Details

Time bar (total: 1.5m)

sample80.0ms

Algorithm
intervals
Results
44.0ms134×body1280valid
15.0ms67×body640valid
6.0ms42×body320valid
3.0ms256×pre80true
1.0ms13×body160valid

simplify15.5s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0915
12315
217915
360615
488215
5147915
6272715
7297715
8311415
9324015
done500015

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize13.0ms

Local error

Found 3 expressions with local error:

0.3b
(* (+ n 1.0) (log (+ n 1.0)))
0.3b
(* n (log n))
4.6b
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
28×log-prod
25×*-un-lft-identity
19×add-sqr-sqrt
15×add-cube-cbrt
14×distribute-rgt-in distribute-lft-in
9×pow1
8×associate-*r* associate--l+
7×add-exp-log associate-*l* add-cbrt-cube
6×associate--r+
5×distribute-lft-out add-log-exp
2×pow-prod-down associate-*l/ prod-exp log-pow *-commutative cbrt-unprod unswap-sqr
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
3 → 81
Calls
3 calls:
48.0ms
(* (+ n 1.0) (log (+ n 1.0)))
9.0ms
(* n (log n))
45.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series795.0ms

Counts
3 → 9
Calls
3 calls:
108.0ms
(* (+ n 1.0) (log (+ n 1.0)))
352.0ms
(* n (log n))
335.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify1.0m

Counts
90 → 90
Iterations

Useful iterations: done (1.0m)

IterNodesCost
01711210
135231115
done50001035

prune239.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n))))
0.0b
(- (+ (- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n)))) (/ 0.5 n)) 1.0)
0.5b
(/ 0.16666666666666669 (* n n))

rewrite2.3s

Algorithm
rewrite-expression-head
Rules
22×add-log-exp
16×*-un-lft-identity
9×add-sqr-sqrt
8×add-exp-log diff-log add-cbrt-cube
5×add-cube-cbrt sum-log distribute-lft-out--
3×pow1 times-frac associate-/l*
2×cbrt-undiv sub-neg flip3-- div-exp flip-- distribute-lft-out difference-of-squares
1×associate--l- associate-+l- frac-2neg prod-exp associate--l+ clear-num associate-/r* cbrt-unprod div-inv associate--r+
Counts
3 → 58
Calls
3 calls:
57.0ms
(- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n))))
2.2s
(- (+ (- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n)))) (/ 0.5 n)) 1.0)
10.0ms
(/ 0.16666666666666669 (* n n))

series729.0ms

Counts
3 → 9
Calls
3 calls:
637.0ms
(- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n))))
62.0ms
(- (+ (- 1.0 (+ (* 1.0 (- (log n))) (/ 0.16666666666666669 (* n n)))) (/ 0.5 n)) 1.0)
30.0ms
(/ 0.16666666666666669 (* n n))

simplify1.0s

Counts
67 → 67
Iterations

Useful iterations: done (1.0s)

IterNodesCost
01371197
17351161
done50001010

prune249.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))
0.0b
(+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0)))
0.5b
(/ 0.16666666666666669 (* n n))
6.0b
(exp (+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))))

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
53×add-log-exp
32×*-un-lft-identity
22×sum-log
12×diff-log distribute-lft-out
9×add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube
8×associate-+l+
7×associate-+r-
6×log-prod exp-prod associate--l+ rem-exp-log
4×pow1 flip3-- frac-add flip--
3×distribute-rgt-in associate-+l- associate-+r+ distribute-lft-in times-frac associate-/l* distribute-lft-out--
2×cbrt-undiv +-commutative sub-neg flip3-+ exp-diff div-exp flip-+
1×frac-2neg exp-sum prod-exp clear-num associate-/r* cbrt-unprod div-inv
Counts
4 → 96
Calls
4 calls:
148.0ms
(+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))
337.0ms
(+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0)))
15.0ms
(/ 0.16666666666666669 (* n n))
1.1s
(exp (+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))))

series256.0ms

Counts
4 → 12
Calls
4 calls:
75.0ms
(+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))
60.0ms
(+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0)))
41.0ms
(/ 0.16666666666666669 (* n n))
80.0ms
(exp (+ 1.0 (+ (- (* 1.0 (log n)) (/ 0.16666666666666669 (* n n))) (- (/ 0.5 n) 1.0))))

simplify1.6s

Counts
108 → 108
Iterations

Useful iterations: done (1.6s)

IterNodesCost
02162220
113042077
done50021931

prune466.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01520
11820
done1820

end0.0ms

sample4.6s

Algorithm
intervals
Results
2.2s3669×body1280valid
1.6s2599×body640valid
395.0ms1300×body320valid
119.0ms8000×pre80true
66.0ms432×body160valid