(FPCore (N) :precision binary64 (- (log (+ N 1.0)) (log N)))
(FPCore (N)
:precision binary64
(if (<= (- (log (+ N 1.0)) (log N)) 5e-5)
(+
(/ 1.0 N)
(+ (/ -0.5 (* N N)) (/ (/ (+ (/ -0.25 N) 0.3333333333333333) (* N N)) N)))
(log (/ (+ N 1.0) N))))double code(double N) {
return log((N + 1.0)) - log(N);
}
double code(double N) {
double tmp;
if ((log((N + 1.0)) - log(N)) <= 5e-5) {
tmp = (1.0 / N) + ((-0.5 / (N * N)) + ((((-0.25 / N) + 0.3333333333333333) / (N * N)) / N));
} else {
tmp = log(((N + 1.0) / N));
}
return tmp;
}
real(8) function code(n)
real(8), intent (in) :: n
code = log((n + 1.0d0)) - log(n)
end function
real(8) function code(n)
real(8), intent (in) :: n
real(8) :: tmp
if ((log((n + 1.0d0)) - log(n)) <= 5d-5) then
tmp = (1.0d0 / n) + (((-0.5d0) / (n * n)) + (((((-0.25d0) / n) + 0.3333333333333333d0) / (n * n)) / n))
else
tmp = log(((n + 1.0d0) / n))
end if
code = tmp
end function
public static double code(double N) {
return Math.log((N + 1.0)) - Math.log(N);
}
public static double code(double N) {
double tmp;
if ((Math.log((N + 1.0)) - Math.log(N)) <= 5e-5) {
tmp = (1.0 / N) + ((-0.5 / (N * N)) + ((((-0.25 / N) + 0.3333333333333333) / (N * N)) / N));
} else {
tmp = Math.log(((N + 1.0) / N));
}
return tmp;
}
def code(N): return math.log((N + 1.0)) - math.log(N)
def code(N): tmp = 0 if (math.log((N + 1.0)) - math.log(N)) <= 5e-5: tmp = (1.0 / N) + ((-0.5 / (N * N)) + ((((-0.25 / N) + 0.3333333333333333) / (N * N)) / N)) else: tmp = math.log(((N + 1.0) / N)) return tmp
function code(N) return Float64(log(Float64(N + 1.0)) - log(N)) end
function code(N) tmp = 0.0 if (Float64(log(Float64(N + 1.0)) - log(N)) <= 5e-5) tmp = Float64(Float64(1.0 / N) + Float64(Float64(-0.5 / Float64(N * N)) + Float64(Float64(Float64(Float64(-0.25 / N) + 0.3333333333333333) / Float64(N * N)) / N))); else tmp = log(Float64(Float64(N + 1.0) / N)); end return tmp end
function tmp = code(N) tmp = log((N + 1.0)) - log(N); end
function tmp_2 = code(N) tmp = 0.0; if ((log((N + 1.0)) - log(N)) <= 5e-5) tmp = (1.0 / N) + ((-0.5 / (N * N)) + ((((-0.25 / N) + 0.3333333333333333) / (N * N)) / N)); else tmp = log(((N + 1.0) / N)); end tmp_2 = tmp; end
code[N_] := N[(N[Log[N[(N + 1.0), $MachinePrecision]], $MachinePrecision] - N[Log[N], $MachinePrecision]), $MachinePrecision]
code[N_] := If[LessEqual[N[(N[Log[N[(N + 1.0), $MachinePrecision]], $MachinePrecision] - N[Log[N], $MachinePrecision]), $MachinePrecision], 5e-5], N[(N[(1.0 / N), $MachinePrecision] + N[(N[(-0.5 / N[(N * N), $MachinePrecision]), $MachinePrecision] + N[(N[(N[(N[(-0.25 / N), $MachinePrecision] + 0.3333333333333333), $MachinePrecision] / N[(N * N), $MachinePrecision]), $MachinePrecision] / N), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[Log[N[(N[(N + 1.0), $MachinePrecision] / N), $MachinePrecision]], $MachinePrecision]]
\log \left(N + 1\right) - \log N
\begin{array}{l}
\mathbf{if}\;\log \left(N + 1\right) - \log N \leq 5 \cdot 10^{-5}:\\
\;\;\;\;\frac{1}{N} + \left(\frac{-0.5}{N \cdot N} + \frac{\frac{\frac{-0.25}{N} + 0.3333333333333333}{N \cdot N}}{N}\right)\\
\mathbf{else}:\\
\;\;\;\;\log \left(\frac{N + 1}{N}\right)\\
\end{array}
Results
if (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) < 5.00000000000000024e-5Initial program 59.5
Simplified59.5
Taylor expanded in N around inf 0.0
Simplified0.0
Applied egg-rr0.0
if 5.00000000000000024e-5 < (-.f64 (log.f64 (+.f64 N 1)) (log.f64 N)) Initial program 0.1
Simplified0.1
Applied egg-rr0.1
Final simplification0.1
| Alternative 1 | |
|---|---|
| Error | 0.5 |
| Cost | 6724 |
| Alternative 2 | |
|---|---|
| Error | 0.7 |
| Cost | 6660 |
| Alternative 3 | |
|---|---|
| Error | 31.0 |
| Cost | 192 |
| Alternative 4 | |
|---|---|
| Error | 61.1 |
| Cost | 64 |
herbie shell --seed 2022318
(FPCore (N)
:name "2log (problem 3.3.6)"
:precision binary64
(- (log (+ N 1.0)) (log N)))