
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
double code(double x, double y, double z) {
return x + (((y - x) * 6.0) * 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 - x) * 6.0d0) * z)
end function
public static double code(double x, double y, double z) {
return x + (((y - x) * 6.0) * z);
}
def code(x, y, z): return x + (((y - x) * 6.0) * z)
function code(x, y, z) return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z)) end
function tmp = code(x, y, z) tmp = x + (((y - x) * 6.0) * z); end
code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 10 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))
double code(double x, double y, double z) {
return x + (((y - x) * 6.0) * 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 - x) * 6.0d0) * z)
end function
public static double code(double x, double y, double z) {
return x + (((y - x) * 6.0) * z);
}
def code(x, y, z): return x + (((y - x) * 6.0) * z)
function code(x, y, z) return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z)) end
function tmp = code(x, y, z) tmp = x + (((y - x) * 6.0) * z); end
code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + \left(\left(y - x\right) \cdot 6\right) \cdot z
\end{array}
(FPCore (x y z) :precision binary64 (fma (- y x) (* 6.0 z) x))
double code(double x, double y, double z) {
return fma((y - x), (6.0 * z), x);
}
function code(x, y, z) return fma(Float64(y - x), Float64(6.0 * z), x) end
code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision] + x), $MachinePrecision]
\begin{array}{l}
\\
\mathsf{fma}\left(y - x, 6 \cdot z, x\right)
\end{array}
(FPCore (x y z) :precision binary64 (if (<= x -7e+82) (* x (+ 1.0 (* z -6.0))) (if (<= x 7.4e-82) (+ x (* 6.0 (* y z))) (+ x (* -6.0 (* x z))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -7e+82) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.4e-82) {
tmp = x + (6.0 * (y * z));
} else {
tmp = x + (-6.0 * (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 (x <= (-7d+82)) then
tmp = x * (1.0d0 + (z * (-6.0d0)))
else if (x <= 7.4d-82) then
tmp = x + (6.0d0 * (y * z))
else
tmp = x + ((-6.0d0) * (x * z))
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -7e+82) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.4e-82) {
tmp = x + (6.0 * (y * z));
} else {
tmp = x + (-6.0 * (x * z));
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -7e+82: tmp = x * (1.0 + (z * -6.0)) elif x <= 7.4e-82: tmp = x + (6.0 * (y * z)) else: tmp = x + (-6.0 * (x * z)) return tmp
function code(x, y, z) tmp = 0.0 if (x <= -7e+82) tmp = Float64(x * Float64(1.0 + Float64(z * -6.0))); elseif (x <= 7.4e-82) tmp = Float64(x + Float64(6.0 * Float64(y * z))); else tmp = Float64(x + Float64(-6.0 * Float64(x * z))); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -7e+82) tmp = x * (1.0 + (z * -6.0)); elseif (x <= 7.4e-82) tmp = x + (6.0 * (y * z)); else tmp = x + (-6.0 * (x * z)); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -7e+82], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.4e-82], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -7 \cdot 10^{+82}:\\
\;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\
\mathbf{elif}\;x \leq 7.4 \cdot 10^{-82}:\\
\;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\
\mathbf{else}:\\
\;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= x -3.2e+86) (* x (+ 1.0 (* z -6.0))) (if (<= x 7.8e-82) (+ x (* 6.0 (* y z))) (+ x (* z (* x -6.0))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -3.2e+86) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.8e-82) {
tmp = x + (6.0 * (y * z));
} else {
tmp = x + (z * (x * -6.0));
}
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 (x <= (-3.2d+86)) then
tmp = x * (1.0d0 + (z * (-6.0d0)))
else if (x <= 7.8d-82) then
tmp = x + (6.0d0 * (y * z))
else
tmp = x + (z * (x * (-6.0d0)))
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -3.2e+86) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.8e-82) {
tmp = x + (6.0 * (y * z));
} else {
tmp = x + (z * (x * -6.0));
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -3.2e+86: tmp = x * (1.0 + (z * -6.0)) elif x <= 7.8e-82: tmp = x + (6.0 * (y * z)) else: tmp = x + (z * (x * -6.0)) return tmp
function code(x, y, z) tmp = 0.0 if (x <= -3.2e+86) tmp = Float64(x * Float64(1.0 + Float64(z * -6.0))); elseif (x <= 7.8e-82) tmp = Float64(x + Float64(6.0 * Float64(y * z))); else tmp = Float64(x + Float64(z * Float64(x * -6.0))); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -3.2e+86) tmp = x * (1.0 + (z * -6.0)); elseif (x <= 7.8e-82) tmp = x + (6.0 * (y * z)); else tmp = x + (z * (x * -6.0)); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -3.2e+86], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-82], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -3.2 \cdot 10^{+86}:\\
\;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\
\mathbf{elif}\;x \leq 7.8 \cdot 10^{-82}:\\
\;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\
\mathbf{else}:\\
\;\;\;\;x + z \cdot \left(x \cdot -6\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= x -5.5e+83) (* x (+ 1.0 (* z -6.0))) (if (<= x 7.8e-82) (+ x (* z (* y 6.0))) (+ x (* z (* x -6.0))))))
double code(double x, double y, double z) {
double tmp;
if (x <= -5.5e+83) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.8e-82) {
tmp = x + (z * (y * 6.0));
} else {
tmp = x + (z * (x * -6.0));
}
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 (x <= (-5.5d+83)) then
tmp = x * (1.0d0 + (z * (-6.0d0)))
else if (x <= 7.8d-82) then
tmp = x + (z * (y * 6.0d0))
else
tmp = x + (z * (x * (-6.0d0)))
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (x <= -5.5e+83) {
tmp = x * (1.0 + (z * -6.0));
} else if (x <= 7.8e-82) {
tmp = x + (z * (y * 6.0));
} else {
tmp = x + (z * (x * -6.0));
}
return tmp;
}
def code(x, y, z): tmp = 0 if x <= -5.5e+83: tmp = x * (1.0 + (z * -6.0)) elif x <= 7.8e-82: tmp = x + (z * (y * 6.0)) else: tmp = x + (z * (x * -6.0)) return tmp
function code(x, y, z) tmp = 0.0 if (x <= -5.5e+83) tmp = Float64(x * Float64(1.0 + Float64(z * -6.0))); elseif (x <= 7.8e-82) tmp = Float64(x + Float64(z * Float64(y * 6.0))); else tmp = Float64(x + Float64(z * Float64(x * -6.0))); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (x <= -5.5e+83) tmp = x * (1.0 + (z * -6.0)); elseif (x <= 7.8e-82) tmp = x + (z * (y * 6.0)); else tmp = x + (z * (x * -6.0)); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[x, -5.5e+83], N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.8e-82], N[(x + N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -5.5 \cdot 10^{+83}:\\
\;\;\;\;x \cdot \left(1 + z \cdot -6\right)\\
\mathbf{elif}\;x \leq 7.8 \cdot 10^{-82}:\\
\;\;\;\;x + z \cdot \left(y \cdot 6\right)\\
\mathbf{else}:\\
\;\;\;\;x + z \cdot \left(x \cdot -6\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= z -0.17) (not (<= z 90000000.0))) (* -6.0 (* x z)) x))
double code(double x, double y, double z) {
double tmp;
if ((z <= -0.17) || !(z <= 90000000.0)) {
tmp = -6.0 * (x * z);
} else {
tmp = x;
}
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 <= (-0.17d0)) .or. (.not. (z <= 90000000.0d0))) then
tmp = (-6.0d0) * (x * z)
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -0.17) || !(z <= 90000000.0)) {
tmp = -6.0 * (x * z);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -0.17) or not (z <= 90000000.0): tmp = -6.0 * (x * z) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -0.17) || !(z <= 90000000.0)) tmp = Float64(-6.0 * Float64(x * z)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -0.17) || ~((z <= 90000000.0))) tmp = -6.0 * (x * z); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 90000000\right):\\
\;\;\;\;-6 \cdot \left(x \cdot z\right)\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (or (<= z -0.17) (not (<= z 90000000.0))) (* x (* z -6.0)) x))
double code(double x, double y, double z) {
double tmp;
if ((z <= -0.17) || !(z <= 90000000.0)) {
tmp = x * (z * -6.0);
} else {
tmp = x;
}
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 <= (-0.17d0)) .or. (.not. (z <= 90000000.0d0))) then
tmp = x * (z * (-6.0d0))
else
tmp = x
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if ((z <= -0.17) || !(z <= 90000000.0)) {
tmp = x * (z * -6.0);
} else {
tmp = x;
}
return tmp;
}
def code(x, y, z): tmp = 0 if (z <= -0.17) or not (z <= 90000000.0): tmp = x * (z * -6.0) else: tmp = x return tmp
function code(x, y, z) tmp = 0.0 if ((z <= -0.17) || !(z <= 90000000.0)) tmp = Float64(x * Float64(z * -6.0)); else tmp = x; end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if ((z <= -0.17) || ~((z <= 90000000.0))) tmp = x * (z * -6.0); else tmp = x; end tmp_2 = tmp; end
code[x_, y_, z_] := If[Or[LessEqual[z, -0.17], N[Not[LessEqual[z, 90000000.0]], $MachinePrecision]], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], x]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.17 \lor \neg \left(z \leq 90000000\right):\\
\;\;\;\;x \cdot \left(z \cdot -6\right)\\
\mathbf{else}:\\
\;\;\;\;x\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (if (<= z -0.17) (* x (* z -6.0)) (if (<= z 90000000.0) x (* z (* x -6.0)))))
double code(double x, double y, double z) {
double tmp;
if (z <= -0.17) {
tmp = x * (z * -6.0);
} else if (z <= 90000000.0) {
tmp = x;
} else {
tmp = z * (x * -6.0);
}
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 <= (-0.17d0)) then
tmp = x * (z * (-6.0d0))
else if (z <= 90000000.0d0) then
tmp = x
else
tmp = z * (x * (-6.0d0))
end if
code = tmp
end function
public static double code(double x, double y, double z) {
double tmp;
if (z <= -0.17) {
tmp = x * (z * -6.0);
} else if (z <= 90000000.0) {
tmp = x;
} else {
tmp = z * (x * -6.0);
}
return tmp;
}
def code(x, y, z): tmp = 0 if z <= -0.17: tmp = x * (z * -6.0) elif z <= 90000000.0: tmp = x else: tmp = z * (x * -6.0) return tmp
function code(x, y, z) tmp = 0.0 if (z <= -0.17) tmp = Float64(x * Float64(z * -6.0)); elseif (z <= 90000000.0) tmp = x; else tmp = Float64(z * Float64(x * -6.0)); end return tmp end
function tmp_2 = code(x, y, z) tmp = 0.0; if (z <= -0.17) tmp = x * (z * -6.0); elseif (z <= 90000000.0) tmp = x; else tmp = z * (x * -6.0); end tmp_2 = tmp; end
code[x_, y_, z_] := If[LessEqual[z, -0.17], N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 90000000.0], x, N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;z \leq -0.17:\\
\;\;\;\;x \cdot \left(z \cdot -6\right)\\
\mathbf{elif}\;z \leq 90000000:\\
\;\;\;\;x\\
\mathbf{else}:\\
\;\;\;\;z \cdot \left(x \cdot -6\right)\\
\end{array}
\end{array}
(FPCore (x y z) :precision binary64 (+ x (* z (* (- y x) 6.0))))
double code(double x, double y, double z) {
return x + (z * ((y - x) * 6.0));
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x + (z * ((y - x) * 6.0d0))
end function
public static double code(double x, double y, double z) {
return x + (z * ((y - x) * 6.0));
}
def code(x, y, z): return x + (z * ((y - x) * 6.0))
function code(x, y, z) return Float64(x + Float64(z * Float64(Float64(y - x) * 6.0))) end
function tmp = code(x, y, z) tmp = x + (z * ((y - x) * 6.0)); end
code[x_, y_, z_] := N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x + z \cdot \left(\left(y - x\right) \cdot 6\right)
\end{array}
(FPCore (x y z) :precision binary64 (* x (+ 1.0 (* z -6.0))))
double code(double x, double y, double z) {
return x * (1.0 + (z * -6.0));
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x * (1.0d0 + (z * (-6.0d0)))
end function
public static double code(double x, double y, double z) {
return x * (1.0 + (z * -6.0));
}
def code(x, y, z): return x * (1.0 + (z * -6.0))
function code(x, y, z) return Float64(x * Float64(1.0 + Float64(z * -6.0))) end
function tmp = code(x, y, z) tmp = x * (1.0 + (z * -6.0)); end
code[x_, y_, z_] := N[(x * N[(1.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x \cdot \left(1 + z \cdot -6\right)
\end{array}
(FPCore (x y z) :precision binary64 x)
double code(double x, double y, double z) {
return x;
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x
end function
public static double code(double x, double y, double z) {
return x;
}
def code(x, y, z): return x
function code(x, y, z) return x end
function tmp = code(x, y, z) tmp = x; end
code[x_, y_, z_] := x
\begin{array}{l}
\\
x
\end{array}
(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))
double code(double x, double y, double z) {
return x - ((6.0 * z) * (x - y));
}
real(8) function code(x, y, z)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8), intent (in) :: z
code = x - ((6.0d0 * z) * (x - y))
end function
public static double code(double x, double y, double z) {
return x - ((6.0 * z) * (x - y));
}
def code(x, y, z): return x - ((6.0 * z) * (x - y))
function code(x, y, z) return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y))) end
function tmp = code(x, y, z) tmp = x - ((6.0 * z) * (x - y)); end
code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
x - \left(6 \cdot z\right) \cdot \left(x - y\right)
\end{array}
herbie shell --seed 2023343
(FPCore (x y z)
:name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
:precision binary64
:herbie-target
(- x (* (* 6.0 z) (- x y)))
(+ x (* (* (- y x) 6.0) z)))