Details

Time bar (total: 6.5s)

sample42.0ms

Algorithm
intervals
Results
13.0ms54×body1280valid
7.0ms44×body640valid
6.0ms229×body80nan
6.0ms135×body80valid
2.0ms17×body320valid
0.0ms6×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

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: 28.8b

Counts
2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

2.0b
(- (log (+ N 1.0)) (log N))
3.6b
(log (+ N 1.0))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×pow1 add-sqr-sqrt
6×add-log-exp
5×add-cube-cbrt log-pow
4×log-div diff-log associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out
1×sub-neg flip3-- rem-log-exp flip-- difference-of-squares
Counts
2 → 44
Calls
2 calls:
10.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series141.0ms

Counts
2 → 6
Calls
2 calls:
97.0ms
(- (log (+ N 1.0)) (log N))
43.0ms
(log (+ N 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0211284
1560270
21900258
35002255

prune88.0ms

Filtered
50 candidates to 33 candidates (34.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New47350
Fresh000
Picked101
Done000
Total48351

Merged error: 0.0b

Counts
51 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

1.9b
(log (/ (+ N 1.0) N))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×log-prod
12×log-div times-frac
11×add-sqr-sqrt add-cube-cbrt
6×associate-/l*
5×distribute-lft-out
4×add-exp-log
3×log-rec associate-/r*
2×pow1 rem-log-exp clear-num associate-/l/
1×frac-2neg flip3-+ div-exp log-pow add-cbrt-cube flip-+ div-inv add-log-exp
Counts
1 → 41
Calls
1 calls:
6.0ms
(log (/ (+ N 1.0) N))

series86.0ms

Counts
1 → 3
Calls
1 calls:
86.0ms
(log (/ (+ N 1.0) N))

simplify75.0ms

Algorithm
egg-herbie
Counts
44 → 44
Iterations

Useful iterations: 2 (16.0ms)

IterNodesCost
0228287
1635267
22602259
35002259

prune61.0ms

Filtered
44 candidates to 29 candidates (34.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New43144
Fresh112
Picked011
Done000
Total44347

Merged error: 0.0b

Counts
47 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (/ (+ N 1.0) N))
0.2b
(cbrt (/ (+ N 1.0) N))
1.9b
(log (cbrt (/ (+ N 1.0) N)))
1.9b
(log (cbrt (/ (+ N 1.0) N)))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
64×cbrt-prod
48×cbrt-div times-frac
46×add-sqr-sqrt add-cube-cbrt
38×log-prod
24×log-div
16×distribute-lft-out associate-/l*
12×associate-/r*
8×associate-/l/
6×pow1 add-exp-log
4×frac-2neg flip3-+ pow1/3 clear-num log-pow add-cbrt-cube flip-+ div-inv add-log-exp
2×rem-log-exp
Counts
4 → 154
Calls
4 calls:
5.0ms
(cbrt (/ (+ N 1.0) N))
5.0ms
(cbrt (/ (+ N 1.0) N))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))

series711.0ms

Counts
4 → 12
Calls
4 calls:
137.0ms
(cbrt (/ (+ N 1.0) N))
132.0ms
(cbrt (/ (+ N 1.0) N))
222.0ms
(log (cbrt (/ (+ N 1.0) N)))
220.0ms
(log (cbrt (/ (+ N 1.0) N)))

simplify122.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
03391368
19281308
237941280
350011244

prune376.0ms

Filtered
166 candidates to 126 candidates (24.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1651166
Fresh011
Picked101
Done011
Total1663169

Merged error: 0.0b

Counts
169 → 3

localize25.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt N)
0.7b
(cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))
1.9b
(log (cbrt (/ (+ N 1.0) N)))
2.8b
(+ (log (cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (cbrt (/ (sqrt (+ N 1.0)) (cbrt N)))))

rewrite153.0ms

Algorithm
rewrite-expression-head
Rules
731×cbrt-prod
445×*-un-lft-identity
435×add-sqr-sqrt
432×times-frac
307×add-cube-cbrt
264×log-prod
252×sqrt-prod
196×associate-+l+
108×cbrt-div
96×swap-sqr associate-*r* associate-*l*
72×distribute-lft-out
69×log-div
64×unswap-sqr
63×associate-/r*
49×associate-+r+
39×associate-+l-
25×associate-/l*
18×associate-+r-
16×*-commutative
9×pow1
8×log-pow associate-/l/ add-log-exp
6×sqrt-div
5×add-exp-log flip3-+ pow1/3 flip-+
4×frac-2neg clear-num sum-log add-cbrt-cube div-inv
1×+-commutative rem-log-exp
Counts
4 → 613
Calls
4 calls:
1.0ms
(cbrt N)
27.0ms
(cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))
59.0ms
(+ (log (cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (cbrt (/ (sqrt (+ N 1.0)) (cbrt N)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
184.0ms
(cbrt N)
180.0ms
(cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))
212.0ms
(log (cbrt (/ (+ N 1.0) N)))
614.0ms
(+ (log (cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (cbrt (/ (sqrt (+ N 1.0)) (cbrt N)))))

simplify164.0ms

Algorithm
egg-herbie
Counts
625 → 625
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
016519176
146139039
250038885

prune1.8s

Filtered
625 candidates to 350 candidates (44.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New6241625
Fresh011
Picked101
Done011
Total6253628

Merged error: 0.0b

Counts
628 → 3

regimes25.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.9b

bsearch27.0ms

Steps
ItersRangePoint
8
45.72067326335533
96283.49646244562
7828.3924782253

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02411
12411

end0.0ms

sample1.2s

Algorithm
intervals
Results
416.0ms1707×body1280valid
189.0ms1247×body640valid
187.0ms7872×body80nan
175.0ms4137×body80valid
63.0ms623×body320valid
18.0ms286×body160valid