Details

Time bar (total: 6.9s)

sample45.0ms

Algorithm
intervals
Results
13.0ms54×body1280valid
8.0ms229×body80nan
6.0ms44×body640valid
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

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
11×log-prod
6×add-log-exp
4×log-div fma-neg diff-log associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out
1×sub-neg flip3-- rem-log-exp flip-- difference-of-squares
Counts
2 → 68
Calls
2 calls:
8.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series150.0ms

Counts
2 → 6
Calls
2 calls:
99.0ms
(- (log (+ N 1.0)) (log N))
51.0ms
(log (+ N 1.0))

simplify125.0ms

Algorithm
egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
0276601
1839450
23608355
35001351

prune109.0ms

Filtered
74 candidates to 43 candidates (41.9%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New71374
Fresh000
Picked101
Done000
Total72375

Merged error: 0.0b

Counts
75 → 3

localize5.0ms

Local error

Found 1 expressions with local error:

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

rewrite8.0ms

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×expm1-log1p-u frac-2neg flip3-+ div-exp log-pow add-cbrt-cube flip-+ log1p-expm1-u div-inv add-log-exp
Counts
1 → 43
Calls
1 calls:
6.0ms
(log (/ (+ N 1.0) N))

series89.0ms

Counts
1 → 3
Calls
1 calls:
89.0ms
(log (/ (+ N 1.0) N))

simplify82.0ms

Algorithm
egg-herbie
Counts
46 → 46
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0236294
1668271
22741264
35002260

prune68.0ms

Filtered
46 candidates to 32 candidates (30.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New44246
Fresh202
Picked011
Done000
Total46349

Merged error: 0.0b

Counts
49 → 3

localize9.0ms

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)))

rewrite33.0ms

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×expm1-log1p-u frac-2neg flip3-+ pow1/3 clear-num log-pow add-cbrt-cube flip-+ log1p-expm1-u div-inv add-log-exp
2×rem-log-exp
Counts
4 → 162
Calls
4 calls:
6.0ms
(cbrt (/ (+ N 1.0) N))
6.0ms
(cbrt (/ (+ N 1.0) N))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))

series729.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(cbrt (/ (+ N 1.0) N))
137.0ms
(cbrt (/ (+ N 1.0) N))
228.0ms
(log (cbrt (/ (+ N 1.0) N)))
224.0ms
(log (cbrt (/ (+ N 1.0) N)))

simplify130.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 3 (113.0ms)

IterNodesCost
03531400
19941336
241391312
350011292

prune414.0ms

Filtered
174 candidates to 138 candidates (20.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1731174
Fresh011
Picked101
Done011
Total1743177

Merged error: 0.0b

Counts
177 → 3

localize22.0ms

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)))))

rewrite157.0ms

Algorithm
rewrite-expression-head
Rules
731×cbrt-prod
446×*-un-lft-identity
436×add-sqr-sqrt
432×times-frac
308×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
10×pow1 log-pow
8×associate-/l/ add-log-exp
6×pow1/3 sqrt-div
5×add-exp-log fma-def flip3-+ flip-+
4×expm1-log1p-u frac-2neg clear-num sum-log add-cbrt-cube log1p-expm1-u div-inv
1×+-commutative rem-log-exp
Counts
4 → 626
Calls
4 calls:
1.0ms
(cbrt N)
31.0ms
(cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))
7.0ms
(log (cbrt (/ (+ N 1.0) N)))
66.0ms
(+ (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:
194.0ms
(cbrt N)
192.0ms
(cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))
442.0ms
(log (cbrt (/ (+ N 1.0) N)))
419.0ms
(+ (log (cbrt (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (log (cbrt (/ (sqrt (+ N 1.0)) (cbrt N)))))

simplify168.0ms

Algorithm
egg-herbie
Counts
638 → 638
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
016789235
147469090
250019081

prune2.0s

Filtered
638 candidates to 386 candidates (39.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New6371638
Fresh011
Picked101
Done011
Total6383641

Merged error: 0.0b

Counts
641 → 3

regimes22.0ms

Accuracy

100% (0.0b remaining)

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

bsearch34.0ms

Steps
ItersRangePoint
8
45.72067326335533
96283.49646244562
7828.3924782253

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0219
1219

end0.0ms

sample1.2s

Algorithm
intervals
Results
419.0ms1707×body1280valid
186.0ms1247×body640valid
182.0ms7872×body80nan
170.0ms4137×body80valid
59.0ms623×body320valid
17.0ms286×body160valid