Details

Time bar (total: 3.5s)

sample44.0ms

Algorithm
intervals
Results
13.0ms44×body1280valid
11.0ms38×body640valid
7.0ms138×body80valid
3.0ms24×body320valid
1.0ms12×body160valid

simplify6.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.9b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.2b
(log (+ N 1.0))
3.4b
(- (log (+ N 1.0)) (log N))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
5×add-cube-cbrt log-pow
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 41
Calls
2 calls:
3.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

series10.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(log (+ N 1.0))
7.0ms
(- (log (+ N 1.0)) (log N))

simplify59.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 2 (17.0ms)

IterNodesCost
0232285
1628264
22171244
35001244

prune83.0ms

Filtered
47 candidates to 34 candidates (27.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New45247
Fresh000
Picked101
Done000
Total46248

Merged error: 0.0b

Counts
48 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
3.3b
(log (/ (+ N 1.0) N))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
33×*-un-lft-identity
24×times-frac
19×add-sqr-sqrt add-cube-cbrt
16×log-prod
7×add-exp-log distribute-lft-out
4×add-cbrt-cube associate-/l*
3×pow1 associate-/r*
2×div-exp rem-log-exp div-inv associate-/l/ add-log-exp
1×cbrt-undiv log-div frac-2neg flip3-+ clear-num log-pow flip-+
Counts
2 → 60
Calls
2 calls:
5.0ms
(/ (+ N 1.0) N)
5.0ms
(log (/ (+ N 1.0) N))

series8.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(/ (+ N 1.0) N)
4.0ms
(log (/ (+ N 1.0) N))

simplify97.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0221370
1736343
23220333
35002333

prune73.0ms

Filtered
66 candidates to 46 candidates (30.3%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New66066
Fresh011
Picked011
Done000
Total66268

Merged error: 0.0b

Counts
68 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
0.0b
(- (/ 0.3333333333333333 N) 0.5)
0.1b
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
0.3b
(/ 1 (pow N 2))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
65×add-sqr-sqrt
58×times-frac
45×*-un-lft-identity
37×add-cube-cbrt
33×add-exp-log
28×associate-*l*
23×unpow-prod-down
12×div-exp
11×add-cbrt-cube
10×prod-exp
9×unpow2 unswap-sqr sqr-pow
8×associate-/r* add-log-exp
6×pow1 pow-to-exp rec-exp 1-exp associate-*r* pow-exp
5×sub-neg flip3-- frac-add flip--
4×distribute-rgt-in frac-times associate-+l+ distribute-lft-in associate-*r/ difference-of-squares
3×associate-/l*
2×cbrt-undiv associate-*l/ cbrt-unprod div-inv distribute-lft-out--
1×+-commutative pow-flip frac-2neg flip3-+ diff-log pow-prod-down clear-num sum-log *-commutative flip-+ inv-pow
Counts
4 → 165
Calls
4 calls:
15.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
7.0ms
(- (/ 0.3333333333333333 N) 0.5)
19.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
5.0ms
(/ 1 (pow N 2))

series15.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ (* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5)) (/ 1.0 N))
3.0ms
(- (/ 0.3333333333333333 N) 0.5)
6.0ms
(* (/ 1 (pow N 2)) (- (/ 0.3333333333333333 N) 0.5))
2.0ms
(/ 1 (pow N 2))

simplify80.0ms

Algorithm
egg-herbie
Counts
177 → 177
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05971157
12754966
25001903

prune196.0ms

Filtered
177 candidates to 101 candidates (42.9%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1743177
Fresh000
Picked101
Done011
Total1754179

Merged error: 0.0b

Counts
179 → 4

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 1 (pow N 2))
2.3b
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
13.4b
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
17.4b
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
108×associate-*l/
82×frac-add
60×associate-*r/
52×add-exp-log
42×associate-/l/
32×frac-times
29×flip3-+ flip-+
28×add-sqr-sqrt
27×times-frac
26×add-cube-cbrt *-un-lft-identity
23×prod-exp
22×add-cbrt-cube
18×flip3-- flip--
14×div-exp
12×unpow-prod-down
11×pow1
9×associate-/r*
8×associate-/r/
7×cbrt-unprod
6×pow-to-exp rec-exp 1-exp associate-*r* pow-exp associate-/l*
4×cbrt-undiv associate-*l* pow-prod-down unpow2 add-log-exp sqr-pow
2×frac-2neg clear-num *-commutative div-inv
1×distribute-rgt-in pow-flip distribute-lft-in inv-pow unswap-sqr
Counts
4 → 189
Calls
4 calls:
5.0ms
(/ 1 (pow N 2))
54.0ms
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
34.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
11.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))

series23.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(/ 1 (pow N 2))
9.0ms
(/ (+ (* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N) (* (+ (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)) (+ (* 0.5 0.5) (* (/ 0.3333333333333333 N) 0.5))) 1.0)) (* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N)))))
9.0ms
(* (* (/ 1 (pow N 2)) (- (pow (/ 0.3333333333333333 N) 3) (pow 0.5 3))) N)
4.0ms
(* N (+ (* 0.5 (+ 0.5 (/ 0.3333333333333333 N))) (* (/ 0.3333333333333333 N) (/ 0.3333333333333333 N))))

simplify66.0ms

Algorithm
egg-herbie
Counts
201 → 201
Iterations

Useful iterations: 1 (35.0ms)

IterNodesCost
012163158
150012873

prune1.3s

Filtered
201 candidates to 136 candidates (32.3%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New2001201
Fresh112
Picked011
Done011
Total2014205

Merged error: 0.0b

Counts
205 → 4

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 29.2b

bsearch18.0ms

Steps
ItersRangePoint
9
0.6495860155997162
52552.246590622155
7443.8141419858675

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04730
14730

end0.0ms

sample1.2s

Algorithm
intervals
Results
489.0ms1669×body1280valid
248.0ms1298×body640valid
209.0ms4106×body80valid
82.0ms612×body320valid
25.0ms315×body160valid

Profiling

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