Details

Time bar (total: 20.1s)

sample118.0ms

Algorithm
intervals
Results
36.0ms55×body1280valid
28.0ms136×body80valid
18.0ms39×body640valid
17.0ms233×body80nan
4.0ms15×body320valid
3.0ms11×body160valid

simplify12.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
12.0ms
(- (log (+ N 1)) (log N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize11.0ms

Local error

Found 2 expressions with local error:

3.5b
(log (+ N 1))
3.4b
(- (log (+ N 1)) (log N))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
11×log-prod
7×add-sqr-sqrt pow1
5×log-pow add-cube-cbrt
4×log-div associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- flip3-+ add-cbrt-cube flip-+ insert-posit16 distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 43
Calls
2 calls:
Slowest
16.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series139.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
97.0ms
(- (log (+ N 1)) (log N))
42.0ms
(log (+ N 1))

simplify1.7s

Counts
29 → 49
Calls
29 calls:
Slowest
436.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
207.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
194.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
186.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
156.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))

prune462.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

Local error

Found 2 expressions with local error:

3.4b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite26.0ms

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 insert-posit16 div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Counts
2 → 62
Calls
2 calls:
Slowest
21.0ms
(/ (+ N 1) N)
3.0ms
(log (/ (+ N 1) N))

series150.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
81.0ms
(log (/ (+ N 1) N))
69.0ms
(/ (+ N 1) N)

simplify1.9s

Counts
57 → 68
Calls
57 calls:
Slowest
360.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
232.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
199.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
152.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
100.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune476.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

3.3b
(log (sqrt (/ (+ N 1) N)))
3.3b
(log (sqrt (/ (+ N 1) N)))
0.1b
(sqrt (/ (+ N 1) N))
0.1b
(sqrt (/ (+ N 1) N))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
64×sqrt-prod
62×*-un-lft-identity
50×times-frac
44×add-sqr-sqrt
38×log-prod add-cube-cbrt
12×distribute-lft-out
10×pow1
6×add-exp-log log-pow
4×rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div insert-posit16 div-inv add-log-exp
2×log-div rem-log-exp
Counts
4 → 122
Calls
4 calls:
Slowest
11.0ms
(sqrt (/ (+ N 1) N))
8.0ms
(sqrt (/ (+ N 1) N))
4.0ms
(log (sqrt (/ (+ N 1) N)))
4.0ms
(log (sqrt (/ (+ N 1) N)))

series304.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
107.0ms
(log (sqrt (/ (+ N 1) N)))
97.0ms
(log (sqrt (/ (+ N 1) N)))
51.0ms
(sqrt (/ (+ N 1) N))
48.0ms
(sqrt (/ (+ N 1) N))

simplify2.7s

Counts
96 → 134
Calls
96 calls:
Slowest
242.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
230.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
208.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
184.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
145.0ms
(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.4s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize97.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (log (sqrt (/ (sqrt (+ N 1)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1)) (cbrt N)))))
3.3b
(log (sqrt (/ (+ N 1) N)))
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite59.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
82×log-prod
71×*-un-lft-identity
61×times-frac
49×associate-+r+
47×add-sqr-sqrt add-cube-cbrt
27×cbrt-prod
16×distribute-lft-out
14×associate-+l+
12×pow1
11×log-pow
5×add-exp-log
4×add-cbrt-cube insert-posit16 add-log-exp
3×log-div sqrt-pow1 pow1/2 sqrt-div div-inv
2×pow1/3
1×+-commutative associate-+r- sum-log flip3-+ rem-log-exp associate-+l- flip-+
Counts
4 → 139
Calls
4 calls:
Slowest
51.0ms
(+ (log (sqrt (/ (sqrt (+ N 1)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1)) (cbrt N)))))
4.0ms
(log (sqrt (/ (+ N 1) N)))
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series946.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
294.0ms
(cbrt N)
292.0ms
(cbrt N)
273.0ms
(+ (log (sqrt (/ (sqrt (+ N 1)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ N 1)) (cbrt N)))))
88.0ms
(log (sqrt (/ (+ N 1) N)))

simplify3.4s

Counts
113 → 151
Calls
113 calls:
Slowest
259.0ms
(- (+ (log (pow (/ 1 N) 1/12)) (+ (* 1/2 (/ 1 N)) (log (pow N 1/12)))) (* 1/4 (/ 1 (pow N 2))))
242.0ms
(- (+ (* 1/2 (/ 1 N)) (+ (log (* (exp (* 1/4 (- (log -1) (log (/ -1 N))))) (* (pow (/ -1 N) 1/6) (sqrt (/ 1 (cbrt -1)))))) (log (* (/ (exp (* 1/4 (- (log -1) (log (/ -1 N))))) (cbrt -1)) (pow (/ -1 N) 1/3))))) (* 1/4 (/ 1 (pow N 2))))
214.0ms
(- (+ (* 1/2 N) (+ (log (pow (/ 1 N) 1/3)) (log (pow (/ 1 N) 1/6)))) (* 1/4 (pow N 2)))
212.0ms
(+ (log (/ (sqrt (+ N 1)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ N 1)) (cbrt N))))
210.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))

prune2.5s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes68.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.7b

bsearch42.0ms

end0.0ms

sample3.5s

Algorithm
intervals
Results
1.0s7928×body80nan
1.0s1725×body1280valid
561.0ms1284×body640valid
421.0ms4030×body80valid
205.0ms626×body320valid
55.0ms335×body160valid