Details

Time bar (total: 5.5s)

sample68.0ms

Algorithm
intervals
Results
33.0ms114×body1280valid
18.0ms85×body640valid
5.0ms42×body320valid
3.0ms256×pre80true
1.0ms15×body160valid

simplify155.0ms

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

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 63.0b

Counts
2 → 1

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)))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
31×add-sqr-sqrt
28×log-prod
15×add-cube-cbrt
14×distribute-rgt-in distribute-lft-in associate-*l*
9×pow1
8×associate-*r* associate--l+
7×add-exp-log add-cbrt-cube distribute-lft-out
6×associate--r+ distribute-lft-out-- unswap-sqr
5×add-log-exp
4×difference-of-squares
2×pow-prod-down associate-*l/ prod-exp log-pow *-commutative cbrt-unprod
1×sub-neg flip3-- flip3-+ diff-log flip-- flip-+
Counts
3 → 91
Calls
3 calls:
9.0ms
(* (+ n 1.0) (log (+ n 1.0)))
4.0ms
(* n (log n))
22.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series428.0ms

Counts
3 → 9
Calls
3 calls:
67.0ms
(* (+ n 1.0) (log (+ n 1.0)))
175.0ms
(* n (log n))
185.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify55.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0437765
11814709
25002690

prune200.0ms

Filtered
100 candidates to 68 candidates (68.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New991100
Fresh000
Picked101
Done000
Total1001101

Merged error: 0.0b

Counts
101 → 1

localize18.0ms

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)
0.1b
(* 0.16666666666666669 (/ 1 (pow n 2)))
0.8b
(/ 1 (pow n 2))

rewrite151.0ms

Algorithm
rewrite-expression-head
Rules
117×*-un-lft-identity
92×times-frac
91×add-sqr-sqrt
69×add-cube-cbrt
56×associate--r+
54×associate-+l+
52×log-prod
33×add-exp-log
29×associate--l- associate-+l-
28×associate-*r*
26×distribute-rgt-in unpow-prod-down distribute-lft-in
23×add-log-exp
17×distribute-lft-out--
16×associate-/r*
14×associate-*r/ distribute-lft-out
12×div-exp
11×associate-*l* add-cbrt-cube
10×prod-exp unpow2 sqr-pow
9×unswap-sqr
8×pow1 diff-log
7×associate-/l*
6×pow-to-exp rec-exp pow-flip 1-exp pow-exp div-inv
5×sum-log
4×associate--l+
3×+-commutative sub-neg pow-unpow clear-num un-div-inv
2×cbrt-undiv flip3-- frac-2neg flip-- cbrt-unprod difference-of-squares
1×pow-pow pow-prod-down *-commutative inv-pow
Counts
4 → 243
Calls
4 calls:
49.0ms
(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
67.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
15.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
6.0ms
(/ 1 (pow n 2))

series434.0ms

Counts
4 → 12
Calls
4 calls:
350.0ms
(- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
42.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
25.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
17.0ms
(/ 1 (pow n 2))

simplify79.0ms

Algorithm
egg-herbie
Counts
255 → 255
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
09241763
130761521
250011400

prune573.0ms

Filtered
255 candidates to 157 candidates (61.6%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New2541255
Fresh000
Picked101
Done000
Total2551256

Merged error: 0b

Counts
256 → 1

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (- 1.0 (* (log 1) 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))))
0.8b
(/ 0.16666666666666669 (pow n 2))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
174×*-un-lft-identity
76×frac-sub
62×distribute-lft-out--
60×times-frac
58×add-sqr-sqrt
56×add-cube-cbrt
52×associate-+r+ log-prod
40×add-log-exp
32×associate--l+ associate--r+
30×distribute-lft-out
26×distribute-rgt-in distribute-lft-in
23×flip3-- flip--
22×associate-*l*
20×associate-/r*
19×flip3-+ flip-+ associate-/l*
18×diff-log
12×unpow-prod-down log-rec distribute-rgt-neg-out
9×pow1 clear-num sum-log
8×add-exp-log
7×associate--l- associate--r-
6×unsub-neg log-pow
5×frac-2neg add-cbrt-cube div-inv
4×+-commutative associate-+l+ unpow2 sqr-pow
3×sub-neg div-exp
1×cbrt-undiv pow-to-exp pow-exp difference-of-squares
Counts
3 → 225
Calls
3 calls:
58.0ms
(- (- 1.0 (* (log 1) 1.0)) (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
22.0ms
(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
6.0ms
(/ 0.16666666666666669 (pow n 2))

series406.0ms

Counts
3 → 9
Calls
3 calls:
40.0ms
(- (- 1.0 (* (log 1) 1.0)) (- (+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n)))) (/ 0.5 n)))
340.0ms
(+ (+ 1.0 (/ 0.16666666666666669 (pow n 2))) (* 1.0 (log (/ 1 n))))
26.0ms
(/ 0.16666666666666669 (pow n 2))

simplify81.0ms

Algorithm
egg-herbie
Counts
234 → 234
Iterations

Useful iterations: 1 (31.0ms)

IterNodesCost
014425298
150025079

prune725.0ms

Filtered
234 candidates to 150 candidates (64.1%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New2340234
Fresh000
Picked011
Done000
Total2341235

Merged error: 0b

Counts
235 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02513
12513

end0.0ms

sample1.9s

Algorithm
intervals
Results
1.0s3576×body1280valid
501.0ms2668×body640valid
163.0ms1304×body320valid
72.0ms8000×pre80true
39.0ms452×body160valid