Details

Time bar (total: 4.5s)

sample50.0ms

Algorithm
intervals
Results
13.0ms48×body1280valid
7.0ms250×body80nan
7.0ms39×body640valid
7.0ms134×body80valid
3.0ms25×body320valid
1.0ms10×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

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: 28.6b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

2.8b
(- (log (+ N 1.0)) (log N))
4.2b
(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))

series174.0ms

Counts
2 → 6
Calls
2 calls:
115.0ms
(- (log (+ N 1.0)) (log N))
59.0ms
(log (+ N 1.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
47 → 47
Iterations

Useful iterations: 3 (48.0ms)

IterNodesCost
0212281
1547264
21874250
35001247

prune122.0ms

Filtered
47 candidates to 33 candidates (29.8%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New45247
Fresh000
Picked101
Done000
Total46248

Merged error: 0.0b

Counts
48 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ (+ N 1.0) N)
2.6b
(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)
4.0ms
(log (/ (+ N 1.0) N))

series162.0ms

Counts
2 → 6
Calls
2 calls:
60.0ms
(/ (+ N 1.0) N)
101.0ms
(log (/ (+ N 1.0) N))

simplify99.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 2 (18.0ms)

IterNodesCost
0233373
1773351
23489339
35002339

prune160.0ms

Filtered
66 candidates to 45 candidates (31.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New64266
Fresh011
Picked011
Done000
Total64468

Merged error: 0.0b

Counts
68 → 4

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (log (/ (+ N 1.0) N)))
0.3b
(* (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))))
2.6b
(log (/ (+ N 1.0) N))
2.6b
(log (/ (+ N 1.0) N))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×add-sqr-sqrt
32×log-prod
30×sqrt-prod
29×pow1 add-cube-cbrt
24×times-frac
12×add-exp-log
11×swap-sqr
9×sqrt-pow1 pow1/2 log-pow
7×associate-*r* associate-*l*
6×add-cbrt-cube distribute-lft-out
5×pow-prod-up
4×rem-log-exp add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×log-div div-exp div-inv
1×pow2 rem-sqrt-square pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 122
Calls
4 calls:
1.0ms
(sqrt (log (/ (+ N 1.0) N)))
9.0ms
(* (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))))
4.0ms
(log (/ (+ N 1.0) N))
4.0ms
(log (/ (+ N 1.0) N))

series489.0ms

Counts
4 → 12
Calls
4 calls:
182.0ms
(sqrt (log (/ (+ N 1.0) N)))
104.0ms
(* (sqrt (log (/ (+ N 1.0) N))) (sqrt (log (/ (+ N 1.0) N))))
100.0ms
(log (/ (+ N 1.0) N))
101.0ms
(log (/ (+ N 1.0) N))

simplify48.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0358915
11476839
25001790

prune351.0ms

Filtered
134 candidates to 75 candidates (44.0%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New1313134
Fresh112
Picked101
Done011
Total1335138

Merged error: 0.0b

Counts
138 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

1.1b
(exp (sqrt (log (/ (+ N 1.0) N))))
1.6b
(log (exp (sqrt (log (/ (+ N 1.0) N)))))
2.6b
(log (/ (+ N 1.0) N))
2.6b
(log (/ (+ N 1.0) N))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
37×*-un-lft-identity
35×log-prod
25×add-sqr-sqrt add-cube-cbrt
24×times-frac
14×exp-prod
12×log-pow
10×add-exp-log
9×pow1
8×sqrt-prod
6×distribute-lft-out
5×rem-log-exp add-log-exp
4×add-cbrt-cube
2×log-div div-exp div-inv
1×rem-exp-log
Counts
4 → 88
Calls
4 calls:
2.0ms
(exp (sqrt (log (/ (+ N 1.0) N))))
3.0ms
(log (exp (sqrt (log (/ (+ N 1.0) N)))))
4.0ms
(log (/ (+ N 1.0) N))
4.0ms
(log (/ (+ N 1.0) N))

series551.0ms

Counts
4 → 12
Calls
4 calls:
161.0ms
(exp (sqrt (log (/ (+ N 1.0) N))))
185.0ms
(log (exp (sqrt (log (/ (+ N 1.0) N)))))
104.0ms
(log (/ (+ N 1.0) N))
100.0ms
(log (/ (+ N 1.0) N))

simplify40.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0411816
11318760
25001716

prune532.0ms

Filtered
100 candidates to 72 candidates (28.0%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New1000100
Fresh033
Picked011
Done011
Total1005105

Merged error: 0.0b

Counts
105 → 5

regimes45.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.0b

bsearch42.0ms

Steps
ItersRangePoint
9
1325.407106289753
170944420.23003155
10613.272105470618

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02410
12410

end0.0ms

sample1.5s

Algorithm
intervals
Results
481.0ms1762×body1280valid
233.0ms7856×body80nan
223.0ms1244×body640valid
200.0ms4121×body80valid
71.0ms590×body320valid
20.0ms283×body160valid

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