Details

Time bar (total: 35.1s)

sample157.0ms

Algorithm
intervals
Results
68.0ms36×body2560valid
50.0ms72×body1280valid
15.0ms57×body640valid
4.0ms101×body80valid
3.0ms19×body320valid
2.0ms56×body80nan
1.0ms11×body160valid

simplify3.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01015
12515
26015
314315
435515
5107715
6442915
done500015

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.7b

localize9.0ms

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))

rewrite890.0ms

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:
330.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
189.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
17.0ms
(pow (+ 1.0 (/ i n)) n)
333.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
374.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
219.0ms
(pow (+ 1.0 (/ i n)) n)
360.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.7s

Counts
333 → 333
Iterations

Useful iterations: done (1.7s)

IterNodesCost
04797415
112756800
239406406
done50006350

prune859.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize18.0ms

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)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

rewrite899.0ms

Algorithm
rewrite-expression-head
Rules
4525×times-frac
3383×add-sqr-sqrt
1961×*-un-lft-identity
1535×add-cube-cbrt
1356×unpow-prod-down
1344×difference-of-squares
1008×cube-prod
843×sqr-pow
210×distribute-lft-out--
143×div-inv
127×associate-/l*
42×difference-cubes
19×add-exp-log
16×add-cbrt-cube
13×associate-/r*
8×cbrt-undiv div-exp
7×pow1 pow-unpow
4×expm1-log1p-u log1p-expm1-u add-log-exp
3×pow-to-exp pow-pow pow-exp distribute-lft-out
2×div-sub
1×frac-2neg clear-num associate-/r/ associate-/l/
Counts
4 → 1872
Calls
4 calls:
17.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
17.0ms
(pow (+ 1.0 (/ i n)) n)
17.0ms
(pow (+ 1.0 (/ i n)) n)
621.0ms
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

series8.1s

Counts
4 → 12
Calls
4 calls:
223.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
215.0ms
(pow (+ 1.0 (/ i n)) n)
212.0ms
(pow (+ 1.0 (/ i n)) n)
7.5s
(/ (/ (- (pow (pow (+ 1.0 (/ i n)) n) 3) (pow 1.0 3)) (fma 1.0 (+ (pow (+ 1.0 (/ i n)) n) 1.0) (pow (+ 1.0 (/ i n)) (* 2 n)))) (/ i n))

simplify924.0ms

Counts
1884 → 1884
Iterations

Useful iterations: done (770.0ms)

IterNodesCost
01977148003
done5000144379

prune5.0s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 18.1b

localize10.0ms

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
230×add-sqr-sqrt
198×*-un-lft-identity
150×add-cube-cbrt
120×log-pow
105×exp-prod
48×unpow-prod-down prod-diff difference-of-squares
29×log-prod
26×exp-sum
24×sqr-pow
20×pow1
16×distribute-lft-out--
13×associate-/r* div-inv
11×associate-/l*
10×add-exp-log
9×add-cbrt-cube
8×fma-neg distribute-lft-out
6×add-log-exp
4×expm1-log1p-u log1p-expm1-u
3×cbrt-undiv pow-unpow div-exp
2×sub-neg log-div exp-diff
1×pow-to-exp flip3-- pow-pow frac-2neg diff-log div-sub rem-log-exp pow-exp clear-num associate-/r/ flip--
Counts
4 → 303
Calls
4 calls:
317.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
177.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms
(pow (+ 1.0 (/ i n)) n)
962.0ms
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series1.0s

Counts
4 → 12
Calls
4 calls:
242.0ms
(log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0)))
243.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
208.0ms
(pow (+ 1.0 (/ i n)) n)
342.0ms
(/ (log (exp (- (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify1.4s

Counts
315 → 315
Iterations

Useful iterations: done (1.4s)

IterNodesCost
05188373
110946976
232416505
done50006401

prune628.0ms

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)

rewrite815.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
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-*l* pow-prod-down log1p-expm1-u 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
Counts
4 → 139
Calls
4 calls:
328.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
285.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
177.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms
(pow (+ 1.0 (/ i n)) n)

series945.0ms

Counts
4 → 12
Calls
4 calls:
348.0ms
(* (* 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))
240.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
206.0ms
(pow (+ 1.0 (/ i n)) n)

simplify881.0ms

Counts
151 → 151
Iterations

Useful iterations: done (877.0ms)

IterNodesCost
02662849
16422487
218012130
done50012066

prune272.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 6.9b

regimes120.0ms

Accuracy

38.5% (15.9b remaining)

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

bsearch337.0ms

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

simplify5.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
040121
15299
done5299

end0.0ms

sample4.3s

Algorithm
intervals
Results
1.6s920×body2560valid
1.6s2453×body1280valid
419.0ms1579×body640valid
123.0ms842×body320valid
117.0ms3108×body80valid
59.0ms2195×body80nan
41.0ms440×body160valid
32.0ms9×body5120valid