?

Average Error: 0.3 → 0.3
Time: 6.1s
Precision: binary64
Cost: 6656

?

\[\left(0 \leq scale \land scale \leq 100\right) \land \left(0 \leq \alpha \land \alpha \leq 1\right)\]
\[\frac{scale}{\log \left(\frac{1}{\alpha}\right)} \]
\[\frac{scale}{-\log \alpha} \]
(FPCore (scale alpha) :precision binary64 (/ scale (log (/ 1.0 alpha))))
(FPCore (scale alpha) :precision binary64 (/ scale (- (log alpha))))
double code(double scale, double alpha) {
	return scale / log((1.0 / alpha));
}
double code(double scale, double alpha) {
	return scale / -log(alpha);
}
real(8) function code(scale, alpha)
    real(8), intent (in) :: scale
    real(8), intent (in) :: alpha
    code = scale / log((1.0d0 / alpha))
end function
real(8) function code(scale, alpha)
    real(8), intent (in) :: scale
    real(8), intent (in) :: alpha
    code = scale / -log(alpha)
end function
public static double code(double scale, double alpha) {
	return scale / Math.log((1.0 / alpha));
}
public static double code(double scale, double alpha) {
	return scale / -Math.log(alpha);
}
def code(scale, alpha):
	return scale / math.log((1.0 / alpha))
def code(scale, alpha):
	return scale / -math.log(alpha)
function code(scale, alpha)
	return Float64(scale / log(Float64(1.0 / alpha)))
end
function code(scale, alpha)
	return Float64(scale / Float64(-log(alpha)))
end
function tmp = code(scale, alpha)
	tmp = scale / log((1.0 / alpha));
end
function tmp = code(scale, alpha)
	tmp = scale / -log(alpha);
end
code[scale_, alpha_] := N[(scale / N[Log[N[(1.0 / alpha), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
code[scale_, alpha_] := N[(scale / (-N[Log[alpha], $MachinePrecision])), $MachinePrecision]
\frac{scale}{\log \left(\frac{1}{\alpha}\right)}
\frac{scale}{-\log \alpha}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 0.3

    \[\frac{scale}{\log \left(\frac{1}{\alpha}\right)} \]
  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{scale}{-\log \alpha}} \]
    Proof

    [Start]0.3

    \[ \frac{scale}{\log \left(\frac{1}{\alpha}\right)} \]

    log-rec [=>]0.3

    \[ \frac{scale}{\color{blue}{-\log \alpha}} \]
  3. Final simplification0.3

    \[\leadsto \frac{scale}{-\log \alpha} \]

Alternatives

Alternative 1
Error61.4
Cost6592
\[\frac{scale}{\log \alpha} \]

Error

Reproduce?

herbie shell --seed 1 
(FPCore (scale alpha)
  :name "scale / log(1 / alpha)"
  :precision binary64
  :pre (and (and (<= 0.0 scale) (<= scale 100.0)) (and (<= 0.0 alpha) (<= alpha 1.0)))
  (/ scale (log (/ 1.0 alpha))))