213635e-279
8
-1.3601455321591097e-243
-2.517502579755847e-248
-1.4029318248824242e-247
7
-53.660684837311074
-1.3335098637510872
-1.396127674736418

simplify6.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
065265
182265
done82265

end0.0ms

sample4.8s

Algorithm
intervals
Results
1.8s977×body2560valid
1.8s2502×body1280valid
450.0ms1544×body640valid
151.0ms898×body320valid
133.0ms3031×body80valid
76.0ms2261×body80nan
48.0ms471×body160valid
25.0ms8×body5120valid