Details

Time bar (total: 18.1s)

sample121.0ms

Algorithm
intervals
Results
36.0ms298×body80nan
27.0ms46×body1280valid
20.0ms48×body640valid
14.0ms136×body80valid
4.0ms15×body320valid
2.0ms11×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (log (+ N 1)) (log N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.9b

localize26.0ms

Local error

Found 2 expressions with local error:

3.4b
(log (+ N 1))
3.1b
(- (log (+ N 1)) (log N))

rewrite18.0ms

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
11.0ms
(- (log (+ N 1)) (log N))
6.0ms
(log (+ N 1))

series129.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
88.0ms
(- (log (+ N 1)) (log N))
41.0ms
(log (+ N 1))

simplify1.7s

Counts
29 → 49
Calls
29 calls:
Slowest
369.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
253.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
221.0ms
(- (/ 1 N) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ 1 N))))
212.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
187.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune349.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

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
13.0ms
(/ (+ N 1) N)
3.0ms
(log (/ (+ N 1) N))

series121.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
60.0ms
(log (/ (+ N 1) N))
60.0ms
(/ (+ N 1) N)

simplify1.8s

Counts
57 → 68
Calls
57 calls:
Slowest
303.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
196.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
194.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
134.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))
106.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune410.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b
(log (sqrt (/ (+ N 1) N)))
3.2b
(log (sqrt (/ (+ N 1) N)))
0.1b
(sqrt (/ (+ N 1) N))
0.1b
(sqrt (/ (+ N 1) N))

rewrite34.0ms

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
10.0ms
(sqrt (/ (+ N 1) N))
7.0ms
(log (sqrt (/ (+ N 1) N)))
7.0ms
(log (sqrt (/ (+ N 1) N)))
7.0ms
(sqrt (/ (+ N 1) N))

series281.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(log (sqrt (/ (+ N 1) N)))
83.0ms
(log (sqrt (/ (+ N 1) N)))
51.0ms
(sqrt (/ (+ N 1) N))
41.0ms
(sqrt (/ (+ N 1) N))

simplify2.7s

Counts
96 → 134
Calls
96 calls:
Slowest
265.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
233.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
213.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
182.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
150.0ms
(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

3.4b
(log (+ N 1))
3.1b
(- (log (+ N 1)) (log N))
0.7b
(exp (log (- (log (+ N 1)) (log N))))
0.0b
(log (- (log (+ N 1)) (log N)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
27×log-prod
26×*-un-lft-identity
19×pow1
16×add-sqr-sqrt
15×log-pow
12×distribute-lft-out--
10×add-cube-cbrt
8×log-div exp-sum
6×add-exp-log
4×exp-prod add-cbrt-cube associate--l+ insert-posit16 add-log-exp
3×flip3-- flip-- associate--r+ difference-of-squares
2×associate--l- flip3-+ exp-diff rem-log-exp flip-+ distribute-lft-out
1×sub-neg diff-log rem-exp-log
Counts
4 → 86
Calls
4 calls:
Slowest
8.0ms
(- (log (+ N 1)) (log N))
6.0ms
(exp (log (- (log (+ N 1)) (log N))))
4.0ms
(log (- (log (+ N 1)) (log N)))
3.0ms
(log (+ N 1))

series311.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
96.0ms
(- (log (+ N 1)) (log N))
91.0ms
(exp (log (- (log (+ N 1)) (log N))))
91.0ms
(log (- (log (+ N 1)) (log N)))
33.0ms
(log (+ N 1))

simplify4.7s

Counts
61 → 98
Calls
61 calls:
Slowest
781.0ms
(- (+ (* 5/24 (/ 1 (pow N 2))) (+ (log (/ -1 N)) (log -1))) (* 1/2 (/ 1 N)))
373.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
252.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
236.0ms
(- (+ (* 1/2 (/ (pow N 2) (log N))) (log (- (log N)))) (+ (/ N (log N)) (* 1/2 (/ (pow N 2) (pow (log N) 2)))))
235.0ms
(log (- (pow (log (+ N 1)) 3) (pow (log N) 3)))

prune821.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes64.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.3b

bsearch42.0ms

end0.0ms

sample3.2s

Algorithm
intervals
Results
1.1s1750×body1280valid
652.0ms8141×body80nan
536.0ms1218×body640valid
387.0ms4094×body80valid
209.0ms638×body320valid
74.0ms300×body160valid