Details

Time bar (total: 31.3s)

sample87.0ms

Algorithm
intervals
Results
28.0ms54×body1280valid
14.0ms137×body80valid
13.0ms36×body640valid
13.0ms209×body80nan
5.0ms18×body320valid
2.0ms11×body160valid

simplify11.0ms

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

prune29.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.1b

localize14.0ms

Local error

Found 1 expressions with local error:

3.0b
(- (log1p N) (log N))

rewrite6.0ms

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
6.0ms
(- (log1p N) (log N))

series62.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
62.0ms
(- (log1p N) (log N))

simplify3.0s

Counts
55 → 40
Calls
55 calls:
Slowest
441.0ms
(* (* (- (log1p N) (log N)) (- (log1p N) (log N))) (- (log1p N) (log N)))
249.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
228.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
160.0ms
(fma 1 (log1p N) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))
160.0ms
(fma (* (cbrt (log1p N)) (cbrt (log1p N))) (cbrt (log1p N)) (- (* (cbrt (log N)) (* (cbrt (log N)) (cbrt (log N))))))

prune285.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 2 expressions with local error:

3.1b
(log (/ (+ 1 N) N))
0.0b
(/ (+ 1 N) N)

rewrite22.0ms

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

series109.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
57.0ms
(/ (+ 1 N) N)
52.0ms
(log (/ (+ 1 N) N))

simplify4.0s

Counts
100 → 72
Calls
100 calls:
Slowest
553.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
384.0ms
(* (* (/ (+ 1 N) N) (/ (+ 1 N) N)) (/ (+ 1 N) N))
353.0ms
(/ (* (* (+ 1 N) (+ 1 N)) (+ 1 N)) (* (* N N) N))
231.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))
217.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 1 (pow N 2))))

prune475.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

3.1b
(log (/ (+ 1 N) N))
3.1b
(log (/ (+ 1 N) N))
0.3b
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
0.1b
(sqrt (log (/ (+ 1 N) N)))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
43×*-un-lft-identity
42×add-sqr-sqrt
32×log-prod
30×sqrt-prod
29×pow1 add-cube-cbrt
24×times-frac
12×add-exp-log
11×swap-sqr
9×sqrt-pow1 pow1/2 log-pow
7×associate-*r* associate-*l*
6×add-cbrt-cube distribute-lft-out
5×pow-prod-up
4×expm1-log1p-u rem-log-exp insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×log-div div-exp div-inv
1×pow2 rem-sqrt-square rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 134
Calls
4 calls:
Slowest
14.0ms
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
7.0ms
(log (/ (+ 1 N) N))
7.0ms
(log (/ (+ 1 N) N))
6.0ms
(sqrt (log (/ (+ 1 N) N)))

series241.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
72.0ms
(log (/ (+ 1 N) N))
64.0ms
(sqrt (log (/ (+ 1 N) N)))
54.0ms
(* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N))))
51.0ms
(log (/ (+ 1 N) N))

simplify8.7s

Counts
190 → 146
Calls
190 calls:
Slowest
433.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
418.0ms
(- (+ (* 1/2 (/ N (sqrt (- (log N))))) (sqrt (- (log N)))) (+ (* 1/8 (/ (pow N 2) (pow (sqrt (- (log N))) 3))) (* 1/4 (/ (pow N 2) (sqrt (- (log N)))))))
379.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
299.0ms
(* (* (* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N)))) (sqrt (log (/ (+ 1 N) N)))) (* (* (sqrt (log (/ (+ 1 N) N))) (sqrt (log (/ (+ 1 N) N)))) (sqrt (log (/ (+ 1 N) N)))))
259.0ms
(- (+ (* 1/3 (/ 1 (pow N 3))) (/ 1 N)) (* 1/2 (/ 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:

3.1b
(log (/ (+ 1 N) N))
3.1b
(log (/ (+ 1 N) N))
0.8b
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
0.1b
(sqrt (log (/ (+ 1 N) N)))

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
37×log-pow
32×pow1 log-prod
27×add-sqr-sqrt
26×add-cube-cbrt
25×exp-prod
24×times-frac
18×distribute-rgt-out
14×distribute-lft-out
11×sqrt-pow1 pow1/2
10×add-exp-log
8×exp-to-pow
5×add-log-exp
4×expm1-log1p-u add-cbrt-cube rem-log-exp sqrt-prod insert-posit16 log1p-expm1-u
2×log-div distribute-lft1-in div-exp distribute-rgt1-in div-inv rem-exp-log
1×rem-sqrt-square sum-log exp-sum
Counts
4 → 123
Calls
4 calls:
Slowest
29.0ms
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
7.0ms
(sqrt (log (/ (+ 1 N) N)))
4.0ms
(log (/ (+ 1 N) N))
4.0ms
(log (/ (+ 1 N) N))

series319.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
101.0ms
(exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))
90.0ms
(sqrt (log (/ (+ 1 N) N)))
68.0ms
(log (/ (+ 1 N) N))
61.0ms
(log (/ (+ 1 N) N))

simplify7.7s

Counts
158 → 135
Calls
158 calls:
Slowest
496.0ms
(- (+ (* 1/2 (/ N (sqrt (- (log N))))) (sqrt (- (log N)))) (+ (* 1/8 (/ (pow N 2) (pow (sqrt (- (log N))) 3))) (* 1/4 (/ (pow N 2) (sqrt (- (log N)))))))
457.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
442.0ms
(* (* (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N)))))) (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N))))))) (exp (+ (log (sqrt (log (/ (+ 1 N) N)))) (log (sqrt (log (/ (+ 1 N) N)))))))
440.0ms
(* (* (log (/ (+ 1 N) N)) (log (/ (+ 1 N) N))) (log (/ (+ 1 N) N)))
366.0ms
(- (+ (pow (sqrt (- (log N))) 2) N) (* 1/2 (pow N 2)))

prune1.8s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes27.0ms

Accuracy

100% (0.0b remaining)

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

bsearch42.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
971.0ms1684×body1280valid
617.0ms7809×body80nan
513.0ms1275×body640valid
448.0ms4113×body80valid
157.0ms619×body320valid
49.0ms309×body160valid