
(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 11 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 (/ v (- 1.0 m))) -1.0)))
double code(double m, double v) {
return (1.0 - m) * ((m / (v / (1.0 - m))) + -1.0);
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
code = (1.0d0 - m) * ((m / (v / (1.0d0 - m))) + (-1.0d0))
end function
public static double code(double m, double v) {
return (1.0 - m) * ((m / (v / (1.0 - m))) + -1.0);
}
def code(m, v): return (1.0 - m) * ((m / (v / (1.0 - m))) + -1.0)
function code(m, v) return Float64(Float64(1.0 - m) * Float64(Float64(m / Float64(v / Float64(1.0 - m))) + -1.0)) end
function tmp = code(m, v) tmp = (1.0 - m) * ((m / (v / (1.0 - m))) + -1.0); end
code[m_, v_] := N[(N[(1.0 - m), $MachinePrecision] * N[(N[(m / N[(v / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(1 - m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} + -1\right)
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 2.8e-24) (+ -1.0 (/ m v)) (* m (* (- 1.0 m) (/ (- 1.0 m) v)))))
double code(double m, double v) {
double tmp;
if (m <= 2.8e-24) {
tmp = -1.0 + (m / v);
} else {
tmp = m * ((1.0 - m) * ((1.0 - 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 <= 2.8d-24) then
tmp = (-1.0d0) + (m / v)
else
tmp = m * ((1.0d0 - m) * ((1.0d0 - m) / v))
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 2.8e-24) {
tmp = -1.0 + (m / v);
} else {
tmp = m * ((1.0 - m) * ((1.0 - m) / v));
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 2.8e-24: tmp = -1.0 + (m / v) else: tmp = m * ((1.0 - m) * ((1.0 - m) / v)) return tmp
function code(m, v) tmp = 0.0 if (m <= 2.8e-24) tmp = Float64(-1.0 + Float64(m / v)); else tmp = Float64(m * Float64(Float64(1.0 - m) * Float64(Float64(1.0 - m) / v))); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 2.8e-24) tmp = -1.0 + (m / v); else tmp = m * ((1.0 - m) * ((1.0 - m) / v)); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 2.8e-24], N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision], N[(m * N[(N[(1.0 - m), $MachinePrecision] * N[(N[(1.0 - m), $MachinePrecision] / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 2.8 \cdot 10^{-24}:\\
\;\;\;\;-1 + \frac{m}{v}\\
\mathbf{else}:\\
\;\;\;\;m \cdot \left(\left(1 - m\right) \cdot \frac{1 - m}{v}\right)\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 4.2e-25) (+ -1.0 (/ m v)) (* (- 1.0 m) (* (- 1.0 m) (/ m v)))))
double code(double m, double v) {
double tmp;
if (m <= 4.2e-25) {
tmp = -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 <= 4.2d-25) then
tmp = (-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 <= 4.2e-25) {
tmp = -1.0 + (m / v);
} else {
tmp = (1.0 - m) * ((1.0 - m) * (m / v));
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 4.2e-25: tmp = -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 <= 4.2e-25) tmp = Float64(-1.0 + Float64(m / v)); else tmp = Float64(Float64(1.0 - m) * Float64(Float64(1.0 - m) * Float64(m / v))); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 4.2e-25) tmp = -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, 4.2e-25], N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] * N[(N[(1.0 - m), $MachinePrecision] * N[(m / v), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 4.2 \cdot 10^{-25}:\\
\;\;\;\;-1 + \frac{m}{v}\\
\mathbf{else}:\\
\;\;\;\;\left(1 - m\right) \cdot \left(\left(1 - m\right) \cdot \frac{m}{v}\right)\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 2.7e-21) (+ -1.0 (/ m v)) (/ (- 1.0 m) (/ (/ v m) (- 1.0 m)))))
double code(double m, double v) {
double tmp;
if (m <= 2.7e-21) {
tmp = -1.0 + (m / v);
} else {
tmp = (1.0 - m) / ((v / m) / (1.0 - m));
}
return tmp;
}
real(8) function code(m, v)
real(8), intent (in) :: m
real(8), intent (in) :: v
real(8) :: tmp
if (m <= 2.7d-21) then
tmp = (-1.0d0) + (m / v)
else
tmp = (1.0d0 - m) / ((v / m) / (1.0d0 - m))
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 2.7e-21) {
tmp = -1.0 + (m / v);
} else {
tmp = (1.0 - m) / ((v / m) / (1.0 - m));
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 2.7e-21: tmp = -1.0 + (m / v) else: tmp = (1.0 - m) / ((v / m) / (1.0 - m)) return tmp
function code(m, v) tmp = 0.0 if (m <= 2.7e-21) tmp = Float64(-1.0 + Float64(m / v)); else tmp = Float64(Float64(1.0 - m) / Float64(Float64(v / m) / Float64(1.0 - m))); end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 2.7e-21) tmp = -1.0 + (m / v); else tmp = (1.0 - m) / ((v / m) / (1.0 - m)); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 2.7e-21], N[(-1.0 + N[(m / v), $MachinePrecision]), $MachinePrecision], N[(N[(1.0 - m), $MachinePrecision] / N[(N[(v / m), $MachinePrecision] / N[(1.0 - m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 2.7 \cdot 10^{-21}:\\
\;\;\;\;-1 + \frac{m}{v}\\
\mathbf{else}:\\
\;\;\;\;\frac{1 - m}{\frac{\frac{v}{m}}{1 - m}}\\
\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 (if (<= m 2.4e-197) -1.0 (if (<= m 3.2e-137) (/ m v) (if (<= m 4.5e-106) -1.0 (+ m (/ m v))))))
double code(double m, double v) {
double tmp;
if (m <= 2.4e-197) {
tmp = -1.0;
} else if (m <= 3.2e-137) {
tmp = m / v;
} else if (m <= 4.5e-106) {
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 <= 2.4d-197) then
tmp = -1.0d0
else if (m <= 3.2d-137) then
tmp = m / v
else if (m <= 4.5d-106) 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 <= 2.4e-197) {
tmp = -1.0;
} else if (m <= 3.2e-137) {
tmp = m / v;
} else if (m <= 4.5e-106) {
tmp = -1.0;
} else {
tmp = m + (m / v);
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 2.4e-197: tmp = -1.0 elif m <= 3.2e-137: tmp = m / v elif m <= 4.5e-106: tmp = -1.0 else: tmp = m + (m / v) return tmp
function code(m, v) tmp = 0.0 if (m <= 2.4e-197) tmp = -1.0; elseif (m <= 3.2e-137) tmp = Float64(m / v); elseif (m <= 4.5e-106) 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 <= 2.4e-197) tmp = -1.0; elseif (m <= 3.2e-137) tmp = m / v; elseif (m <= 4.5e-106) tmp = -1.0; else tmp = m + (m / v); end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 2.4e-197], -1.0, If[LessEqual[m, 3.2e-137], N[(m / v), $MachinePrecision], If[LessEqual[m, 4.5e-106], -1.0, N[(m + N[(m / v), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 2.4 \cdot 10^{-197}:\\
\;\;\;\;-1\\
\mathbf{elif}\;m \leq 3.2 \cdot 10^{-137}:\\
\;\;\;\;\frac{m}{v}\\
\mathbf{elif}\;m \leq 4.5 \cdot 10^{-106}:\\
\;\;\;\;-1\\
\mathbf{else}:\\
\;\;\;\;m + \frac{m}{v}\\
\end{array}
\end{array}
(FPCore (m v) :precision binary64 (if (<= m 3.5e-198) -1.0 (if (or (<= m 7e-137) (not (<= m 4.5e-106))) (/ m v) -1.0)))
double code(double m, double v) {
double tmp;
if (m <= 3.5e-198) {
tmp = -1.0;
} else if ((m <= 7e-137) || !(m <= 4.5e-106)) {
tmp = m / v;
} else {
tmp = -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 <= 3.5d-198) then
tmp = -1.0d0
else if ((m <= 7d-137) .or. (.not. (m <= 4.5d-106))) then
tmp = m / v
else
tmp = -1.0d0
end if
code = tmp
end function
public static double code(double m, double v) {
double tmp;
if (m <= 3.5e-198) {
tmp = -1.0;
} else if ((m <= 7e-137) || !(m <= 4.5e-106)) {
tmp = m / v;
} else {
tmp = -1.0;
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 3.5e-198: tmp = -1.0 elif (m <= 7e-137) or not (m <= 4.5e-106): tmp = m / v else: tmp = -1.0 return tmp
function code(m, v) tmp = 0.0 if (m <= 3.5e-198) tmp = -1.0; elseif ((m <= 7e-137) || !(m <= 4.5e-106)) tmp = Float64(m / v); else tmp = -1.0; end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 3.5e-198) tmp = -1.0; elseif ((m <= 7e-137) || ~((m <= 4.5e-106))) tmp = m / v; else tmp = -1.0; end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 3.5e-198], -1.0, If[Or[LessEqual[m, 7e-137], N[Not[LessEqual[m, 4.5e-106]], $MachinePrecision]], N[(m / v), $MachinePrecision], -1.0]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 3.5 \cdot 10^{-198}:\\
\;\;\;\;-1\\
\mathbf{elif}\;m \leq 7 \cdot 10^{-137} \lor \neg \left(m \leq 4.5 \cdot 10^{-106}\right):\\
\;\;\;\;\frac{m}{v}\\
\mathbf{else}:\\
\;\;\;\;-1\\
\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 1.25e-25) -1.0 m))
double code(double m, double v) {
double tmp;
if (m <= 1.25e-25) {
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 <= 1.25d-25) 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 <= 1.25e-25) {
tmp = -1.0;
} else {
tmp = m;
}
return tmp;
}
def code(m, v): tmp = 0 if m <= 1.25e-25: tmp = -1.0 else: tmp = m return tmp
function code(m, v) tmp = 0.0 if (m <= 1.25e-25) tmp = -1.0; else tmp = m; end return tmp end
function tmp_2 = code(m, v) tmp = 0.0; if (m <= 1.25e-25) tmp = -1.0; else tmp = m; end tmp_2 = tmp; end
code[m_, v_] := If[LessEqual[m, 1.25e-25], -1.0, m]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;m \leq 1.25 \cdot 10^{-25}:\\
\;\;\;\;-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 2024008
(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)))