Details

Time bar (total: 16.0s)

sample73.0ms

Algorithm
intervals
Results
20.0ms55×body1280valid
19.0ms32×body640valid
11.0ms249×body80nan
9.0ms139×body80valid
3.0ms21×body320valid
1.0ms9×body160valid

simplify11.0ms

Calls
1 calls:
Slowest
11.0ms
(- (log (+ N 1)) (log N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.7b

localize15.0ms

Local error

Found 2 expressions with local error:

3.4b
(log (+ N 1))
2.1b
(- (log (+ N 1)) (log N))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
7×*-un-lft-identity
6×add-sqr-sqrt log-prod
4×pow1 log-div add-cube-cbrt
3×associate--l+ add-exp-log
2×associate--l- flip3-+ add-cbrt-cube log-pow flip-+ insert-posit16 distribute-lft-out-- add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Calls
2 calls:
Slowest
11.0ms
(- (log (+ N 1)) (log N))
2.0ms
(log (+ N 1))

series133.0ms

Calls
2 calls:
Slowest
96.0ms
(- (log (+ N 1)) (log N))
37.0ms
(log (+ N 1))

simplify1.5s

Calls
22 calls:
Slowest
418.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
180.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
170.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
153.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
151.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune388.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

2.3b
(log (/ (+ N 1) N))
0.0b
(/ (+ N 1) N)

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt log-prod *-un-lft-identity add-cube-cbrt
3×pow1 add-exp-log associate-/l*
2×add-cbrt-cube insert-posit16 div-inv add-log-exp associate-/l/
1×log-div clear-num frac-2neg flip3-+ rem-log-exp log-pow flip-+
Calls
2 calls:
Slowest
6.0ms
(/ (+ N 1) N)
2.0ms
(log (/ (+ N 1) N))

series67.0ms

Calls
2 calls:
Slowest
49.0ms
(log (/ (+ N 1) N))
18.0ms
(/ (+ N 1) N)

simplify628.0ms

Calls
16 calls:
Slowest
173.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
159.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
133.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
25.0ms
(- (* N N) (* 1 1))
18.0ms
(+ (pow N 3) (pow 1 3))

prune226.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

2.3b
(log (sqrt (/ (+ N 1) N)))
2.3b
(log (sqrt (/ (+ N 1) N)))
0.1b
(sqrt (/ (+ N 1) N))
0.1b
(sqrt (/ (+ N 1) N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
16×sqrt-prod
14×log-prod
12×add-sqr-sqrt
10×*-un-lft-identity add-cube-cbrt
6×pow1 add-exp-log
4×add-cbrt-cube pow1/2 sqrt-div log-pow insert-posit16 div-inv add-log-exp
2×rem-sqrt-square log-div rem-log-exp
Calls
4 calls:
Slowest
1.0ms
(log (sqrt (/ (+ N 1) N)))
1.0ms
(log (sqrt (/ (+ N 1) N)))
1.0ms
(sqrt (/ (+ N 1) N))
1.0ms
(sqrt (/ (+ N 1) N))

series149.0ms

Calls
4 calls:
Slowest
50.0ms
(log (sqrt (/ (+ N 1) N)))
48.0ms
(log (sqrt (/ (+ N 1) N)))
28.0ms
(sqrt (/ (+ N 1) N))
22.0ms
(sqrt (/ (+ N 1) N))

simplify1.4s

Calls
42 calls:
Slowest
189.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
176.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
148.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
142.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
139.0ms
(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune624.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

18.3b
(+ (log (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (- (log (cbrt (+ N 1))) (log N)))
3.4b
(log (cbrt (+ N 1)))
3.4b
(log (* (cbrt (+ N 1)) (cbrt (+ N 1))))
0.3b
(- (log (cbrt (+ N 1))) (log N))

rewrite91.0ms

Algorithm
rewrite-expression-head
Rules
28×cbrt-div *-un-lft-identity
24×pow1
20×log-div log-prod
19×log-pow
15×flip3-+ flip-+
12×add-sqr-sqrt associate--l+
10×add-cube-cbrt
9×cbrt-prod distribute-lft-out
8×frac-times associate-+r+ add-exp-log associate-+l- distribute-lft-out--
5×pow1/3 pow-prod-down add-log-exp
4×add-cbrt-cube associate-*l/ associate-*r/ insert-posit16
3×rem-log-exp
2×associate--l- sum-log sub-neg diff-log pow-prod-up
1×pow2 +-commutative associate-+l+ associate-+r- pow-plus flip3-- prod-exp flip-- difference-of-squares
Calls
4 calls:
Slowest
63.0ms
(+ (log (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (- (log (cbrt (+ N 1))) (log N)))
12.0ms
(log (* (cbrt (+ N 1)) (cbrt (+ N 1))))
11.0ms
(- (log (cbrt (+ N 1))) (log N))
3.0ms
(log (cbrt (+ N 1)))

series302.0ms

Calls
4 calls:
Slowest
111.0ms
(+ (log (* (cbrt (+ N 1)) (cbrt (+ N 1)))) (- (log (cbrt (+ N 1))) (log N)))
74.0ms
(- (log (cbrt (+ N 1))) (log N))
67.0ms
(log (cbrt (+ N 1)))
49.0ms
(log (* (cbrt (+ N 1)) (cbrt (+ N 1))))

simplify5.5s

Calls
77 calls:
Slowest
464.0ms
(- (+ (log (/ 1 N)) (+ (/ 1 N) (+ (log (pow (/ 1 N) -1/3)) (log (pow (/ 1 N) -2/3))))) (* 1/2 (/ 1 (pow N 2))))
362.0ms
(- (+ (* 1/3 (/ 1 N)) (* 2/3 (log (/ -1 N)))) (+ (* 1/6 (/ 1 (pow N 2))) (* 2/3 (log -1))))
349.0ms
(- (+ (* 1/3 (/ 1 N)) (* 1/3 (log -1))) (+ (* 1/6 (/ 1 (pow N 2))) (* 1/3 (log (/ -1 N)))))
321.0ms
(- (+ (log (/ 1 N)) (+ (* 1/3 (/ 1 N)) (log (pow (/ 1 N) -1/3)))) (* 1/6 (/ 1 (pow N 2))))
276.0ms
(- (+ (* 2/3 (log (/ -1 N))) (+ (/ 1 N) (log (pow (/ -1 N) -2/3)))) (+ (* 1/2 (/ 1 (pow N 2))) (* 2/3 (log -1))))

prune1.3s

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch45.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.1s1713×body1280valid
882.0ms4111×body80valid
575.0ms7956×body80nan
479.0ms1276×body640valid
143.0ms578×body320valid
50.0ms322×body160valid