Details

Time bar (total: 36.1s)

sample164.0ms

Algorithm
intervals
Results
70.0ms36×body2560valid
51.0ms72×body1280valid
16.0ms57×body640valid
4.0ms101×body80valid
3.0ms19×body320valid
2.0ms56×body80nan
1.0ms11×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
25915
313915
433815
598615
6405915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

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)
5.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite829.0ms

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:
333.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
160.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
301.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
384.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
256.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
216.0ms
(pow (+ 1.0 (/ i n)) n)
365.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.6s

Counts
293 → 293
Iterations

Useful iterations: done (1.6s)

IterNodesCost
04376469
111836125
237645875
done50015867

prune777.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize25.0ms

Local error

Found 4 expressions with local error:

5.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
5.8b
(pow (+ 1.0 (/ i n)) n)
5.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
4569×times-frac
3397×add-sqr-sqrt
1975×*-un-lft-identity
1549×add-cube-cbrt
1356×unpow-prod-down
1344×difference-of-squares
1008×cube-prod
843×sqr-pow
210×distribute-lft-out--
145×div-inv
129×associate-/l*
42×difference-cubes
29×associate-/r/
19×add-exp-log
16×add-cbrt-cube
14×flip3-+ flip-+
13×associate-/r*
8×cbrt-undiv div-exp
7×pow1 pow-unpow
4×add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out
2×div-sub
1×frac-2neg clear-num associate-/l/
Counts
4 → 1892
Calls
4 calls:
18.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
17.0ms
(pow (+ 1.0 (/ i n)) n)
19.0ms
(pow (+ 1.0 (/ i n)) n)
985.0ms
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

series8.3s

Counts
4 → 12
Calls
4 calls:
224.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
227.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(pow (+ 1.0 (/ i n)) n)
7.6s
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (+ (* 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0)) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

simplify1.3s

Counts
1904 → 1904
Iterations

Useful iterations: done (1.1s)

IterNodesCost
02035154096
done5001150200

prune5.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize12.0ms

Local error

Found 4 expressions with local error:

2.0b
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
2.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
251×times-frac
200×add-sqr-sqrt
154×*-un-lft-identity
120×add-cube-cbrt log-pow
105×exp-prod
48×difference-of-squares
20×pow1 unpow-prod-down
17×sqr-pow
16×distribute-lft-out--
13×associate-/r* div-inv
11×associate-/l*
10×add-exp-log
9×add-cbrt-cube
6×add-log-exp
5×log-prod
3×cbrt-undiv pow-unpow div-exp
2×sub-neg log-div exp-diff exp-sum
1×pow-to-exp flip3-- pow-pow frac-2neg diff-log div-sub rem-log-exp pow-exp clear-num associate-/r/ flip-- distribute-lft-out
Counts
4 → 239
Calls
4 calls:
315.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
156.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
1.0s
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
250.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
259.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms
(pow (+ 1.0 (/ i n)) n)
358.0ms
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify1.5s

Counts
251 → 251
Iterations

Useful iterations: done (1.5s)

IterNodesCost
04286501
19565742
230095556
done50015536

prune562.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 18.1b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
2.1b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)

rewrite789.0ms

Algorithm
rewrite-expression-head
Rules
44×add-sqr-sqrt
29×*-un-lft-identity
28×associate-*r*
22×times-frac
19×add-exp-log add-cube-cbrt
18×add-cbrt-cube
12×pow1 difference-of-squares
8×unpow-prod-down
7×prod-exp cbrt-unprod
6×add-log-exp
5×sqr-pow
4×associate-*l* pow-prod-down distribute-lft-out--
3×pow-unpow
2×cbrt-undiv associate-*r/ div-exp *-commutative unswap-sqr
1×pow-to-exp sub-neg flip3-- pow-pow diff-log associate-*l/ pow-exp flip-- div-inv distribute-lft-out
Counts
4 → 99
Calls
4 calls:
330.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
288.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
150.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)

series978.0ms

Counts
4 → 12
Calls
4 calls:
366.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
150.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
248.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)

simplify964.0ms

Counts
111 → 111
Iterations

Useful iterations: done (961.0ms)

IterNodesCost
02241903
15491812
216311596
done50001579

prune228.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

regimes123.0ms

Accuracy

38.5% (15.9b remaining)

Error of 24.2b against oracle of 8.3b and baseline of 34.1b

bsearch355.0ms

Steps
ItersRangePoint
5
3.3828081305530477e-141
1.0521807154220545e-140
6.434758453518078e-141
4
-5.741572183895783e+79
-3.038399861871603e+79
-3.460770537187881e+79
7
-9.43474742152184e+92
-7.3683384343589245e+90
-4.971792173734568e+92
8
-4.2451930517767634e+133
-5.490427991378311e+129
-2.260823056891884e+130

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
041120
15697
done5697

end0.0ms

sample4.4s

Algorithm
intervals
Results
1.7s2453×body1280valid
1.6s920×body2560valid
431.0ms1579×body640valid
130.0ms842×body320valid
124.0ms3108×body80valid
62.0ms2195×body80nan
43.0ms440×body160valid
35.0ms9×body5120valid