Details

Time bar (total: 21.7s)

sample79.0ms

Algorithm
intervals
Results
28.0ms55×body1280valid
12.0ms39×body640valid
12.0ms233×body80nan
11.0ms136×body80valid
3.0ms15×body320valid
2.0ms11×body160valid

simplify22.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
22.0ms
(- (log (+ N 1)) (log N))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.4b

localize15.0ms

Local error

Found 1 expressions with local error:

3.4b
(- (log1p N) (log N))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt prod-diff
10×add-cube-cbrt
5×pow1
4×log-pow
3×log-prod fma-neg associate--r+
2×diff-log distribute-lft-out-- add-log-exp
1×expm1-log1p-u log1p-udef sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
Counts
1 → 37
Calls
1 calls:
Slowest
11.0ms
(- (log1p N) (log N))

series75.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
75.0ms
(- (log1p N) (log N))

simplify2.2s

Counts
38 → 40
Calls
38 calls:
Slowest
226.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
216.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
188.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
173.0ms
(fma (sqrt (log1p N)) (sqrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
152.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))

prune305.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 2 expressions with local error:

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

rewrite28.0ms

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
20.0ms
(/ (+ 1 N) N)
8.0ms
(log (/ (+ 1 N) N))

series114.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
60.0ms
(/ (+ 1 N) N)
54.0ms
(log (/ (+ 1 N) N))

simplify2.0s

Counts
57 → 72
Calls
57 calls:
Slowest
336.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
215.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
202.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
147.0ms
(- N (+ (log N) (* 1/2 (pow N 2))))
121.0ms
(log (/ (* (cbrt (+ 1 N)) (cbrt (+ 1 N))) (* (cbrt N) (cbrt N))))

prune566.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite39.0ms

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
12.0ms
(log (sqrt (/ (+ 1 N) N)))
9.0ms
(sqrt (/ (+ 1 N) N))
9.0ms
(log (sqrt (/ (+ 1 N) N)))
6.0ms
(sqrt (/ (+ 1 N) N))

series272.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
106.0ms
(log (sqrt (/ (+ 1 N) N)))
80.0ms
(log (sqrt (/ (+ 1 N) N)))
49.0ms
(sqrt (/ (+ 1 N) N))
37.0ms
(sqrt (/ (+ 1 N) N))

simplify2.9s

Counts
96 → 142
Calls
96 calls:
Slowest
265.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
259.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
259.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
231.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
140.0ms
(- (+ (* 1/2 (/ 1 N)) 1) (* 1/8 (/ 1 (pow N 2))))

prune1.6s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
101×sqrt-prod
82×log-prod
72×*-un-lft-identity
61×times-frac
49×associate-+r+
48×add-sqr-sqrt add-cube-cbrt
27×cbrt-prod
16×distribute-lft-out
14×pow1 associate-+l+ log-pow
6×fma-def
5×add-exp-log
4×expm1-log1p-u sqrt-pow1 add-cbrt-cube pow1/2 insert-posit16 log1p-expm1-u add-log-exp
3×log-div sqrt-div div-inv
2×pow1/3
1×+-commutative associate-+r- sum-log flip3-+ rem-log-exp associate-+l- flip-+
Counts
4 → 153
Calls
4 calls:
Slowest
51.0ms
(+ (log (sqrt (/ (sqrt (+ 1 N)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ 1 N)) (cbrt N)))))
5.0ms
(log (sqrt (/ (+ 1 N) N)))
1.0ms
(cbrt N)
1.0ms
(cbrt N)

series892.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
293.0ms
(+ (log (sqrt (/ (sqrt (+ 1 N)) (* (cbrt N) (cbrt N))))) (log (sqrt (/ (sqrt (+ 1 N)) (cbrt N)))))
286.0ms
(cbrt N)
232.0ms
(cbrt N)
81.0ms
(log (sqrt (/ (+ 1 N) N)))

simplify4.0s

Counts
116 → 165
Calls
116 calls:
Slowest
307.0ms
(- (+ (log (pow (/ 1 N) 1/12)) (+ (* 1/2 (/ 1 N)) (log (pow N 1/12)))) (* 1/4 (/ 1 (pow N 2))))
280.0ms
(- (+ (* 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))))
277.0ms
(- (+ (* 1/2 N) (+ (log (pow (/ 1 N) 1/3)) (log (pow (/ 1 N) 1/6)))) (* 1/4 (pow N 2)))
247.0ms
(- (+ (* 1/6 (/ 1 (pow N 3))) (* 1/2 (/ 1 N))) (* 1/4 (/ 1 (pow N 2))))
232.0ms
(+ (log (/ (sqrt (+ 1 N)) (* (cbrt N) (cbrt N)))) (log (/ (sqrt (+ 1 N)) (cbrt N))))

prune2.9s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

100% (0.0b remaining)

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

bsearch59.0ms

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s1725×body1280valid
540.0ms7928×body80nan
497.0ms1284×body640valid
433.0ms4030×body80valid
154.0ms626×body320valid
65.0ms335×body160valid