Details

Time bar (total: 4.9s)

sample67.0ms

Algorithm
intervals
Results
30.0ms99×body1280valid
20.0ms104×body640valid
6.0ms43×body320valid
3.0ms256×pre80true
1.0ms10×body160valid

simplify151.0ms

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
1324678
1433088
1550028

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

localize11.0ms

Local error

Found 3 expressions with local error:

0.3b
(* n (log n))
0.3b
(* (+ n 1.0) (log (+ n 1.0)))
5.3b
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite37.0ms

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:
4.0ms
(* n (log n))
8.0ms
(* (+ n 1.0) (log (+ n 1.0)))
22.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series430.0ms

Counts
3 → 9
Calls
3 calls:
174.0ms
(* n (log n))
68.0ms
(* (+ n 1.0) (log (+ n 1.0)))
187.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

simplify56.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0431766
11784709
25002688

prune157.0ms

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 3 expressions with local error:

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)))
1.1b
(/ 1 (pow n 2))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
74×add-sqr-sqrt times-frac
54×add-cube-cbrt
32×add-exp-log
29×associate--l- associate-+l-
28×associate-+l+ associate-*r* associate--r+
26×unpow-prod-down log-prod
17×add-log-exp
16×associate-/r*
14×associate-*r/
13×distribute-rgt-in distribute-lft-in
12×div-exp distribute-lft-out--
10×prod-exp add-cbrt-cube distribute-lft-out unpow2 sqr-pow
9×unswap-sqr
7×pow1 associate-*l* associate-/l*
6×pow-to-exp rec-exp pow-flip diff-log 1-exp pow-exp
4×associate--l+ sum-log div-inv
3×pow-unpow clear-num un-div-inv
2×cbrt-undiv +-commutative sub-neg frac-2neg cbrt-unprod
1×flip3-- pow-pow pow-prod-down *-commutative flip-- inv-pow difference-of-squares
Counts
3 → 196
Calls
3 calls:
69.0ms
(- (+ (- 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))

series86.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
30.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
17.0ms
(/ 1 (pow n 2))

simplify66.0ms

Algorithm
egg-herbie
Counts
205 → 205
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
07361336
125171134
250021034

prune340.0ms

Filtered
205 candidates to 118 candidates (57.6%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New2041205
Fresh000
Picked101
Done000
Total2051206

Merged error: 0b

Counts
206 → 1

localize22.0ms

Local error

Found 3 expressions with local error:

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

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
146×*-un-lft-identity
76×frac-sub
62×distribute-lft-out--
40×add-log-exp
35×distribute-lft-out
30×add-sqr-sqrt
28×add-cube-cbrt
24×times-frac
23×flip3-- flip--
22×associate-*l*
20×associate-/r*
19×flip3-+ flip-+ associate-/l*
18×diff-log
14×pow1
12×distribute-lft-neg-out associate-+r- unpow-prod-down log-rec
11×log-pow
9×clear-num sum-log
8×add-exp-log
7×associate--l- associate--r-
6×unsub-neg associate--l+ associate--r+
5×frac-2neg add-cbrt-cube
4×+-commutative associate-+r+ unpow2 sqr-pow
3×sub-neg div-exp
1×cbrt-undiv pow-to-exp pow-exp div-inv difference-of-squares
Counts
3 → 173
Calls
3 calls:
65.0ms
(- (- 1.0 (* (log (/ (sqrt 1) 1)) 1.0)) (- (+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* (log (/ 1 n)) 1.0))) (/ 0.5 n)))
30.0ms
(+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* (log (/ 1 n)) 1.0)))
5.0ms
(/ 0.16666666666666669 (pow n 2))

series418.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(- (- 1.0 (* (log (/ (sqrt 1) 1)) 1.0)) (- (+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* (log (/ 1 n)) 1.0))) (/ 0.5 n)))
340.0ms
(+ 1.0 (+ (/ 0.16666666666666669 (pow n 2)) (* (log (/ 1 n)) 1.0)))
30.0ms
(/ 0.16666666666666669 (pow n 2))

simplify259.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
011195225
150015147

prune495.0ms

Filtered
182 candidates to 105 candidates (57.7%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1820182
Fresh000
Picked011
Done000
Total1821183

Merged error: 0b

Counts
183 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02715
12715

end0.0ms

sample2.0s

Algorithm
intervals
Results
1.1s3663×body1280valid
515.0ms2593×body640valid
178.0ms1315×body320valid
74.0ms8000×pre80true
36.0ms429×body160valid