
(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 (if (<= y -21000000.0) (+ x (/ -1.0 (+ (* t 0.5) (/ t (* y z))))) (if (<= y 2.2e-7) (- x (* y (/ (expm1 z) t))) (- x (/ (log1p (* y z)) t)))))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= -21000000.0) {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z))));
} else if (y <= 2.2e-7) {
tmp = x - (y * (expm1(z) / t));
} else {
tmp = x - (log1p((y * z)) / t);
}
return tmp;
}
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= -21000000.0) {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z))));
} else if (y <= 2.2e-7) {
tmp = x - (y * (Math.expm1(z) / t));
} else {
tmp = x - (Math.log1p((y * z)) / t);
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= -21000000.0: tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z)))) elif y <= 2.2e-7: tmp = x - (y * (math.expm1(z) / t)) else: tmp = x - (math.log1p((y * z)) / t) return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= -21000000.0) tmp = Float64(x + Float64(-1.0 / Float64(Float64(t * 0.5) + Float64(t / Float64(y * z))))); elseif (y <= 2.2e-7) tmp = Float64(x - Float64(y * Float64(expm1(z) / t))); else tmp = Float64(x - Float64(log1p(Float64(y * z)) / t)); end return tmp end
code[x_, y_, z_, t_] := If[LessEqual[y, -21000000.0], N[(x + N[(-1.0 / N[(N[(t * 0.5), $MachinePrecision] + N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.2e-7], N[(x - N[(y * N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[Log[1 + N[(y * z), $MachinePrecision]], $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -21000000:\\
\;\;\;\;x + \frac{-1}{t \cdot 0.5 + \frac{t}{y \cdot z}}\\
\mathbf{elif}\;y \leq 2.2 \cdot 10^{-7}:\\
\;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{\mathsf{log1p}\left(y \cdot z\right)}{t}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= y -21000000.0) (+ x (/ -1.0 (+ (* t 0.5) (/ t (* y z))))) (- x (* y (/ (expm1 z) t)))))
double code(double x, double y, double z, double t) {
double tmp;
if (y <= -21000000.0) {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z))));
} else {
tmp = x - (y * (expm1(z) / t));
}
return tmp;
}
public static double code(double x, double y, double z, double t) {
double tmp;
if (y <= -21000000.0) {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z))));
} else {
tmp = x - (y * (Math.expm1(z) / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if y <= -21000000.0: tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z)))) else: tmp = x - (y * (math.expm1(z) / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if (y <= -21000000.0) tmp = Float64(x + Float64(-1.0 / Float64(Float64(t * 0.5) + Float64(t / Float64(y * z))))); else tmp = Float64(x - Float64(y * Float64(expm1(z) / t))); end return tmp end
code[x_, y_, z_, t_] := If[LessEqual[y, -21000000.0], N[(x + N[(-1.0 / N[(N[(t * 0.5), $MachinePrecision] + N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(N[(Exp[z] - 1), $MachinePrecision] / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -21000000:\\
\;\;\;\;x + \frac{-1}{t \cdot 0.5 + \frac{t}{y \cdot z}}\\
\mathbf{else}:\\
\;\;\;\;x - y \cdot \frac{\mathsf{expm1}\left(z\right)}{t}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -9.2e+98) x (+ x (/ -1.0 (+ (* t 0.5) (/ t (* y z)))))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -9.2e+98) {
tmp = x;
} else {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * 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 <= (-9.2d+98)) then
tmp = x
else
tmp = x + ((-1.0d0) / ((t * 0.5d0) + (t / (y * z))))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -9.2e+98) {
tmp = x;
} else {
tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z))));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -9.2e+98: tmp = x else: tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z)))) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -9.2e+98) tmp = x; else tmp = Float64(x + Float64(-1.0 / Float64(Float64(t * 0.5) + Float64(t / Float64(y * z))))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -9.2e+98) tmp = x; else tmp = x + (-1.0 / ((t * 0.5) + (t / (y * z)))); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -9.2e+98], x, N[(x + N[(-1.0 / N[(N[(t * 0.5), $MachinePrecision] + N[(t / N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -9.2 \cdot 10^{+98}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;x + \frac{-1}{t \cdot 0.5 + \frac{t}{y \cdot z}}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= t -1.05e-192) x (if (<= t 3.4e-212) (* (- y) (/ z t)) x)))
double code(double x, double y, double z, double t) {
double tmp;
if (t <= -1.05e-192) {
tmp = x;
} else if (t <= 3.4e-212) {
tmp = -y * (z / t);
} else {
tmp = x;
}
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 (t <= (-1.05d-192)) then
tmp = x
else if (t <= 3.4d-212) then
tmp = -y * (z / t)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (t <= -1.05e-192) {
tmp = x;
} else if (t <= 3.4e-212) {
tmp = -y * (z / t);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if t <= -1.05e-192: tmp = x elif t <= 3.4e-212: tmp = -y * (z / t) else: tmp = x return tmp
function code(x, y, z, t) tmp = 0.0 if (t <= -1.05e-192) tmp = x; elseif (t <= 3.4e-212) tmp = Float64(Float64(-y) * Float64(z / t)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (t <= -1.05e-192) tmp = x; elseif (t <= 3.4e-212) tmp = -y * (z / t); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[t, -1.05e-192], x, If[LessEqual[t, 3.4e-212], N[((-y) * N[(z / t), $MachinePrecision]), $MachinePrecision], x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -1.05 \cdot 10^{-192}:\\
\;\;\;\;x\\
\mathbf{elif}\;t \leq 3.4 \cdot 10^{-212}:\\
\;\;\;\;\left(-y\right) \cdot \frac{z}{t}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= t -1.1e-192) x (if (<= t 2.2e-212) (/ y (/ (- t) z)) x)))
double code(double x, double y, double z, double t) {
double tmp;
if (t <= -1.1e-192) {
tmp = x;
} else if (t <= 2.2e-212) {
tmp = y / (-t / z);
} else {
tmp = x;
}
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 (t <= (-1.1d-192)) then
tmp = x
else if (t <= 2.2d-212) then
tmp = y / (-t / z)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (t <= -1.1e-192) {
tmp = x;
} else if (t <= 2.2e-212) {
tmp = y / (-t / z);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if t <= -1.1e-192: tmp = x elif t <= 2.2e-212: tmp = y / (-t / z) else: tmp = x return tmp
function code(x, y, z, t) tmp = 0.0 if (t <= -1.1e-192) tmp = x; elseif (t <= 2.2e-212) tmp = Float64(y / Float64(Float64(-t) / z)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (t <= -1.1e-192) tmp = x; elseif (t <= 2.2e-212) tmp = y / (-t / z); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[t, -1.1e-192], x, If[LessEqual[t, 2.2e-212], N[(y / N[((-t) / z), $MachinePrecision]), $MachinePrecision], x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -1.1 \cdot 10^{-192}:\\
\;\;\;\;x\\
\mathbf{elif}\;t \leq 2.2 \cdot 10^{-212}:\\
\;\;\;\;\frac{y}{\frac{-t}{z}}\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -8.4e+14) x (- x (* z (/ y t)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -8.4e+14) {
tmp = x;
} else {
tmp = x - (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) :: tmp
if (z <= (-8.4d+14)) then
tmp = x
else
tmp = x - (z * (y / t))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t) {
double tmp;
if (z <= -8.4e+14) {
tmp = x;
} else {
tmp = x - (z * (y / t));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -8.4e+14: tmp = x else: tmp = x - (z * (y / t)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -8.4e+14) tmp = x; else tmp = Float64(x - Float64(z * Float64(y / t))); end return tmp end
function tmp_2 = code(x, y, z, t) tmp = 0.0; if (z <= -8.4e+14) tmp = x; else tmp = x - (z * (y / t)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -8.4e+14], x, N[(x - N[(z * N[(y / t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -8.4 \cdot 10^{+14}:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;x - z \cdot \frac{y}{t}\\
\end{array}
\end{array}
(FPCore (x y z t) :precision binary64 (if (<= z -3.5e+16) x (- x (/ y (/ t z)))))
double code(double x, double y, double z, double t) {
double tmp;
if (z <= -3.5e+16) {
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 <= (-3.5d+16)) 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 <= -3.5e+16) {
tmp = x;
} else {
tmp = x - (y / (t / z));
}
return tmp;
}
def code(x, y, z, t): tmp = 0 if z <= -3.5e+16: tmp = x else: tmp = x - (y / (t / z)) return tmp
function code(x, y, z, t) tmp = 0.0 if (z <= -3.5e+16) 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 <= -3.5e+16) tmp = x; else tmp = x - (y / (t / z)); end tmp_2 = tmp; end
code[x_, y_, z_, t_] := If[LessEqual[z, -3.5e+16], x, N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -3.5 \cdot 10^{+16}:\\
\;\;\;\;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 2023343
(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)))