Details

Time bar (total: 5.2s)

sample51.0ms

Algorithm
intervals
Results
14.0ms50×body1280valid
9.0ms292×body80nan
8.0ms43×body640valid
7.0ms142×body80valid
2.0ms14×body320valid
1.0ms7×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.1b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.5b
(- (log (+ N 1.0)) (log N))
3.2b
(log (+ N 1.0))

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:
6.0ms
(- (log (+ N 1.0)) (log N))
3.0ms
(log (+ N 1.0))

series142.0ms

Counts
2 → 6
Calls
2 calls:
95.0ms
(- (log (+ N 1.0)) (log N))
47.0ms
(log (+ N 1.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (51.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune97.0ms

Filtered
47 candidates to 33 candidates (70.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New44347
Fresh000
Picked101
Done000
Total45348

Merged error: 0.1b

Counts
48 → 3

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
2.3b
(log (/ (+ N 1.0) N))

rewrite16.0ms

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)
8.0ms
(log (/ (+ N 1.0) N))

series132.0ms

Counts
2 → 6
Calls
2 calls:
46.0ms
(/ (+ N 1.0) N)
86.0ms
(log (/ (+ N 1.0) N))

simplify103.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0233373
1773351
23489339
35002339

prune101.0ms

Filtered
66 candidates to 45 candidates (68.2%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New64266
Fresh022
Picked011
Done000
Total64569

Merged error: 0.1b

Counts
69 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)
2.8b
(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
57×log-prod
55×*-un-lft-identity
49×times-frac
46×associate-+r+
37×add-sqr-sqrt add-cube-cbrt
30×cbrt-prod
28×sqrt-prod
11×associate-+l+ distribute-lft-out
8×pow1
4×add-exp-log log-pow add-cbrt-cube add-log-exp
3×pow1/3
2×log-div div-inv
1×+-commutative associate-+l- associate-+r- flip3-+ sum-log flip-+
Counts
4 → 107
Calls
4 calls:
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)
19.0ms
(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

series876.0ms

Counts
4 → 12
Calls
4 calls:
180.0ms
(cbrt N)
187.0ms
(cbrt N)
180.0ms
(cbrt N)
328.0ms
(+ (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (cbrt N))))

simplify50.0ms

Algorithm
egg-herbie
Counts
119 → 119
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
05351335
117671269
250011169

prune314.0ms

Filtered
119 candidates to 87 candidates (73.1%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1172119
Fresh123
Picked101
Done101
Total1204124

Merged error: 0.1b

Counts
124 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)
2.8b
(- (* (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (* (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (cbrt N)))))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
114×log-prod
98×times-frac
95×*-un-lft-identity
92×associate--r+
67×add-sqr-sqrt add-cube-cbrt
57×distribute-rgt-in distribute-lft-in
56×sqrt-prod
51×cbrt-prod
22×associate--l+
14×distribute-lft-out
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube div-inv
3×pow1/3
1×sub-neg flip3-- diff-log flip-- difference-of-squares
Counts
4 → 160
Calls
4 calls:
1.0ms
(cbrt N)
1.0ms
(cbrt N)
1.0ms
(cbrt N)
26.0ms
(- (* (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (* (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (cbrt N)))))

series988.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(cbrt N)
180.0ms
(cbrt N)
182.0ms
(cbrt N)
445.0ms
(- (* (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1.0)) (* (cbrt N) (cbrt N))))) (* (log (/ (sqrt (+ N 1.0)) (cbrt N))) (log (/ (sqrt (+ N 1.0)) (cbrt N)))))

simplify92.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 2 (56.0ms)

IterNodesCost
09874176
130024076
250014038

prune548.0ms

Filtered
172 candidates to 120 candidates (69.8%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1711172
Fresh033
Picked011
Done000
Total1715176

Merged error: 0.1b

Counts
176 → 5

regimes33.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.5b

bsearch24.0ms

Steps
ItersRangePoint
5
3001.138716904689
7137.79058365099
3450.721878219202

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02920
12920

end0.0ms

sample1.5s

Algorithm
intervals
Results
507.0ms1739×body1280valid
241.0ms7845×body80nan
230.0ms1244×body640valid
205.0ms4099×body80valid
73.0ms597×body320valid
25.0ms321×body160valid

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