Details

Time bar (total: 3.8s)

sample84.0ms

Algorithm
intervals
Results
41.0ms109×body1280valid
22.0ms87×body640valid
8.0ms44×body320valid
3.0ms256×pre80true
2.0ms16×body160valid

simplify160.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0188
1438
21238
32128
43748
54968
67158
79678
811218
912218
1014818
1116598
1220398
1323768
1432098
1550018

prune3.0ms

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:

0.3b
(* n (log n))
0.3b
(* (+ n 1.0) (log (+ n 1.0)))
5.6b
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

rewrite26.0ms

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:
4.0ms
(* n (log n))
8.0ms
(* (+ n 1.0) (log (+ n 1.0)))
12.0ms
(- (* (+ n 1.0) (log (+ n 1.0))) (* n (log n)))

series33.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(* n (log n))
5.0ms
(* (+ n 1.0) (log (+ n 1.0)))
13.0ms
(- (* (+ 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
0439660
11891592
25001573

prune128.0ms

Filtered
63 candidates to 90 candidates (-42.9%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New89190
Fresh000
Picked101
Done000
Total90191

Merged error: 0.0b

Counts
91 → 1

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
0.0b
(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
0.1b
(* 0.16666666666666669 (/ 1 (pow n 2)))
0.8b
(/ 1 (pow n 2))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
56×times-frac
54×add-log-exp
48×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*r*
23×unpow-prod-down
19×diff-log
18×sum-log
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r*
6×pow1 pow-to-exp rec-exp 1-exp pow-exp
5×associate--l+
4×flip3-+ frac-sub flip-+ distribute-lft-out--
3×sub-neg associate-*l* associate-/l*
2×cbrt-undiv flip3-- flip-- cbrt-unprod div-inv difference-of-squares
1×associate--l- pow-flip frac-2neg associate-*r/ pow-prod-down clear-num un-div-inv *-commutative associate--r+ inv-pow
Counts
4 → 170
Calls
4 calls:
14.0ms
(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
16.0ms
(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
11.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms
(/ 1 (pow n 2))

series23.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2)))))
7.0ms
(- (- (+ (* 1.0 (log 1)) (+ (* 0.5 (/ 1 n)) 1.0)) (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) 1.0)
3.0ms
(* 0.16666666666666669 (/ 1 (pow n 2)))
5.0ms
(/ 1 (pow n 2))

simplify93.0ms

Algorithm
egg-herbie
Counts
182 → 182
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
07721815
134041597
250031491

prune334.0ms

Filtered
98 candidates to 182 candidates (-85.7%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New1811182
Fresh000
Picked101
Done000
Total1821183

Merged error: 0b

Counts
183 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 0.5 (/ 1 n))
0.0b
(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
0.7b
(/ 0.16666666666666669 (pow n 2))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
35×add-sqr-sqrt times-frac
29×*-un-lft-identity
28×add-cube-cbrt
17×add-exp-log
13×associate-*r*
12×unpow-prod-down
10×add-cbrt-cube
8×associate-/r*
5×pow1 div-exp add-log-exp
4×prod-exp unpow2 sqr-pow
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv associate-*r/ un-div-inv frac-sub cbrt-unprod div-inv
1×pow-to-exp sub-neg rec-exp flip3-- frac-2neg diff-log 1-exp pow-prod-down pow-exp clear-num *-commutative flip--
Counts
3 → 99
Calls
3 calls:
7.0ms
(* 0.5 (/ 1 n))
9.0ms
(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
6.0ms
(/ 0.16666666666666669 (pow n 2))

series11.0ms

Counts
3 → 9
Calls
3 calls:
2.0ms
(* 0.5 (/ 1 n))
6.0ms
(- (* 0.5 (/ 1 n)) (/ 0.16666666666666669 (pow n 2)))
3.0ms
(/ 0.16666666666666669 (pow n 2))

simplify47.0ms

Algorithm
egg-herbie
Counts
108 → 108
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0387508
11669446
25001425

prune127.0ms

Filtered
70 candidates to 108 candidates (-54.3%)
Pruning

1 alts after pruning (0 fresh and 1 done)

PrunedKeptTotal
New1080108
Fresh000
Picked011
Done000
Total1081109

Merged error: 0b

Counts
109 → 1

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0198
1198

end0.0ms

sample2.6s

Algorithm
intervals
Results
1.4s3617×body1280valid
674.0ms2641×body640valid
229.0ms1300×body320valid
88.0ms8000×pre80true
49.0ms442×body160valid

Profiling

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