
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
double code(double x, double y, double z) {
return (x + (y * (z - x))) / z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x + (y * (z - x))) / z
end function
public static double code(double x, double y, double z) {
return (x + (y * (z - x))) / z;
}
def code(x, y, z): return (x + (y * (z - x))) / z
function code(x, y, z) return Float64(Float64(x + Float64(y * Float64(z - x))) / z) end
function tmp = code(x, y, z) tmp = (x + (y * (z - x))) / z; end
code[x_, y_, z_] := N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + y \cdot \left(z - x\right)}{z}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 10 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (/ (+ x (* y (- z x))) z))
double code(double x, double y, double z) {
return (x + (y * (z - x))) / z;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (x + (y * (z - x))) / z
end function
public static double code(double x, double y, double z) {
return (x + (y * (z - x))) / z;
}
def code(x, y, z): return (x + (y * (z - x))) / z
function code(x, y, z) return Float64(Float64(x + Float64(y * Float64(z - x))) / z) end
function tmp = code(x, y, z) tmp = (x + (y * (z - x))) / z; end
code[x_, y_, z_] := N[(N[(x + N[(y * N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / z), $MachinePrecision]
\begin{array}{l}
\\
\frac{x + y \cdot \left(z - x\right)}{z}
\end{array}
(FPCore (x y z) :precision binary64 (- y (* (/ x z) (+ y -1.0))))
double code(double x, double y, double z) {
return y - ((x / z) * (y + -1.0));
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = y - ((x / z) * (y + (-1.0d0)))
end function
public static double code(double x, double y, double z) {
return y - ((x / z) * (y + -1.0));
}
def code(x, y, z): return y - ((x / z) * (y + -1.0))
function code(x, y, z) return Float64(y - Float64(Float64(x / z) * Float64(y + -1.0))) end
function tmp = code(x, y, z) tmp = y - ((x / z) * (y + -1.0)); end
code[x_, y_, z_] := N[(y - N[(N[(x / z), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
y - \frac{x}{z} \cdot \left(y + -1\right)
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= z -4.4e-60) (not (<= z 1.35e+54))) (+ y (/ x z)) (* (/ x z) (- 1.0 y))))
double code(double x, double y, double z) {
double tmp;
if ((z <= -4.4e-60) || !(z <= 1.35e+54)) {
tmp = y + (x / z);
} else {
tmp = (x / z) * (1.0 - y);
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((z <= (-4.4d-60)) .or. (.not. (z <= 1.35d+54))) then
tmp = y + (x / z)
else
tmp = (x / z) * (1.0d0 - y)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -4.4e-60) || !(z <= 1.35e+54)) {
tmp = y + (x / z);
} else {
tmp = (x / z) * (1.0 - y);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -4.4e-60) or not (z <= 1.35e+54): tmp = y + (x / z) else: tmp = (x / z) * (1.0 - y) return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -4.4e-60) || !(z <= 1.35e+54)) tmp = Float64(y + Float64(x / z)); else tmp = Float64(Float64(x / z) * Float64(1.0 - y)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -4.4e-60) || ~((z <= 1.35e+54))) tmp = y + (x / z); else tmp = (x / z) * (1.0 - y); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -4.4e-60], N[Not[LessEqual[z, 1.35e+54]], $MachinePrecision]], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(x / z), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -4.4 \cdot 10^{-60} \lor \neg \left(z \leq 1.35 \cdot 10^{+54}\right):\\
\;\;\;\;y + \frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;\frac{x}{z} \cdot \left(1 - y\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= y -4.5e+16) (not (<= y 1.0))) (* (- z x) (/ y z)) (+ y (/ x z))))
double code(double x, double y, double z) {
double tmp;
if ((y <= -4.5e+16) || !(y <= 1.0)) {
tmp = (z - x) * (y / z);
} else {
tmp = y + (x / z);
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((y <= (-4.5d+16)) .or. (.not. (y <= 1.0d0))) then
tmp = (z - x) * (y / z)
else
tmp = y + (x / z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((y <= -4.5e+16) || !(y <= 1.0)) {
tmp = (z - x) * (y / z);
} else {
tmp = y + (x / z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (y <= -4.5e+16) or not (y <= 1.0): tmp = (z - x) * (y / z) else: tmp = y + (x / z) return tmp
function code(x, y, z) tmp = 0.0 if ((y <= -4.5e+16) || !(y <= 1.0)) tmp = Float64(Float64(z - x) * Float64(y / z)); else tmp = Float64(y + Float64(x / z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((y <= -4.5e+16) || ~((y <= 1.0))) tmp = (z - x) * (y / z); else tmp = y + (x / z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+16], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[(z - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.5 \cdot 10^{+16} \lor \neg \left(y \leq 1\right):\\
\;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\
\mathbf{else}:\\
\;\;\;\;y + \frac{x}{z}\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= y -4.5e+16) (not (<= y 1.0))) (/ y (/ z (- z x))) (+ y (/ x z))))
double code(double x, double y, double z) {
double tmp;
if ((y <= -4.5e+16) || !(y <= 1.0)) {
tmp = y / (z / (z - x));
} else {
tmp = y + (x / z);
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if ((y <= (-4.5d+16)) .or. (.not. (y <= 1.0d0))) then
tmp = y / (z / (z - x))
else
tmp = y + (x / z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((y <= -4.5e+16) || !(y <= 1.0)) {
tmp = y / (z / (z - x));
} else {
tmp = y + (x / z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if (y <= -4.5e+16) or not (y <= 1.0): tmp = y / (z / (z - x)) else: tmp = y + (x / z) return tmp
function code(x, y, z) tmp = 0.0 if ((y <= -4.5e+16) || !(y <= 1.0)) tmp = Float64(y / Float64(z / Float64(z - x))); else tmp = Float64(y + Float64(x / z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((y <= -4.5e+16) || ~((y <= 1.0))) tmp = y / (z / (z - x)); else tmp = y + (x / z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[y, -4.5e+16], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(y / N[(z / N[(z - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.5 \cdot 10^{+16} \lor \neg \left(y \leq 1\right):\\
\;\;\;\;\frac{y}{\frac{z}{z - x}}\\
\mathbf{else}:\\
\;\;\;\;y + \frac{x}{z}\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= y -4.5e+16) (- y (/ (* y x) z)) (if (<= y 1.0) (+ y (/ x z)) (* (- z x) (/ y z)))))
double code(double x, double y, double z) {
double tmp;
if (y <= -4.5e+16) {
tmp = y - ((y * x) / z);
} else if (y <= 1.0) {
tmp = y + (x / z);
} else {
tmp = (z - x) * (y / z);
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (y <= (-4.5d+16)) then
tmp = y - ((y * x) / z)
else if (y <= 1.0d0) then
tmp = y + (x / z)
else
tmp = (z - x) * (y / z)
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -4.5e+16) {
tmp = y - ((y * x) / z);
} else if (y <= 1.0) {
tmp = y + (x / z);
} else {
tmp = (z - x) * (y / z);
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -4.5e+16: tmp = y - ((y * x) / z) elif y <= 1.0: tmp = y + (x / z) else: tmp = (z - x) * (y / z) return tmp
function code(x, y, z) tmp = 0.0 if (y <= -4.5e+16) tmp = Float64(y - Float64(Float64(y * x) / z)); elseif (y <= 1.0) tmp = Float64(y + Float64(x / z)); else tmp = Float64(Float64(z - x) * Float64(y / z)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -4.5e+16) tmp = y - ((y * x) / z); elseif (y <= 1.0) tmp = y + (x / z); else tmp = (z - x) * (y / z); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -4.5e+16], N[(y - N[(N[(y * x), $MachinePrecision] / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.0], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], N[(N[(z - x), $MachinePrecision] * N[(y / z), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.5 \cdot 10^{+16}:\\
\;\;\;\;y - \frac{y \cdot x}{z}\\
\mathbf{elif}\;y \leq 1:\\
\;\;\;\;y + \frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;\left(z - x\right) \cdot \frac{y}{z}\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= y 9.2e+23) (+ y (/ x z)) (if (<= y 2.9e+150) (* y (/ x (- z))) y)))
double code(double x, double y, double z) {
double tmp;
if (y <= 9.2e+23) {
tmp = y + (x / z);
} else if (y <= 2.9e+150) {
tmp = y * (x / -z);
} else {
tmp = y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (y <= 9.2d+23) then
tmp = y + (x / z)
else if (y <= 2.9d+150) then
tmp = y * (x / -z)
else
tmp = y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= 9.2e+23) {
tmp = y + (x / z);
} else if (y <= 2.9e+150) {
tmp = y * (x / -z);
} else {
tmp = y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= 9.2e+23: tmp = y + (x / z) elif y <= 2.9e+150: tmp = y * (x / -z) else: tmp = y return tmp
function code(x, y, z) tmp = 0.0 if (y <= 9.2e+23) tmp = Float64(y + Float64(x / z)); elseif (y <= 2.9e+150) tmp = Float64(y * Float64(x / Float64(-z))); else tmp = y; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= 9.2e+23) tmp = y + (x / z); elseif (y <= 2.9e+150) tmp = y * (x / -z); else tmp = y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, 9.2e+23], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+150], N[(y * N[(x / (-z)), $MachinePrecision]), $MachinePrecision], y]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 9.2 \cdot 10^{+23}:\\
\;\;\;\;y + \frac{x}{z}\\
\mathbf{elif}\;y \leq 2.9 \cdot 10^{+150}:\\
\;\;\;\;y \cdot \frac{x}{-z}\\
\mathbf{else}:\\
\;\;\;\;y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= y 1.6e+26) (+ y (/ x z)) (if (<= y 3.5e+150) (/ x (/ (- z) y)) y)))
double code(double x, double y, double z) {
double tmp;
if (y <= 1.6e+26) {
tmp = y + (x / z);
} else if (y <= 3.5e+150) {
tmp = x / (-z / y);
} else {
tmp = y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (y <= 1.6d+26) then
tmp = y + (x / z)
else if (y <= 3.5d+150) then
tmp = x / (-z / y)
else
tmp = y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= 1.6e+26) {
tmp = y + (x / z);
} else if (y <= 3.5e+150) {
tmp = x / (-z / y);
} else {
tmp = y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= 1.6e+26: tmp = y + (x / z) elif y <= 3.5e+150: tmp = x / (-z / y) else: tmp = y return tmp
function code(x, y, z) tmp = 0.0 if (y <= 1.6e+26) tmp = Float64(y + Float64(x / z)); elseif (y <= 3.5e+150) tmp = Float64(x / Float64(Float64(-z) / y)); else tmp = y; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= 1.6e+26) tmp = y + (x / z); elseif (y <= 3.5e+150) tmp = x / (-z / y); else tmp = y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, 1.6e+26], N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.5e+150], N[(x / N[((-z) / y), $MachinePrecision]), $MachinePrecision], y]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq 1.6 \cdot 10^{+26}:\\
\;\;\;\;y + \frac{x}{z}\\
\mathbf{elif}\;y \leq 3.5 \cdot 10^{+150}:\\
\;\;\;\;\frac{x}{\frac{-z}{y}}\\
\mathbf{else}:\\
\;\;\;\;y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= y -4.2e-88) y (if (<= y 3.3e-66) (/ x z) y)))
double code(double x, double y, double z) {
double tmp;
if (y <= -4.2e-88) {
tmp = y;
} else if (y <= 3.3e-66) {
tmp = x / z;
} else {
tmp = y;
}
return tmp;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
real(8) :: tmp
if (y <= (-4.2d-88)) then
tmp = y
else if (y <= 3.3d-66) then
tmp = x / z
else
tmp = y
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (y <= -4.2e-88) {
tmp = y;
} else if (y <= 3.3e-66) {
tmp = x / z;
} else {
tmp = y;
}
return tmp;
}
def code(x, y, z): tmp = 0 if y <= -4.2e-88: tmp = y elif y <= 3.3e-66: tmp = x / z else: tmp = y return tmp
function code(x, y, z) tmp = 0.0 if (y <= -4.2e-88) tmp = y; elseif (y <= 3.3e-66) tmp = Float64(x / z); else tmp = y; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (y <= -4.2e-88) tmp = y; elseif (y <= 3.3e-66) tmp = x / z; else tmp = y; end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[y, -4.2e-88], y, If[LessEqual[y, 3.3e-66], N[(x / z), $MachinePrecision], y]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.2 \cdot 10^{-88}:\\
\;\;\;\;y\\
\mathbf{elif}\;y \leq 3.3 \cdot 10^{-66}:\\
\;\;\;\;\frac{x}{z}\\
\mathbf{else}:\\
\;\;\;\;y\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (+ y (/ x z)))
double code(double x, double y, double z) {
return y + (x / z);
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = y + (x / z)
end function
public static double code(double x, double y, double z) {
return y + (x / z);
}
def code(x, y, z): return y + (x / z)
function code(x, y, z) return Float64(y + Float64(x / z)) end
function tmp = code(x, y, z) tmp = y + (x / z); end
code[x_, y_, z_] := N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
y + \frac{x}{z}
\end{array}
(FPCore (x y z) :precision binary64 y)
double code(double x, double y, double z) {
return y;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = y
end function
public static double code(double x, double y, double z) {
return y;
}
def code(x, y, z): return y
function code(x, y, z) return y end
function tmp = code(x, y, z) tmp = y; end
code[x_, y_, z_] := y
\begin{array}{l}
\\
y
\end{array}
(FPCore (x y z) :precision binary64 (- (+ y (/ x z)) (/ y (/ z x))))
double code(double x, double y, double z) {
return (y + (x / z)) - (y / (z / x));
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = (y + (x / z)) - (y / (z / x))
end function
public static double code(double x, double y, double z) {
return (y + (x / z)) - (y / (z / x));
}
def code(x, y, z): return (y + (x / z)) - (y / (z / x))
function code(x, y, z) return Float64(Float64(y + Float64(x / z)) - Float64(y / Float64(z / x))) end
function tmp = code(x, y, z) tmp = (y + (x / z)) - (y / (z / x)); end
code[x_, y_, z_] := N[(N[(y + N[(x / z), $MachinePrecision]), $MachinePrecision] - N[(y / N[(z / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\left(y + \frac{x}{z}\right) - \frac{y}{\frac{z}{x}}
\end{array}
herbie shell --seed 2023343
(FPCore (x y z)
:name "Diagrams.Backend.Rasterific:rasterificRadialGradient from diagrams-rasterific-1.3.1.3"
:precision binary64
:herbie-target
(- (+ y (/ x z)) (/ y (/ z x)))
(/ (+ x (* y (- z x))) z))