Details

Time bar (total: 14.3s)

sample151.0ms

Algorithm
intervals
Results
59.0ms33×body2560valid
50.0ms75×body1280valid
14.0ms53×body640valid
4.0ms28×body320valid
4.0ms104×body80valid
2.0ms69×body80nan
1.0ms11×body160valid

simplify40.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1597
21417
33467
411717
550017
done50017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b
(pow (+ 1.0 (/ i n)) n)
10.6b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite840.0ms

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:
339.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
162.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)
304.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
366.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
253.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
214.0ms
(pow (+ 1.0 (/ i n)) n)
342.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify53.0ms

Counts
293 → 293
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
012263285
150023166
done50023166

prune810.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 24.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.4b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
9.0b
(pow (+ 1.0 (/ i n)) n)

rewrite872.0ms

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:
367.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
317.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
167.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
18.0ms
(pow (+ 1.0 (/ i n)) n)

series1.0s

Counts
4 → 12
Calls
4 calls:
378.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
162.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
255.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
215.0ms
(pow (+ 1.0 (/ i n)) n)

simplify70.0ms

Counts
111 → 111
Iterations

Useful iterations: 2 (60.0ms)

IterNodesCost
0561927
12792821
25001820
done5001820

prune272.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 13.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.5 (pow i 2))
0.1b
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
13.3b
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.1b
(* (pow i 2) (log 1.0))

rewrite603.0ms

Algorithm
rewrite-expression-head
Rules
33×add-sqr-sqrt
25×add-exp-log
21×add-cube-cbrt *-un-lft-identity
19×add-cbrt-cube
15×associate-*r*
12×associate-*l*
11×prod-exp
10×pow1
9×times-frac
8×unpow-prod-down unswap-sqr
7×cbrt-unprod
6×log-prod
4×unpow2 add-log-exp sqr-pow
3×distribute-rgt-in distribute-lft-in pow-prod-down associate-/r* *-commutative associate-/l*
2×cbrt-undiv pow-to-exp div-exp pow-exp associate-/l/
1×flip3-- frac-2neg div-sub associate-*r/ associate-*l/ clear-num log-pow flip-- div-inv
Counts
4 → 112
Calls
4 calls:
12.0ms
(* 0.5 (pow i 2))
304.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
269.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms
(* (pow i 2) (log 1.0))

series529.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* 0.5 (pow i 2))
212.0ms
(* (* 100.0 (/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)) n)
142.0ms
(/ (- (+ (* 1.0 i) (+ (* 0.5 (pow i 2)) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
150.0ms
(* (pow i 2) (log 1.0))

simplify79.0ms

Counts
124 → 124
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
05251450
126211228
250011228
done50011228

prune372.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.0b

localize19.0ms

Local error

Found 4 expressions with local error:

13.3b
(/ (- (+ (* 1.0 i) (+ (* (sqrt (* 0.5 (pow i 2))) (sqrt (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.1b
(* (pow i 2) (log 1.0))
30.7b
(sqrt (* 0.5 (pow i 2)))
30.7b
(sqrt (* 0.5 (pow i 2)))

rewrite1.3s

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
17×add-cube-cbrt *-un-lft-identity
11×add-exp-log
9×times-frac
8×associate-*l* add-cbrt-cube
7×pow1
6×log-prod
4×unpow-prod-down associate-*r* add-log-exp unswap-sqr
3×distribute-rgt-in distribute-lft-in prod-exp associate-/r* associate-/l*
2×sqrt-pow1 pow1/2 sqrt-prod associate-/l/ unpow2 sqr-pow
1×cbrt-undiv pow-to-exp flip3-- frac-2neg div-sub div-exp pow-exp clear-num log-pow *-commutative flip-- cbrt-unprod div-inv
Counts
4 → 84
Calls
4 calls:
1.2s
(/ (- (+ (* 1.0 i) (+ (* (sqrt (* 0.5 (pow i 2))) (sqrt (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
14.0ms
(* (pow i 2) (log 1.0))
5.0ms
(sqrt (* 0.5 (pow i 2)))
5.0ms
(sqrt (* 0.5 (pow i 2)))

series405.0ms

Counts
4 → 12
Calls
4 calls:
187.0ms
(/ (- (+ (* 1.0 i) (+ (* (sqrt (* 0.5 (pow i 2))) (sqrt (* 0.5 (pow i 2)))) (* (log 1.0) n))) (* 0.5 (* (pow i 2) (log 1.0)))) i)
146.0ms
(* (pow i 2) (log 1.0))
35.0ms
(sqrt (* 0.5 (pow i 2)))
36.0ms
(sqrt (* 0.5 (pow i 2)))

simplify48.0ms

Counts
96 → 96
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
03161174
113181014
25001975
done5001975

prune344.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.0b

regimes148.0ms

Accuracy

48.6% (11.7b remaining)

Error of 22.9b against oracle of 11.1b and baseline of 34.0b

bsearch271.0ms

Steps
ItersRangePoint
8
1.5934329611832436e-130
4.113531426965663e-127
1.6134148830388508e-130
8
-7.622341151832115e-247
-6.506148429240512e-251
-9.519350012649904e-251
6
-4.3436177944509636e+95
-5.9618745358935405e+94
-7.766937677453618e+94

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05958
15958
done5958

end0.0ms

sample4.9s

Algorithm
intervals
Results
1.9s1020×body2560valid
1.7s2402×body1280valid
464.0ms1647×body640valid
145.0ms884×body320valid
129.0ms3072×body80valid
73.0ms2291×body80nan
43.0ms438×body160valid
18.0ms5×body5120valid