Details

Time bar (total: 23.9s)

sample88.0ms

Algorithm
intervals
Results
24.0ms46×body1280valid
18.0ms48×body640valid
17.0ms298×body80nan
12.0ms136×body80valid
3.0ms15×body320valid
2.0ms11×body160valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (log (+ N 1)) (log N))

prune13.0ms

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))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×add-sqr-sqrt pow1 prod-diff
14×log-pow add-cube-cbrt
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
Slowest
10.0ms
(- (log (+ N 1)) (log N))
3.0ms
(log (+ N 1))

series122.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
95.0ms
(- (log (+ N 1)) (log N))
26.0ms
(log (+ N 1))

simplify4.1s

Counts
63 → 73
Calls
63 calls:
Slowest
420.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
263.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
215.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
205.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
172.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune608.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

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×expm1-log1p-u div-exp rem-log-exp insert-posit16 log1p-expm1-u div-inv add-log-exp associate-/l/
1×cbrt-undiv log-div clear-num frac-2neg flip3-+ log-pow flip-+
Counts
2 → 66
Calls
2 calls:
Slowest
13.0ms
(/ (+ N 1) N)
4.0ms
(log (/ (+ N 1) N))

series114.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
62.0ms
(/ (+ N 1) N)
52.0ms
(log (/ (+ N 1) N))

simplify1.7s

Counts
57 → 72
Calls
57 calls:
Slowest
282.0ms
(/ (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
211.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
177.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
129.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
122.0ms
(log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (* (cbrt N) (cbrt N))))

prune514.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

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))

rewrite22.0ms

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×expm1-log1p-u rem-sqrt-square sqrt-pow1 add-cbrt-cube pow1/2 sqrt-div insert-posit16 log1p-expm1-u div-inv add-log-exp
2×log-div rem-log-exp
Counts
4 → 130
Calls
4 calls:
Slowest
6.0ms
(sqrt (/ (+ N 1) N))
6.0ms
(sqrt (/ (+ N 1) N))
4.0ms
(log (sqrt (/ (+ N 1) N)))
4.0ms
(log (sqrt (/ (+ N 1) N)))

series306.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
122.0ms
(log (sqrt (/ (+ N 1) N)))
78.0ms
(log (sqrt (/ (+ N 1) N)))
61.0ms
(sqrt (/ (+ N 1) N))
44.0ms
(sqrt (/ (+ N 1) N))

simplify2.8s

Counts
96 → 142
Calls
96 calls:
Slowest
266.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
254.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
210.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
178.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
123.0ms
(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.4s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize39.0ms

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)))

rewrite56.0ms

Algorithm
rewrite-expression-head
Rules
35×*-un-lft-identity
28×pow1
27×log-prod
25×add-sqr-sqrt
24×log-pow
19×add-cube-cbrt
16×prod-diff
12×distribute-lft-out--
8×log-div exp-sum
6×add-exp-log
4×expm1-log1p-u exp-prod add-cbrt-cube fma-neg associate--l+ insert-posit16 log1p-expm1-u 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 → 114
Calls
4 calls:
Slowest
20.0ms
(- (log (+ N 1)) (log N))
15.0ms
(log (- (log (+ N 1)) (log N)))
12.0ms
(exp (log (- (log (+ N 1)) (log N))))
6.0ms
(log (+ N 1))

series291.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
89.0ms
(exp (log (- (log (+ N 1)) (log N))))
84.0ms
(log (- (log (+ N 1)) (log N)))
79.0ms
(- (log (+ N 1)) (log N))
39.0ms
(log (+ N 1))

simplify6.8s

Counts
95 → 126
Calls
95 calls:
Slowest
435.0ms
(- (+ (/ 1 N) (log -1)) (+ (* 1/2 (/ 1 (pow N 2))) (log (/ -1 N))))
316.0ms
(- (+ N (* 1/3 (pow N 3))) (* 1/2 (pow N 2)))
309.0ms
(- (+ (* 5/24 (/ 1 (pow N 2))) (log (/ 1 N))) (* 1/2 (/ 1 N)))
271.0ms
(exp (log (- (pow (log (+ N 1)) 3) (pow (log N) 3))))
239.0ms
(- (+ (* 1/2 (/ (pow N 2) (log N))) (log (- (log N)))) (+ (/ N (log N)) (* 1/2 (/ (pow N 2) (pow (log N) 2)))))

prune1.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes96.0ms

Accuracy

100% (0.0b remaining)

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

bsearch71.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
989.0ms1750×body1280valid
963.0ms1218×body640valid
649.0ms8141×body80nan
387.0ms4094×body80valid
153.0ms638×body320valid
47.0ms300×body160valid