
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- a t))))
double code(double x, double y, double z, double t, double a) {
return x + ((y * (z - t)) / (a - t));
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x + ((y * (z - t)) / (a - t))
end function
public static double code(double x, double y, double z, double t, double a) {
return x + ((y * (z - t)) / (a - t));
}
def code(x, y, z, t, a): return x + ((y * (z - t)) / (a - t))
function code(x, y, z, t, a) return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) end
function tmp = code(x, y, z, t, a) tmp = x + ((y * (z - t)) / (a - t)); end
code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y \cdot \left(z - t\right)}{a - t}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 9 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- a t))))
double code(double x, double y, double z, double t, double a) {
return x + ((y * (z - t)) / (a - t));
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x + ((y * (z - t)) / (a - t))
end function
public static double code(double x, double y, double z, double t, double a) {
return x + ((y * (z - t)) / (a - t));
}
def code(x, y, z, t, a): return x + ((y * (z - t)) / (a - t))
function code(x, y, z, t, a) return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) end
function tmp = code(x, y, z, t, a) tmp = x + ((y * (z - t)) / (a - t)); end
code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y \cdot \left(z - t\right)}{a - t}
\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- a t) (- z t)))))
double code(double x, double y, double z, double t, double a) {
return x + (y / ((a - t) / (z - t)));
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x + (y / ((a - t) / (z - t)))
end function
public static double code(double x, double y, double z, double t, double a) {
return x + (y / ((a - t) / (z - t)));
}
def code(x, y, z, t, a): return x + (y / ((a - t) / (z - t)))
function code(x, y, z, t, a) return Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t)))) end
function tmp = code(x, y, z, t, a) tmp = x + (y / ((a - t) / (z - t))); end
code[x_, y_, z_, t_, a_] := N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y}{\frac{a - t}{z - t}}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (or (<= t -1.55e+35) (not (<= t 1.65e+112))) (+ x y) (+ x (* z (/ y (- a t))))))
double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -1.55e+35) || !(t <= 1.65e+112)) {
tmp = x + y;
} else {
tmp = x + (z * (y / (a - t)));
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if ((t <= (-1.55d+35)) .or. (.not. (t <= 1.65d+112))) then
tmp = x + y
else
tmp = x + (z * (y / (a - t)))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -1.55e+35) || !(t <= 1.65e+112)) {
tmp = x + y;
} else {
tmp = x + (z * (y / (a - t)));
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if (t <= -1.55e+35) or not (t <= 1.65e+112): tmp = x + y else: tmp = x + (z * (y / (a - t))) return tmp
function code(x, y, z, t, a) tmp = 0.0 if ((t <= -1.55e+35) || !(t <= 1.65e+112)) tmp = Float64(x + y); else tmp = Float64(x + Float64(z * Float64(y / Float64(a - t)))); end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if ((t <= -1.55e+35) || ~((t <= 1.65e+112))) tmp = x + y; else tmp = x + (z * (y / (a - t))); end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.55e+35], N[Not[LessEqual[t, 1.65e+112]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -1.55 \cdot 10^{+35} \lor \neg \left(t \leq 1.65 \cdot 10^{+112}\right):\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;x + z \cdot \frac{y}{a - t}\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (or (<= t -1.4e+26) (not (<= t 3.7e+25))) (- x (/ y (+ (/ a t) -1.0))) (+ x (/ z (/ (- a t) y)))))
double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -1.4e+26) || !(t <= 3.7e+25)) {
tmp = x - (y / ((a / t) + -1.0));
} else {
tmp = x + (z / ((a - t) / y));
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if ((t <= (-1.4d+26)) .or. (.not. (t <= 3.7d+25))) then
tmp = x - (y / ((a / t) + (-1.0d0)))
else
tmp = x + (z / ((a - t) / y))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -1.4e+26) || !(t <= 3.7e+25)) {
tmp = x - (y / ((a / t) + -1.0));
} else {
tmp = x + (z / ((a - t) / y));
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if (t <= -1.4e+26) or not (t <= 3.7e+25): tmp = x - (y / ((a / t) + -1.0)) else: tmp = x + (z / ((a - t) / y)) return tmp
function code(x, y, z, t, a) tmp = 0.0 if ((t <= -1.4e+26) || !(t <= 3.7e+25)) tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0))); else tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y))); end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if ((t <= -1.4e+26) || ~((t <= 3.7e+25))) tmp = x - (y / ((a / t) + -1.0)); else tmp = x + (z / ((a - t) / y)); end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -1.4e+26], N[Not[LessEqual[t, 3.7e+25]], $MachinePrecision]], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -1.4 \cdot 10^{+26} \lor \neg \left(t \leq 3.7 \cdot 10^{+25}\right):\\
\;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\
\mathbf{else}:\\
\;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (<= t -1.75e+26) (- x (/ y (/ t (- z t)))) (if (<= t 8.9e+24) (+ x (/ z (/ (- a t) y))) (- x (/ y (+ (/ a t) -1.0))))))
double code(double x, double y, double z, double t, double a) {
double tmp;
if (t <= -1.75e+26) {
tmp = x - (y / (t / (z - t)));
} else if (t <= 8.9e+24) {
tmp = x + (z / ((a - t) / y));
} else {
tmp = x - (y / ((a / t) + -1.0));
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if (t <= (-1.75d+26)) then
tmp = x - (y / (t / (z - t)))
else if (t <= 8.9d+24) then
tmp = x + (z / ((a - t) / y))
else
tmp = x - (y / ((a / t) + (-1.0d0)))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if (t <= -1.75e+26) {
tmp = x - (y / (t / (z - t)));
} else if (t <= 8.9e+24) {
tmp = x + (z / ((a - t) / y));
} else {
tmp = x - (y / ((a / t) + -1.0));
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if t <= -1.75e+26: tmp = x - (y / (t / (z - t))) elif t <= 8.9e+24: tmp = x + (z / ((a - t) / y)) else: tmp = x - (y / ((a / t) + -1.0)) return tmp
function code(x, y, z, t, a) tmp = 0.0 if (t <= -1.75e+26) tmp = Float64(x - Float64(y / Float64(t / Float64(z - t)))); elseif (t <= 8.9e+24) tmp = Float64(x + Float64(z / Float64(Float64(a - t) / y))); else tmp = Float64(x - Float64(y / Float64(Float64(a / t) + -1.0))); end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if (t <= -1.75e+26) tmp = x - (y / (t / (z - t))); elseif (t <= 8.9e+24) tmp = x + (z / ((a - t) / y)); else tmp = x - (y / ((a / t) + -1.0)); end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[LessEqual[t, -1.75e+26], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t, 8.9e+24], N[(x + N[(z / N[(N[(a - t), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(y / N[(N[(a / t), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -1.75 \cdot 10^{+26}:\\
\;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\
\mathbf{elif}\;t \leq 8.9 \cdot 10^{+24}:\\
\;\;\;\;x + \frac{z}{\frac{a - t}{y}}\\
\mathbf{else}:\\
\;\;\;\;x - \frac{y}{\frac{a}{t} + -1}\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (or (<= t -0.0058) (not (<= t 1.25e+22))) (+ x y) (+ x (* z (/ y a)))))
double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -0.0058) || !(t <= 1.25e+22)) {
tmp = x + y;
} else {
tmp = x + (z * (y / a));
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if ((t <= (-0.0058d0)) .or. (.not. (t <= 1.25d+22))) then
tmp = x + y
else
tmp = x + (z * (y / a))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -0.0058) || !(t <= 1.25e+22)) {
tmp = x + y;
} else {
tmp = x + (z * (y / a));
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if (t <= -0.0058) or not (t <= 1.25e+22): tmp = x + y else: tmp = x + (z * (y / a)) return tmp
function code(x, y, z, t, a) tmp = 0.0 if ((t <= -0.0058) || !(t <= 1.25e+22)) tmp = Float64(x + y); else tmp = Float64(x + Float64(z * Float64(y / a))); end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if ((t <= -0.0058) || ~((t <= 1.25e+22))) tmp = x + y; else tmp = x + (z * (y / a)); end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0058], N[Not[LessEqual[t, 1.25e+22]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -0.0058 \lor \neg \left(t \leq 1.25 \cdot 10^{+22}\right):\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;x + z \cdot \frac{y}{a}\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (or (<= t -2700.0) (not (<= t 5200000.0))) (+ x y) (+ x (/ z (/ a y)))))
double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -2700.0) || !(t <= 5200000.0)) {
tmp = x + y;
} else {
tmp = x + (z / (a / y));
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if ((t <= (-2700.0d0)) .or. (.not. (t <= 5200000.0d0))) then
tmp = x + y
else
tmp = x + (z / (a / y))
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if ((t <= -2700.0) || !(t <= 5200000.0)) {
tmp = x + y;
} else {
tmp = x + (z / (a / y));
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if (t <= -2700.0) or not (t <= 5200000.0): tmp = x + y else: tmp = x + (z / (a / y)) return tmp
function code(x, y, z, t, a) tmp = 0.0 if ((t <= -2700.0) || !(t <= 5200000.0)) tmp = Float64(x + y); else tmp = Float64(x + Float64(z / Float64(a / y))); end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if ((t <= -2700.0) || ~((t <= 5200000.0))) tmp = x + y; else tmp = x + (z / (a / y)); end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -2700.0], N[Not[LessEqual[t, 5200000.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z / N[(a / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;t \leq -2700 \lor \neg \left(t \leq 5200000\right):\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;x + \frac{z}{\frac{a}{y}}\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))
double code(double x, double y, double z, double t, double a) {
return x + (y * ((z - t) / (a - t)));
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x + (y * ((z - t) / (a - t)))
end function
public static double code(double x, double y, double z, double t, double a) {
return x + (y * ((z - t) / (a - t)));
}
def code(x, y, z, t, a): return x + (y * ((z - t) / (a - t)))
function code(x, y, z, t, a) return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t)))) end
function tmp = code(x, y, z, t, a) tmp = x + (y * ((z - t) / (a - t))); end
code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + y \cdot \frac{z - t}{a - t}
\end{array}
(FPCore (x y z t a) :precision binary64 (if (<= a -1.5e+239) x (if (<= a 5.1e+174) (+ x y) x)))
double code(double x, double y, double z, double t, double a) {
double tmp;
if (a <= -1.5e+239) {
tmp = x;
} else if (a <= 5.1e+174) {
tmp = x + y;
} else {
tmp = x;
}
return tmp;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
real(8) :: tmp
if (a <= (-1.5d+239)) then
tmp = x
else if (a <= 5.1d+174) then
tmp = x + y
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z, double t, double a) {
double tmp;
if (a <= -1.5e+239) {
tmp = x;
} else if (a <= 5.1e+174) {
tmp = x + y;
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z, t, a): tmp = 0 if a <= -1.5e+239: tmp = x elif a <= 5.1e+174: tmp = x + y else: tmp = x return tmp
function code(x, y, z, t, a) tmp = 0.0 if (a <= -1.5e+239) tmp = x; elseif (a <= 5.1e+174) tmp = Float64(x + y); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z, t, a) tmp = 0.0; if (a <= -1.5e+239) tmp = x; elseif (a <= 5.1e+174) tmp = x + y; else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_, t_, a_] := If[LessEqual[a, -1.5e+239], x, If[LessEqual[a, 5.1e+174], N[(x + y), $MachinePrecision], x]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;a \leq -1.5 \cdot 10^{+239}:\\
\;\;\;\;x\\
\mathbf{elif}\;a \leq 5.1 \cdot 10^{+174}:\\
\;\;\;\;x + y\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y z t a) :precision binary64 x)
double code(double x, double y, double z, double t, double a) {
return x;
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x
end function
public static double code(double x, double y, double z, double t, double a) {
return x;
}
def code(x, y, z, t, a): return x
function code(x, y, z, t, a) return x end
function tmp = code(x, y, z, t, a) tmp = x; end
code[x_, y_, z_, t_, a_] := x
\begin{array}{l}
\\
x
\end{array}
(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- a t) (- z t)))))
double code(double x, double y, double z, double t, double a) {
return x + (y / ((a - t) / (z - t)));
}
real(8) function code(x, y, z, t, a)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8), intent (in) :: t
real(8), intent (in) :: a
code = x + (y / ((a - t) / (z - t)))
end function
public static double code(double x, double y, double z, double t, double a) {
return x + (y / ((a - t) / (z - t)));
}
def code(x, y, z, t, a): return x + (y / ((a - t) / (z - t)))
function code(x, y, z, t, a) return Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t)))) end
function tmp = code(x, y, z, t, a) tmp = x + (y / ((a - t) / (z - t))); end
code[x_, y_, z_, t_, a_] := N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \frac{y}{\frac{a - t}{z - t}}
\end{array}
herbie shell --seed 2023343
(FPCore (x y z t a)
:name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
:precision binary64
:herbie-target
(+ x (/ y (/ (- a t) (- z t))))
(+ x (/ (* y (- z t)) (- a t))))