
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
double code(double x, double y) {
return (x - y) / (x + y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (x + y)
end function
public static double code(double x, double y) {
return (x - y) / (x + y);
}
def code(x, y): return (x - y) / (x + y)
function code(x, y) return Float64(Float64(x - y) / Float64(x + y)) end
function tmp = code(x, y) tmp = (x - y) / (x + y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{x + y}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 7 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
double code(double x, double y) {
return (x - y) / (x + y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (x + y)
end function
public static double code(double x, double y) {
return (x - y) / (x + y);
}
def code(x, y): return (x - y) / (x + y)
function code(x, y) return Float64(Float64(x - y) / Float64(x + y)) end
function tmp = code(x, y) tmp = (x - y) / (x + y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{x + y}
\end{array}
(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))
double code(double x, double y) {
return (x / (x + y)) - (y / (x + y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x / (x + y)) - (y / (x + y))
end function
public static double code(double x, double y) {
return (x / (x + y)) - (y / (x + y));
}
def code(x, y): return (x / (x + y)) - (y / (x + y))
function code(x, y) return Float64(Float64(x / Float64(x + y)) - Float64(y / Float64(x + y))) end
function tmp = code(x, y) tmp = (x / (x + y)) - (y / (x + y)); end
code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{x + y} - \frac{y}{x + y}
\end{array}
Initial program 100.0%
lift-+.f64N/A
div-subN/A
lower--.f64N/A
lower-/.f64N/A
lower-/.f64100.0
Applied egg-rr100.0%
(FPCore (x y) :precision binary64 (if (<= (/ (- x y) (+ x y)) -0.5) (+ -1.0 (/ (+ x x) y)) 1.0))
double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -1.0 + ((x + x) / y);
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (((x - y) / (x + y)) <= (-0.5d0)) then
tmp = (-1.0d0) + ((x + x) / y)
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -1.0 + ((x + x) / y);
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if ((x - y) / (x + y)) <= -0.5: tmp = -1.0 + ((x + x) / y) else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5) tmp = Float64(-1.0 + Float64(Float64(x + x) / y)); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (((x - y) / (x + y)) <= -0.5) tmp = -1.0 + ((x + x) / y); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 + N[(N[(x + x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], 1.0]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\
\;\;\;\;-1 + \frac{x + x}{y}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5Initial program 100.0%
Taylor expanded in x around 0
sub-negN/A
*-lft-identityN/A
associate-*l/N/A
associate-*l*N/A
metadata-evalN/A
+-commutativeN/A
lower-+.f64N/A
associate-*r/N/A
metadata-evalN/A
associate-*l/N/A
metadata-evalN/A
distribute-rgt1-inN/A
metadata-evalN/A
cancel-sign-sub-invN/A
lower-/.f64N/A
cancel-sign-sub-invN/A
metadata-evalN/A
*-lft-identityN/A
lower-+.f6499.4
Simplified99.4%
if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y)) Initial program 100.0%
Taylor expanded in x around inf
Simplified97.3%
(FPCore (x y) :precision binary64 (if (<= (/ (- x y) (+ x y)) -0.5) (- (/ y (+ x y))) 1.0))
double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -(y / (x + y));
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (((x - y) / (x + y)) <= (-0.5d0)) then
tmp = -(y / (x + y))
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -(y / (x + y));
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if ((x - y) / (x + y)) <= -0.5: tmp = -(y / (x + y)) else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5) tmp = Float64(-Float64(y / Float64(x + y))); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (((x - y) / (x + y)) <= -0.5) tmp = -(y / (x + y)); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], (-N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), 1.0]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\
\;\;\;\;-\frac{y}{x + y}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5Initial program 100.0%
Taylor expanded in x around 0
mul-1-negN/A
lower-neg.f6498.3
Simplified98.3%
if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y)) Initial program 100.0%
Taylor expanded in x around inf
Simplified97.3%
Final simplification97.8%
(FPCore (x y) :precision binary64 (if (<= (/ (- x y) (+ x y)) -0.5) (+ -1.0 (/ x y)) 1.0))
double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -1.0 + (x / y);
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (((x - y) / (x + y)) <= (-0.5d0)) then
tmp = (-1.0d0) + (x / y)
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -0.5) {
tmp = -1.0 + (x / y);
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if ((x - y) / (x + y)) <= -0.5: tmp = -1.0 + (x / y) else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (Float64(Float64(x - y) / Float64(x + y)) <= -0.5) tmp = Float64(-1.0 + Float64(x / y)); else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (((x - y) / (x + y)) <= -0.5) tmp = -1.0 + (x / y); else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -0.5], N[(-1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], 1.0]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{x + y} \leq -0.5:\\
\;\;\;\;-1 + \frac{x}{y}\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if (/.f64 (-.f64 x y) (+.f64 x y)) < -0.5Initial program 100.0%
Taylor expanded in x around 0
mul-1-negN/A
lower-neg.f6498.3
Simplified98.3%
Taylor expanded in y around inf
sub-negN/A
metadata-evalN/A
+-commutativeN/A
lower-+.f64N/A
lower-/.f6498.3
Simplified98.3%
if -0.5 < (/.f64 (-.f64 x y) (+.f64 x y)) Initial program 100.0%
Taylor expanded in x around inf
Simplified97.3%
(FPCore (x y) :precision binary64 (if (<= (/ (- x y) (+ x y)) -4e-311) -1.0 1.0))
double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -4e-311) {
tmp = -1.0;
} else {
tmp = 1.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (((x - y) / (x + y)) <= (-4d-311)) then
tmp = -1.0d0
else
tmp = 1.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (((x - y) / (x + y)) <= -4e-311) {
tmp = -1.0;
} else {
tmp = 1.0;
}
return tmp;
}
def code(x, y): tmp = 0 if ((x - y) / (x + y)) <= -4e-311: tmp = -1.0 else: tmp = 1.0 return tmp
function code(x, y) tmp = 0.0 if (Float64(Float64(x - y) / Float64(x + y)) <= -4e-311) tmp = -1.0; else tmp = 1.0; end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (((x - y) / (x + y)) <= -4e-311) tmp = -1.0; else tmp = 1.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision], -4e-311], -1.0, 1.0]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;\frac{x - y}{x + y} \leq -4 \cdot 10^{-311}:\\
\;\;\;\;-1\\
\mathbf{else}:\\
\;\;\;\;1\\
\end{array}
\end{array}
if (/.f64 (-.f64 x y) (+.f64 x y)) < -3.99999999999979e-311Initial program 100.0%
Taylor expanded in x around 0
Simplified98.2%
if -3.99999999999979e-311 < (/.f64 (-.f64 x y) (+.f64 x y)) Initial program 100.0%
Taylor expanded in x around inf
Simplified97.3%
(FPCore (x y) :precision binary64 (/ (- x y) (+ x y)))
double code(double x, double y) {
return (x - y) / (x + y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x - y) / (x + y)
end function
public static double code(double x, double y) {
return (x - y) / (x + y);
}
def code(x, y): return (x - y) / (x + y)
function code(x, y) return Float64(Float64(x - y) / Float64(x + y)) end
function tmp = code(x, y) tmp = (x - y) / (x + y); end
code[x_, y_] := N[(N[(x - y), $MachinePrecision] / N[(x + y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x - y}{x + y}
\end{array}
Initial program 100.0%
(FPCore (x y) :precision binary64 -1.0)
double code(double x, double y) {
return -1.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = -1.0d0
end function
public static double code(double x, double y) {
return -1.0;
}
def code(x, y): return -1.0
function code(x, y) return -1.0 end
function tmp = code(x, y) tmp = -1.0; end
code[x_, y_] := -1.0
\begin{array}{l}
\\
-1
\end{array}
Initial program 100.0%
Taylor expanded in x around 0
Simplified48.0%
(FPCore (x y) :precision binary64 (- (/ x (+ x y)) (/ y (+ x y))))
double code(double x, double y) {
return (x / (x + y)) - (y / (x + y));
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = (x / (x + y)) - (y / (x + y))
end function
public static double code(double x, double y) {
return (x / (x + y)) - (y / (x + y));
}
def code(x, y): return (x / (x + y)) - (y / (x + y))
function code(x, y) return Float64(Float64(x / Float64(x + y)) - Float64(y / Float64(x + y))) end
function tmp = code(x, y) tmp = (x / (x + y)) - (y / (x + y)); end
code[x_, y_] := N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{x}{x + y} - \frac{y}{x + y}
\end{array}
herbie shell --seed 2024208
(FPCore (x y)
:name "Data.Colour.RGB:hslsv from colour-2.3.3, D"
:precision binary64
:alt
(! :herbie-platform default (- (/ x (+ x y)) (/ y (+ x y))))
(/ (- x y) (+ x y)))