
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
double code(double m, double v) {
return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (((m * (1.0d0 - m)) / v) - 1.0d0) * (1.0d0 - m)
end function
public static double code(double m, double v) {
return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
def code(m, v): return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m)
function code(m, v) return Float64(Float64(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * Float64(1.0 - m)) end
function tmp = code(m, v) tmp = (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m); end
code[m_, v_] := N[(N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 13 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (m v) :precision binary64 (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))
double code(double m, double v) {
return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (((m * (1.0d0 - m)) / v) - 1.0d0) * (1.0d0 - m)
end function
public static double code(double m, double v) {
return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m);
}
def code(m, v): return (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m)
function code(m, v) return Float64(Float64(Float64(Float64(m * Float64(1.0 - m)) / v) - 1.0) * Float64(1.0 - m)) end
function tmp = code(m, v) tmp = (((m * (1.0 - m)) / v) - 1.0) * (1.0 - m); end
code[m_, v_] := N[(N[(N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / v), $MachinePrecision] - 1.0), $MachinePrecision] * N[(1.0 - m), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
\end{array}
(FPCore (m v) :precision binary64 (* (- 1.0 m) (+ (/ m (* (/ 1.0 (- 1.0 m)) v)) -1.0)))
double code(double m, double v) {
return (1.0 - m) * ((m / ((1.0 / (1.0 - m)) * v)) + -1.0);
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (1.0d0 - m) * ((m / ((1.0d0 / (1.0d0 - m)) * v)) + (-1.0d0))
end function
public static double code(double m, double v) {
return (1.0 - m) * ((m / ((1.0 / (1.0 - m)) * v)) + -1.0);
}
def code(m, v): return (1.0 - m) * ((m / ((1.0 / (1.0 - m)) * v)) + -1.0)
function code(m, v) return Float64(Float64(1.0 - m) * Float64(Float64(m / Float64(Float64(1.0 / Float64(1.0 - m)) * v)) + -1.0)) end
function tmp = code(m, v) tmp = (1.0 - m) * ((m / ((1.0 / (1.0 - m)) * v)) + -1.0); end
code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(N[(m / N[(N[(1.0 / N[(1.0 - m), $MachinePrecision]), $MachinePrecision] * v), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(1 - m\right) \cdot \left(\frac{m}{\frac{1}{1 - m} \cdot v} + -1\right)
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 1.0) (* (- 1.0 m) (+ -1.0 (/ m v))) (/ (* m (- 1.0 m)) (- v (* m v)))))
double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = (m * (1.0 - m)) / (v - (m * v));
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 1.0d0) then
tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
else
tmp = (m * (1.0d0 - m)) / (v - (m * v))
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = (m * (1.0 - m)) / (v - (m * v));
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.0: tmp = (1.0 - m) * (-1.0 + (m / v)) else: tmp = (m * (1.0 - m)) / (v - (m * v)) return tmp
function code(m, v) tmp = 0.0 if (m <= 1.0) tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v))); else tmp = Float64(Float64(m * Float64(1.0 - m)) / Float64(v - Float64(m * v))); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.0) tmp = (1.0 - m) * (-1.0 + (m / v)); else tmp = (m * (1.0 - m)) / (v - (m * v)); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(m * N[(1.0 - m), $MachinePrecision]), $MachinePrecision] / N[(v - N[(m * v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1:\\
\;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{m \cdot \left(1 - m\right)}{v - m \cdot v}\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 1.0) (* (- 1.0 m) (+ -1.0 (/ m v))) (/ (* (/ m v) (+ m -1.0)) (+ m -1.0))))
double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = ((m / v) * (m + -1.0)) / (m + -1.0);
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 1.0d0) then
tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
else
tmp = ((m / v) * (m + (-1.0d0))) / (m + (-1.0d0))
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = ((m / v) * (m + -1.0)) / (m + -1.0);
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.0: tmp = (1.0 - m) * (-1.0 + (m / v)) else: tmp = ((m / v) * (m + -1.0)) / (m + -1.0) return tmp
function code(m, v) tmp = 0.0 if (m <= 1.0) tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v))); else tmp = Float64(Float64(Float64(m / v) * Float64(m + -1.0)) / Float64(m + -1.0)); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.0) tmp = (1.0 - m) * (-1.0 + (m / v)); else tmp = ((m / v) * (m + -1.0)) / (m + -1.0); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(m / v), $MachinePrecision] * N[(m + -1.0), $MachinePrecision]), $MachinePrecision] / N[(m + -1.0), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1:\\
\;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\
\mathbf{else}:\\
\;\;\;\;\frac{\frac{m}{v} \cdot \left(m + -1\right)}{m + -1}\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 1.0) (* (- 1.0 m) (+ -1.0 (/ m v))) (* (- 1.0 m) (- -1.0 (* m (/ m v))))))
double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = (1.0 - m) * (-1.0 - (m * (m / v)));
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 1.0d0) then
tmp = (1.0d0 - m) * ((-1.0d0) + (m / v))
else
tmp = (1.0d0 - m) * ((-1.0d0) - (m * (m / v)))
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 1.0) {
tmp = (1.0 - m) * (-1.0 + (m / v));
} else {
tmp = (1.0 - m) * (-1.0 - (m * (m / v)));
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.0: tmp = (1.0 - m) * (-1.0 + (m / v)) else: tmp = (1.0 - m) * (-1.0 - (m * (m / v))) return tmp
function code(m, v) tmp = 0.0 if (m <= 1.0) tmp = Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / v))); else tmp = Float64(Float64(1.0 - m) * Float64(-1.0 - Float64(m * Float64(m / v)))); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.0) tmp = (1.0 - m) * (-1.0 + (m / v)); else tmp = (1.0 - m) * (-1.0 - (m * (m / v))); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.0], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 - N[(m * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1:\\
\;\;\;\;\left(1 - m\right) \cdot \left(-1 + \frac{m}{v}\right)\\
\mathbf{else}:\\
\;\;\;\;\left(1 - m\right) \cdot \left(-1 - m \cdot \frac{m}{v}\right)\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (* (- 1.0 m) (+ -1.0 (* (- 1.0 m) (/ m v)))))
double code(double m, double v) {
return (1.0 - m) * (-1.0 + ((1.0 - m) * (m / v)));
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (1.0d0 - m) * ((-1.0d0) + ((1.0d0 - m) * (m / v)))
end function
public static double code(double m, double v) {
return (1.0 - m) * (-1.0 + ((1.0 - m) * (m / v)));
}
def code(m, v): return (1.0 - m) * (-1.0 + ((1.0 - m) * (m / v)))
function code(m, v) return Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(Float64(1.0 - m) * Float64(m / v)))) end
function tmp = code(m, v) tmp = (1.0 - m) * (-1.0 + ((1.0 - m) * (m / v))); end
code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(1 - m\right) \cdot \left(-1 + \left(1 - m\right) \cdot \frac{m}{v}\right)
\end{array}
(FPCore (m v) :precision binary64 (* (- 1.0 m) (+ -1.0 (/ m (/ v (- 1.0 m))))))
double code(double m, double v) {
return (1.0 - m) * (-1.0 + (m / (v / (1.0 - m))));
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (1.0d0 - m) * ((-1.0d0) + (m / (v / (1.0d0 - m))))
end function
public static double code(double m, double v) {
return (1.0 - m) * (-1.0 + (m / (v / (1.0 - m))));
}
def code(m, v): return (1.0 - m) * (-1.0 + (m / (v / (1.0 - m))))
function code(m, v) return Float64(Float64(1.0 - m) * Float64(-1.0 + Float64(m / Float64(v / Float64(1.0 - m))))) end
function tmp = code(m, v) tmp = (1.0 - m) * (-1.0 + (m / (v / (1.0 - m)))); end
code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(-1.0 + N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(1 - m\right) \cdot \left(-1 + \frac{m}{\frac{v}{1 - m}}\right)
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 9e-113) -1.0 (+ m (/ m v))))
double code(double m, double v) {
double tmp;
if (m <= 9e-113) {
tmp = -1.0;
} else {
tmp = m + (m / v);
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 9d-113) then
tmp = -1.0d0
else
tmp = m + (m / v)
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 9e-113) {
tmp = -1.0;
} else {
tmp = m + (m / v);
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 9e-113: tmp = -1.0 else: tmp = m + (m / v) return tmp
function code(m, v) tmp = 0.0 if (m <= 9e-113) tmp = -1.0; else tmp = Float64(m + Float64(m / v)); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 9e-113) tmp = -1.0; else tmp = m + (m / v); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 9e-113], -1.0, N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 9 \cdot 10^{-113}:\\
\;\;\;\;-1\\
\mathbf{else}:\\
\;\;\;\;m + \frac{m}{v}\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (+ -1.0 (+ m (/ m v))))
double code(double m, double v) {
return -1.0 + (m + (m / v));
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (-1.0d0) + (m + (m / v))
end function
public static double code(double m, double v) {
return -1.0 + (m + (m / v));
}
def code(m, v): return -1.0 + (m + (m / v))
function code(m, v) return Float64(-1.0 + Float64(m + Float64(m / v))) end
function tmp = code(m, v) tmp = -1.0 + (m + (m / v)); end
code[m_, v_] := N[(-1.0 + N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
-1 + \left(m + \frac{m}{v}\right)
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 1.05e-113) -1.0 (/ m v)))
double code(double m, double v) {
double tmp;
if (m <= 1.05e-113) {
tmp = -1.0;
} else {
tmp = m / v;
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 1.05d-113) then
tmp = -1.0d0
else
tmp = m / v
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 1.05e-113) {
tmp = -1.0;
} else {
tmp = m / v;
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.05e-113: tmp = -1.0 else: tmp = m / v return tmp
function code(m, v) tmp = 0.0 if (m <= 1.05e-113) tmp = -1.0; else tmp = Float64(m / v); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.05e-113) tmp = -1.0; else tmp = m / v; end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.05e-113], -1.0, N[(m / v), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1.05 \cdot 10^{-113}:\\
\;\;\;\;-1\\
\mathbf{else}:\\
\;\;\;\;\frac{m}{v}\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (+ -1.0 (/ m v)))
double code(double m, double v) {
return -1.0 + (m / v);
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (-1.0d0) + (m / v)
end function
public static double code(double m, double v) {
return -1.0 + (m / v);
}
def code(m, v): return -1.0 + (m / v)
function code(m, v) return Float64(-1.0 + Float64(m / v)) end
function tmp = code(m, v) tmp = -1.0 + (m / v); end
code[m_, v_] := N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
-1 + \frac{m}{v}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 1.8e-41) -1.0 m))
double code(double m, double v) {
double tmp;
if (m <= 1.8e-41) {
tmp = -1.0;
} else {
tmp = m;
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 1.8d-41) then
tmp = -1.0d0
else
tmp = m
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 1.8e-41) {
tmp = -1.0;
} else {
tmp = m;
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.8e-41: tmp = -1.0 else: tmp = m return tmp
function code(m, v) tmp = 0.0 if (m <= 1.8e-41) tmp = -1.0; else tmp = m; end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.8e-41) tmp = -1.0; else tmp = m; end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.8e-41], -1.0, m]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1.8 \cdot 10^{-41}:\\
\;\;\;\;-1\\
\mathbf{else}:\\
\;\;\;\;m\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (+ m -1.0))
double code(double m, double v) {
return m + -1.0;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = m + (-1.0d0)
end function
public static double code(double m, double v) {
return m + -1.0;
}
def code(m, v): return m + -1.0
function code(m, v) return Float64(m + -1.0) end
function tmp = code(m, v) tmp = m + -1.0; end
code[m_, v_] := N[(m + -1.0), $MachinePrecision]
\begin{array}{l}
\\
m + -1
\end{array}
(FPCore (m v) :precision binary64 -1.0)
double code(double m, double v) {
return -1.0;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = -1.0d0
end function
public static double code(double m, double v) {
return -1.0;
}
def code(m, v): return -1.0
function code(m, v) return -1.0 end
function tmp = code(m, v) tmp = -1.0; end
code[m_, v_] := -1.0
\begin{array}{l}
\\
-1
\end{array}
herbie shell --seed 2024006
(FPCore (m v)
:name "b parameter of renormalized beta distribution"
:precision binary64
:pre (and (and (< 0.0 m) (< 0.0 v)) (< v 0.25))
(* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))