
(FPCore (x y z t) :precision binary64 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))
double code(double x, double y, double z, double t) {
return x - (log(((1.0 - y) + (y * exp(z)))) / t);
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x - (log(((1.0d0 - y) + (y * exp(z)))) / t)
end function
public static double code(double x, double y, double z, double t) {
return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}
def code(x, y, z, t): return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)
function code(x, y, z, t) return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t)) end
function tmp = code(x, y, z, t) tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t); end
code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 9 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t) :precision binary64 (- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))
double code(double x, double y, double z, double t) {
return x - (log(((1.0 - y) + (y * exp(z)))) / t);
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x - (log(((1.0d0 - y) + (y * exp(z)))) / t)
end function
public static double code(double x, double y, double z, double t) {
return x - (Math.log(((1.0 - y) + (y * Math.exp(z)))) / t);
}
def code(x, y, z, t): return x - (math.log(((1.0 - y) + (y * math.exp(z)))) / t)
function code(x, y, z, t) return Float64(x - Float64(log(Float64(Float64(1.0 - y) + Float64(y * exp(z)))) / t)) end
function tmp = code(x, y, z, t) tmp = x - (log(((1.0 - y) + (y * exp(z)))) / t); end
code[x_, y_, z_, t_] := N[(x - N[(N[Log[N[(N[(1.0 - y), $MachinePrecision] + N[(y * N[Exp[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{\log \left(\left(1 - y\right) + y \cdot e^{z}\right)}{t}
\end{array}
(FPCore (x y z t) :precision binary64 (- x (/ (log1p (* y (expm1 z))) t)))
double code(double x, double y, double z, double t) {
return x - (log1p((y * expm1(z))) / t);
}
public static double code(double x, double y, double z, double t) {
return x - (Math.log1p((y * Math.expm1(z))) / t);
}
def code(x, y, z, t): return x - (math.log1p((y * math.expm1(z))) / t)
function code(x, y, z, t) return Float64(x - Float64(log1p(Float64(y * expm1(z))) / t)) end
code[x_, y_, z_, t_] := N[(x - N[(N[Log[1 + N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{\mathsf{log1p}\left(y \cdot \mathsf{expm1}\left(z\right)\right)}{t}
\end{array}
(FPCore (x y z t) :precision binary64 (- x (/ (/ 1.0 t) (+ 0.5 (/ 1.0 (* y (expm1 z)))))))
double code(double x, double y, double z, double t) {
return x - ((1.0 / t) / (0.5 + (1.0 / (y * expm1(z)))));
}
public static double code(double x, double y, double z, double t) {
return x - ((1.0 / t) / (0.5 + (1.0 / (y * Math.expm1(z)))));
}
def code(x, y, z, t): return x - ((1.0 / t) / (0.5 + (1.0 / (y * math.expm1(z)))))
function code(x, y, z, t) return Float64(x - Float64(Float64(1.0 / t) / Float64(0.5 + Float64(1.0 / Float64(y * expm1(z)))))) end
code[x_, y_, z_, t_] := N[(x - N[(N[(1.0 / t), $MachinePrecision] / N[(0.5 + N[(1.0 / N[(y * N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{\frac{1}{t}}{0.5 + \frac{1}{y \cdot \mathsf{expm1}\left(z\right)}}
\end{array}
(FPCore (x y z t)
:precision binary64
(if (<= y -6.5e+36)
(-
x
(/
y
(-
(+ (* t -0.5) (/ t z))
(* z (+ (* t -0.25) (* t 0.16666666666666666))))))
(- x (/ y (/ t (expm1 z))))))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= -6.5e+36) {
tmp = x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666)))));
} else {
tmp = x - (y / (t / expm1(z)));
}
return tmp;
}
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= -6.5e+36) {
tmp = x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666)))));
} else {
tmp = x - (y / (t / Math.expm1(z)));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= -6.5e+36: tmp = x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666))))) else: tmp = x - (y / (t / math.expm1(z))) return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= -6.5e+36) tmp = Float64(x - Float64(y / Float64(Float64(Float64(t * -0.5) + Float64(t / z)) - Float64(z * Float64(Float64(t * -0.25) + Float64(t * 0.16666666666666666)))))); else tmp = Float64(x - Float64(y / Float64(t / expm1(z)))); end return tmp end
code[x_, y_, z_, t_] := If[LessEqual[y, -6.5e+36], N[(x - N[(y / N[(N[(N[(t * -0.5), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * -0.25), $MachinePrecision] + N[(t * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(t / N[(Exp[z] - 1), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -6.5 \cdot 10^{+36}:\\
\;\;\;\;x - \frac{y}{\left(t \cdot -0.5 + \frac{t}{z}\right) - z \cdot \left(t \cdot -0.25 + t \cdot 0.16666666666666666\right)}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{t}{\mathsf{expm1}\left(z\right)}}\\
\end{array}
\end{array}
(FPCore (x y z t)
:precision binary64
(-
x
(/
y
(-
(+ (* t -0.5) (/ t z))
(* z (+ (* t -0.25) (* t 0.16666666666666666)))))))
double code(double x, double y, double z, double t) {
return x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666)))));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x - (y / (((t * (-0.5d0)) + (t / z)) - (z * ((t * (-0.25d0)) + (t * 0.16666666666666666d0)))))
end function
public static double code(double x, double y, double z, double t) {
return x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666)))));
}
def code(x, y, z, t): return x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666)))))
function code(x, y, z, t) return Float64(x - Float64(y / Float64(Float64(Float64(t * -0.5) + Float64(t / z)) - Float64(z * Float64(Float64(t * -0.25) + Float64(t * 0.16666666666666666)))))) end
function tmp = code(x, y, z, t) tmp = x - (y / (((t * -0.5) + (t / z)) - (z * ((t * -0.25) + (t * 0.16666666666666666))))); end
code[x_, y_, z_, t_] := N[(x - N[(y / N[(N[(N[(t * -0.5), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision] - N[(z * N[(N[(t * -0.25), $MachinePrecision] + N[(t * 0.16666666666666666), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{y}{\left(t \cdot -0.5 + \frac{t}{z}\right) - z \cdot \left(t \cdot -0.25 + t \cdot 0.16666666666666666\right)}
\end{array}
(FPCore (x y z t) :precision binary64 (- x (/ y (* t (- (+ (* z 0.08333333333333333) (/ 1.0 z)) 0.5)))))
double code(double x, double y, double z, double t) {
return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)));
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x - (y / (t * (((z * 0.08333333333333333d0) + (1.0d0 / z)) - 0.5d0)))
end function
public static double code(double x, double y, double z, double t) {
return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)));
}
def code(x, y, z, t): return x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5)))
function code(x, y, z, t) return Float64(x - Float64(y / Float64(t * Float64(Float64(Float64(z * 0.08333333333333333) + Float64(1.0 / z)) - 0.5)))) end
function tmp = code(x, y, z, t) tmp = x - (y / (t * (((z * 0.08333333333333333) + (1.0 / z)) - 0.5))); end
code[x_, y_, z_, t_] := N[(x - N[(y / N[(t * N[(N[(N[(z * 0.08333333333333333), $MachinePrecision] + N[(1.0 / z), $MachinePrecision]), $MachinePrecision] - 0.5), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \frac{y}{t \cdot \left(\left(z \cdot 0.08333333333333333 + \frac{1}{z}\right) - 0.5\right)}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= y -6.8e+204) x (- x (/ y (+ (* t -0.5) (/ t z))))))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= -6.8e+204) {
tmp = x;
} else {
tmp = x - (y / ((t * -0.5) + (t / z)));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (y <= (-6.8d+204)) then
tmp = x
else
tmp = x - (y / ((t * (-0.5d0)) + (t / z)))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= -6.8e+204) {
tmp = x;
} else {
tmp = x - (y / ((t * -0.5) + (t / z)));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= -6.8e+204: tmp = x else: tmp = x - (y / ((t * -0.5) + (t / z))) return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= -6.8e+204) tmp = x; else tmp = Float64(x - Float64(y / Float64(Float64(t * -0.5) + Float64(t / z)))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (y <= -6.8e+204) tmp = x; else tmp = x - (y / ((t * -0.5) + (t / z))); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[y, -6.8e+204], x, N[(x - N[(y / N[(N[(t * -0.5), $MachinePrecision] + N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -6.8 \cdot 10^{+204}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;x - \frac{y}{t \cdot -0.5 + \frac{t}{z}}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -6.8e+94) x (- x (* y (/ z t)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -6.8e+94) {
tmp = x;
} else {
tmp = x - (y * (z / t));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (z <= (-6.8d+94)) then
tmp = x
else
tmp = x - (y * (z / t))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -6.8e+94) {
tmp = x;
} else {
tmp = x - (y * (z / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -6.8e+94: tmp = x else: tmp = x - (y * (z / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -6.8e+94) tmp = x; else tmp = Float64(x - Float64(y * Float64(z / t))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -6.8e+94) tmp = x; else tmp = x - (y * (z / t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+94], x, N[(x - N[(y * N[(z / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.8 \cdot 10^{+94}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;x - y \cdot \frac{z}{t}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -6.8e+94) x (- x (/ y (/ t z)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -6.8e+94) {
tmp = x;
} else {
tmp = x - (y / (t / z));
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: tmp
if (z <= (-6.8d+94)) then
tmp = x
else
tmp = x - (y / (t / z))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -6.8e+94) {
tmp = x;
} else {
tmp = x - (y / (t / z));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -6.8e+94: tmp = x else: tmp = x - (y / (t / z)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -6.8e+94) tmp = x; else tmp = Float64(x - Float64(y / Float64(t / z))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -6.8e+94) tmp = x; else tmp = x - (y / (t / z)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -6.8e+94], x, N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -6.8 \cdot 10^{+94}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{t}{z}}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 x)
double code(double x, double y, double z, double t) {
return x;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
code = x
end function
public static double code(double x, double y, double z, double t) {
return x;
}
def code(x, y, z, t): return x
function code(x, y, z, t) return x end
function tmp = code(x, y, z, t) tmp = x; end
code[x_, y_, z_, t_] := x
\begin{array}{l}
\\
x
\end{array}
(FPCore (x y z t)
:precision binary64
(let* ((t_1 (/ (- 0.5) (* y t))))
(if (< z -2.8874623088207947e+119)
(- (- x (/ t_1 (* z z))) (* t_1 (/ (/ 2.0 z) (* z z))))
(- x (/ (log (+ 1.0 (* z y))) t)))))
double code(double x, double y, double z, double t) {
double t_1 = -0.5 / (y * t);
double tmp;
if (z < -2.8874623088207947e+119) {
tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
} else {
tmp = x - (log((1.0 + (z * y))) / t);
}
return tmp;
}
real(8) function code(x, y, z, t)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8) :: t_1
real(8) :: tmp
t_1 = -0.5d0 / (y * t)
if (z < (-2.8874623088207947d+119)) then
tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0d0 / z) / (z * z)))
else
tmp = x - (log((1.0d0 + (z * y))) / t)
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double t_1 = -0.5 / (y * t);
double tmp;
if (z < -2.8874623088207947e+119) {
tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z)));
} else {
tmp = x - (Math.log((1.0 + (z * y))) / t);
}
return tmp;
}
def code(x, y, z, t): t_1 = -0.5 / (y * t) tmp = 0 if z < -2.8874623088207947e+119: tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z))) else: tmp = x - (math.log((1.0 + (z * y))) / t) return tmp
function code(x, y, z, t) t_1 = Float64(Float64(-0.5) / Float64(y * t)) tmp = 0.0 if (z < -2.8874623088207947e+119) tmp = Float64(Float64(x - Float64(t_1 / Float64(z * z))) - Float64(t_1 * Float64(Float64(2.0 / z) / Float64(z * z)))); else tmp = Float64(x - Float64(log(Float64(1.0 + Float64(z * y))) / t)); end return tmp end
function tmp_2 = code(x, y, z, t) t_1 = -0.5 / (y * t); tmp = 0.0; if (z < -2.8874623088207947e+119) tmp = (x - (t_1 / (z * z))) - (t_1 * ((2.0 / z) / (z * z))); else tmp = x - (log((1.0 + (z * y))) / t); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := Block[{t$95$1 = N[((-0.5) / N[(y * t), $MachinePrecision]), $MachinePrecision]}, If[Less[z, -2.8874623088207947e+119], N[(N[(x - N[(t$95$1 / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(t$95$1 * N[(N[(2.0 / z), $MachinePrecision] / N[(z * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[N[(1.0 + N[(z * y), $MachinePrecision]), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
t_1 := \frac{-0.5}{y \cdot t}\\
\mathbf{if}\;z < -2.8874623088207947 \cdot 10^{+119}:\\
\;\;\;\;\left(x - \frac{t_1}{z \cdot z}\right) - t_1 \cdot \frac{\frac{2}{z}}{z \cdot z}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{\log \left(1 + z \cdot y\right)}{t}\\
\end{array}
\end{array}
herbie shell --seed 2024008
(FPCore (x y z t)
:name "System.Random.MWC.Distributions:truncatedExp from mwc-random-0.13.3.2"
:precision binary64
:herbie-target
(if (< z -2.8874623088207947e+119) (- (- x (/ (/ (- 0.5) (* y t)) (* z z))) (* (/ (- 0.5) (* y t)) (/ (/ 2.0 z) (* z z)))) (- x (/ (log (+ 1.0 (* z y))) t)))
(- x (/ (log (+ (- 1.0 y) (* y (exp z)))) t)))