Details

Time bar (total: 6.6s)

sample98.0ms

Algorithm
intervals
Results
47.0ms113×body1280valid
23.0ms80×body640valid
11.0ms46×body320valid
5.0ms256×pre80true
2.0ms17×body160valid

simplify153.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0188
1438
21238
32128
43748
54968
67158
79678
811218
912218
1014978
1117528
1221328
1324698
1433148
1550018

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 63.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (+ n 1.0) (log (+ n 1.0)))
0.2b
(* n (log n))
6.3b
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite32.0ms

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:
14.0ms
(* (+ n 1.0) (log (+ n 1.0)))
4.0ms
(* n (log n))
10.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series27.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(* (+ n 1.0) (log (+ n 1.0)))
8.0ms
(* n (log n))
14.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify52.0ms

Algorithm
egg-herbie
Counts
90 → 90
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0419643
11786587
25001568

prune483.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.0b
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
0.2b
(* 0.16666666666666669 (/ 1 (pow n 2)))
1.0b
(/ 1 (pow n 2))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
56×times-frac
52×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*r*
23×unpow-prod-down add-log-exp
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×diff-log associate-/r*
6×pow1 pow-to-exp rec-exp 1-exp pow-exp
5×sum-log distribute-lft-out--
3×associate-*l* associate-/l*
2×cbrt-undiv sub-neg flip3-- flip-- cbrt-unprod div-inv distribute-lft-out difference-of-squares
1×associate--l- associate-+l- pow-flip frac-2neg associate-*r/ pow-prod-down associate--l+ clear-num un-div-inv *-commutative associate--r+ inv-pow
Counts
4 → 157
Calls
4 calls:
7.0ms
(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
308.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
14.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
4.0ms
(/ 1 (pow n 2))

series25.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
6.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
2.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
4.0ms
(/ 1 (pow n 2))

simplify58.0ms

Algorithm
egg-herbie
Counts
169 → 169
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
05451163
12183985
25001902

prune874.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b
(- 1.0 (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
0.0b
(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
0.9b
(/ 0.16666666666666669 (pow n 2))

rewrite637.0ms

Algorithm
rewrite-expression-head
Rules
42×times-frac
39×*-un-lft-identity
36×add-sqr-sqrt
34×add-cube-cbrt
26×associate-+r+ log-prod
22×add-log-exp
13×distribute-rgt-in distribute-lft-in
12×unpow-prod-down
8×add-exp-log associate-/r*
7×diff-log
6×sum-log
5×add-cbrt-cube
4×unpow2 sqr-pow
3×pow1 div-exp div-inv associate-/l* associate--r+ distribute-lft-out--
2×sub-neg log-rec distribute-rgt-neg-out
1×cbrt-undiv +-commutative pow-to-exp associate-+l+ flip3-- frac-2neg flip3-+ unsub-neg pow-exp associate--l+ clear-num flip-- flip-+ associate--r- difference-of-squares
Counts
3 → 112
Calls
3 calls:
545.0ms
(- 1.0 (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
83.0ms
(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
4.0ms
(/ 0.16666666666666669 (pow n 2))

series20.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(- 1.0 (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
12.0ms
(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
2.0ms
(/ 0.16666666666666669 (pow n 2))

simplify52.0ms

Algorithm
egg-herbie
Counts
121 → 121
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0570999
11837913
25001865

prune851.0ms

Pruning

1 alts after pruning (0 fresh and 1 done)

Merged error: 0b

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02110
12110

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.5s3571×body1280valid
783.0ms2717×body640valid
253.0ms1268×body320valid
163.0ms8000×pre80true
55.0ms444×body160valid