Details

Time bar (total: 21.7s)

sample174.0ms

Algorithm
intervals
Results
69.0ms35×body2560valid
61.0ms77×body1280valid
15.0ms51×body640valid
4.0ms95×body80valid
4.0ms1×body5120valid
4.0ms20×body320valid
2.0ms61×body80nan
2.0ms14×body160valid

simplify2.0s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01015
12515
25815
313715
431915
594015
6386315
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 41.4b

localize9.0ms

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))

rewrite565.0ms

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:
229.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
105.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
203.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
371.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
212.0ms
(pow (+ 1.0 (/ i n)) n)
352.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.8s

Counts
293 → 293
Iterations

Useful iterations: 2 (809.0ms)

IterNodesCost
04376469
112216125
248455875
done50005875

prune788.0ms

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)

rewrite140.0ms

Algorithm
rewrite-expression-head
Rules
18×*-un-lft-identity
15×add-sqr-sqrt
13×unpow-prod-down
10×add-cube-cbrt
9×pow-unpow
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube sqr-pow
3×pow-to-exp pow-pow pow-exp distribute-lft-out difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 70
Calls
4 calls:
105.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)
210.0ms
(pow (+ 1.0 (/ i n)) n)
350.0ms
(pow (+ 1.0 (/ i n)) n)

simplify911.0ms

Counts
82 → 82
Iterations

Useful iterations: done (908.0ms)

IterNodesCost
0911021
1194932
2495910
31609897
done5001889

prune244.0ms

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)

rewrite568.0ms

Algorithm
rewrite-expression-head
Rules
340×times-frac
314×add-sqr-sqrt
206×*-un-lft-identity
146×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
32×unpow-prod-down
30×add-cbrt-cube
29×sqr-pow
28×distribute-lft-out--
23×div-exp
18×div-inv
13×associate-*l* associate-/r*
12×cbrt-undiv
10×prod-exp
8×unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
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 distribute-lft-out
Counts
4 → 310
Calls
4 calls:
193.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
238.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
102.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
14.0ms
(pow (+ 1.0 (/ i n)) n)

series1.1s

Counts
4 → 12
Calls
4 calls:
291.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
370.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
211.0ms
(pow (+ 1.0 (/ i n)) n)

simplify1.9s

Counts
322 → 322
Iterations

Useful iterations: 2 (946.0ms)

IterNodesCost
04677463
114796375
244995965
done50005965

prune638.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 9.8b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite290.0ms

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
9×add-log-exp
7×pow1 cbrt-unprod
6×log-prod
4×unpow-prod-down
3×distribute-rgt-in rec-exp distribute-lft-in 1-exp sum-log associate-/l*
2×associate-/r/ *-commutative associate-/l/ unpow2 sqr-pow
1×+-commutative frac-times pow-to-exp associate-+r+ flip3-- frac-2neg flip3-+ div-sub associate-*r/ pow-prod-down associate-*l/ pow-exp clear-num log-pow flip-- flip-+
Counts
4 → 215
Calls
4 calls:
8.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
122.0ms
(/ (- (+ (* 1.0 i) (+ (* 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))
141.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

series535.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n)))
147.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n))
140.0ms
(* (pow i 2) (log 1.0))
209.0ms
(* (/ 100.0 i) (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) (/ 1 n)))

simplify1.5s

Counts
227 → 227
Iterations

Useful iterations: 2 (638.0ms)

IterNodesCost
03798307
111507654
239816966
done50016966

prune592.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 9.2b

regimes250.0ms

Accuracy

56.7% (9.7b remaining)

Error of 21.0b against oracle of 11.3b and baseline of 33.7b

bsearch634.0ms

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

simplify5.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
057213
175213
done75213

end0.0ms

sample4.7s

Algorithm
intervals
Results
1.8s2502×body1280valid
1.8s977×body2560valid
467.0ms1544×body640valid
159.0ms898×body320valid
138.0ms3031×body80valid
72.0ms2261×body80nan
50.0ms471×body160valid
25.0ms8×body5120valid