
(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))
double code(double x, double y) {
return ((x - (16.0 / 116.0)) * 3.0) * y;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function
public static double code(double x, double y) {
return ((x - (16.0 / 116.0)) * 3.0) * y;
}
def code(x, y): return ((x - (16.0 / 116.0)) * 3.0) * y
function code(x, y) return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y) end
function tmp = code(x, y) tmp = ((x - (16.0 / 116.0)) * 3.0) * y; end
code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (* (* (- x (/ 16.0 116.0)) 3.0) y))
double code(double x, double y) {
return ((x - (16.0 / 116.0)) * 3.0) * y;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x - (16.0d0 / 116.0d0)) * 3.0d0) * y
end function
public static double code(double x, double y) {
return ((x - (16.0 / 116.0)) * 3.0) * y;
}
def code(x, y): return ((x - (16.0 / 116.0)) * 3.0) * y
function code(x, y) return Float64(Float64(Float64(x - Float64(16.0 / 116.0)) * 3.0) * y) end
function tmp = code(x, y) tmp = ((x - (16.0 / 116.0)) * 3.0) * y; end
code[x_, y_] := N[(N[(N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] * y), $MachinePrecision]
\begin{array}{l}
\\
\left(\left(x - \frac{16}{116}\right) \cdot 3\right) \cdot y
\end{array}
(FPCore (x y) :precision binary64 (* (+ (* x 3.0) -0.41379310344827586) y))
double code(double x, double y) {
return ((x * 3.0) + -0.41379310344827586) * y;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x * 3.0d0) + (-0.41379310344827586d0)) * y
end function
public static double code(double x, double y) {
return ((x * 3.0) + -0.41379310344827586) * y;
}
def code(x, y): return ((x * 3.0) + -0.41379310344827586) * y
function code(x, y) return Float64(Float64(Float64(x * 3.0) + -0.41379310344827586) * y) end
function tmp = code(x, y) tmp = ((x * 3.0) + -0.41379310344827586) * y; end
code[x_, y_] := N[(N[(N[(x * 3.0), $MachinePrecision] + -0.41379310344827586), $MachinePrecision] * y), $MachinePrecision]
\begin{array}{l}
\\
\left(x \cdot 3 + -0.41379310344827586\right) \cdot y
\end{array}
Initial program 99.7%
lift-*.f64N/A
*-commutativeN/A
lift--.f64N/A
sub-negN/A
distribute-lft-inN/A
*-commutativeN/A
lower-+.f64N/A
lower-*.f64N/A
lift-/.f64N/A
metadata-evalN/A
metadata-evalN/A
metadata-eval99.7
Applied rewrites99.7%
(FPCore (x y)
:precision binary64
(let* ((t_0 (- x (/ 16.0 116.0))))
(if (<= t_0 -0.5)
(* y (* x 3.0))
(if (<= t_0 -0.1) (* y -0.41379310344827586) (* 3.0 (* x y))))))
double code(double x, double y) {
double t_0 = x - (16.0 / 116.0);
double tmp;
if (t_0 <= -0.5) {
tmp = y * (x * 3.0);
} else if (t_0 <= -0.1) {
tmp = y * -0.41379310344827586;
} else {
tmp = 3.0 * (x * y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: tmp
t_0 = x - (16.0d0 / 116.0d0)
if (t_0 <= (-0.5d0)) then
tmp = y * (x * 3.0d0)
else if (t_0 <= (-0.1d0)) then
tmp = y * (-0.41379310344827586d0)
else
tmp = 3.0d0 * (x * y)
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = x - (16.0 / 116.0);
double tmp;
if (t_0 <= -0.5) {
tmp = y * (x * 3.0);
} else if (t_0 <= -0.1) {
tmp = y * -0.41379310344827586;
} else {
tmp = 3.0 * (x * y);
}
return tmp;
}
def code(x, y): t_0 = x - (16.0 / 116.0) tmp = 0 if t_0 <= -0.5: tmp = y * (x * 3.0) elif t_0 <= -0.1: tmp = y * -0.41379310344827586 else: tmp = 3.0 * (x * y) return tmp
function code(x, y) t_0 = Float64(x - Float64(16.0 / 116.0)) tmp = 0.0 if (t_0 <= -0.5) tmp = Float64(y * Float64(x * 3.0)); elseif (t_0 <= -0.1) tmp = Float64(y * -0.41379310344827586); else tmp = Float64(3.0 * Float64(x * y)); end return tmp end
function tmp_2 = code(x, y) t_0 = x - (16.0 / 116.0); tmp = 0.0; if (t_0 <= -0.5) tmp = y * (x * 3.0); elseif (t_0 <= -0.1) tmp = y * -0.41379310344827586; else tmp = 3.0 * (x * y); end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], N[(y * N[(x * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, -0.1], N[(y * -0.41379310344827586), $MachinePrecision], N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x - \frac{16}{116}\\
\mathbf{if}\;t\_0 \leq -0.5:\\
\;\;\;\;y \cdot \left(x \cdot 3\right)\\
\mathbf{elif}\;t\_0 \leq -0.1:\\
\;\;\;\;y \cdot -0.41379310344827586\\
\mathbf{else}:\\
\;\;\;\;3 \cdot \left(x \cdot y\right)\\
\end{array}
\end{array}
if (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.5Initial program 99.6%
Taylor expanded in x around inf
lower-*.f6496.1
Applied rewrites96.1%
if -0.5 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.10000000000000001Initial program 99.8%
Taylor expanded in x around 0
Applied rewrites98.4%
if -0.10000000000000001 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) Initial program 99.7%
Taylor expanded in x around inf
lower-*.f64N/A
lower-*.f6497.9
Applied rewrites97.9%
Final simplification97.7%
(FPCore (x y) :precision binary64 (let* ((t_0 (- x (/ 16.0 116.0))) (t_1 (* 3.0 (* x y)))) (if (<= t_0 -0.5) t_1 (if (<= t_0 -0.1) (* y -0.41379310344827586) t_1))))
double code(double x, double y) {
double t_0 = x - (16.0 / 116.0);
double t_1 = 3.0 * (x * y);
double tmp;
if (t_0 <= -0.5) {
tmp = t_1;
} else if (t_0 <= -0.1) {
tmp = y * -0.41379310344827586;
} else {
tmp = t_1;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: t_0
real(8) :: t_1
real(8) :: tmp
t_0 = x - (16.0d0 / 116.0d0)
t_1 = 3.0d0 * (x * y)
if (t_0 <= (-0.5d0)) then
tmp = t_1
else if (t_0 <= (-0.1d0)) then
tmp = y * (-0.41379310344827586d0)
else
tmp = t_1
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = x - (16.0 / 116.0);
double t_1 = 3.0 * (x * y);
double tmp;
if (t_0 <= -0.5) {
tmp = t_1;
} else if (t_0 <= -0.1) {
tmp = y * -0.41379310344827586;
} else {
tmp = t_1;
}
return tmp;
}
def code(x, y): t_0 = x - (16.0 / 116.0) t_1 = 3.0 * (x * y) tmp = 0 if t_0 <= -0.5: tmp = t_1 elif t_0 <= -0.1: tmp = y * -0.41379310344827586 else: tmp = t_1 return tmp
function code(x, y) t_0 = Float64(x - Float64(16.0 / 116.0)) t_1 = Float64(3.0 * Float64(x * y)) tmp = 0.0 if (t_0 <= -0.5) tmp = t_1; elseif (t_0 <= -0.1) tmp = Float64(y * -0.41379310344827586); else tmp = t_1; end return tmp end
function tmp_2 = code(x, y) t_0 = x - (16.0 / 116.0); t_1 = 3.0 * (x * y); tmp = 0.0; if (t_0 <= -0.5) tmp = t_1; elseif (t_0 <= -0.1) tmp = y * -0.41379310344827586; else tmp = t_1; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(x - N[(16.0 / 116.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(x * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -0.5], t$95$1, If[LessEqual[t$95$0, -0.1], N[(y * -0.41379310344827586), $MachinePrecision], t$95$1]]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := x - \frac{16}{116}\\
t_1 := 3 \cdot \left(x \cdot y\right)\\
\mathbf{if}\;t\_0 \leq -0.5:\\
\;\;\;\;t\_1\\
\mathbf{elif}\;t\_0 \leq -0.1:\\
\;\;\;\;y \cdot -0.41379310344827586\\
\mathbf{else}:\\
\;\;\;\;t\_1\\
\end{array}
\end{array}
if (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.5 or -0.10000000000000001 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) Initial program 99.6%
Taylor expanded in x around inf
lower-*.f64N/A
lower-*.f6496.9
Applied rewrites96.9%
if -0.5 < (-.f64 x (/.f64 #s(literal 16 binary64) #s(literal 116 binary64))) < -0.10000000000000001Initial program 99.8%
Taylor expanded in x around 0
Applied rewrites98.4%
Final simplification97.7%
(FPCore (x y) :precision binary64 (* y (fma x 3.0 -0.41379310344827586)))
double code(double x, double y) {
return y * fma(x, 3.0, -0.41379310344827586);
}
function code(x, y) return Float64(y * fma(x, 3.0, -0.41379310344827586)) end
code[x_, y_] := N[(y * N[(x * 3.0 + -0.41379310344827586), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
y \cdot \mathsf{fma}\left(x, 3, -0.41379310344827586\right)
\end{array}
Initial program 99.7%
lift-*.f64N/A
*-commutativeN/A
lift--.f64N/A
sub-negN/A
distribute-lft-inN/A
*-commutativeN/A
lower-fma.f64N/A
lift-/.f64N/A
metadata-evalN/A
metadata-evalN/A
metadata-eval99.7
Applied rewrites99.7%
Final simplification99.7%
(FPCore (x y) :precision binary64 (* y -0.41379310344827586))
double code(double x, double y) {
return y * -0.41379310344827586;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = y * (-0.41379310344827586d0)
end function
public static double code(double x, double y) {
return y * -0.41379310344827586;
}
def code(x, y): return y * -0.41379310344827586
function code(x, y) return Float64(y * -0.41379310344827586) end
function tmp = code(x, y) tmp = y * -0.41379310344827586; end
code[x_, y_] := N[(y * -0.41379310344827586), $MachinePrecision]
\begin{array}{l}
\\
y \cdot -0.41379310344827586
\end{array}
Initial program 99.7%
Taylor expanded in x around 0
Applied rewrites52.0%
Final simplification52.0%
(FPCore (x y) :precision binary64 (* y (- (* x 3.0) 0.41379310344827586)))
double code(double x, double y) {
return y * ((x * 3.0) - 0.41379310344827586);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = y * ((x * 3.0d0) - 0.41379310344827586d0)
end function
public static double code(double x, double y) {
return y * ((x * 3.0) - 0.41379310344827586);
}
def code(x, y): return y * ((x * 3.0) - 0.41379310344827586)
function code(x, y) return Float64(y * Float64(Float64(x * 3.0) - 0.41379310344827586)) end
function tmp = code(x, y) tmp = y * ((x * 3.0) - 0.41379310344827586); end
code[x_, y_] := N[(y * N[(N[(x * 3.0), $MachinePrecision] - 0.41379310344827586), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
y \cdot \left(x \cdot 3 - 0.41379310344827586\right)
\end{array}
herbie shell --seed 2024233
(FPCore (x y)
:name "Data.Colour.CIE:cieLAB from colour-2.3.3, A"
:precision binary64
:alt
(! :herbie-platform default (* y (- (* x 3) 20689655172413793/50000000000000000)))
(* (* (- x (/ 16.0 116.0)) 3.0) y))