
(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))
double code(double x, double y) {
return ((x * 2.0) * y) / (x - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x * 2.0d0) * y) / (x - y)
end function
public static double code(double x, double y) {
return ((x * 2.0) * y) / (x - y);
}
def code(x, y): return ((x * 2.0) * y) / (x - y)
function code(x, y) return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y)) end
function tmp = code(x, y) tmp = ((x * 2.0) * y) / (x - y); end
code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
\end{array}
Sampling outcomes in binary64 precision:
Herbie found 5 alternatives:
| Alternative | Accuracy | Speedup |
|---|
(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))
double code(double x, double y) {
return ((x * 2.0) * y) / (x - y);
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = ((x * 2.0d0) * y) / (x - y)
end function
public static double code(double x, double y) {
return ((x * 2.0) * y) / (x - y);
}
def code(x, y): return ((x * 2.0) * y) / (x - y)
function code(x, y) return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y)) end
function tmp = code(x, y) tmp = ((x * 2.0) * y) / (x - y); end
code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]
\begin{array}{l}
\\
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
\end{array}
(FPCore (x y) :precision binary64 (if (or (<= x -4.4e+135) (not (<= x 1.55e-81))) (* y (/ (* x 2.0) (- x y))) (/ (* x 2.0) (/ (- x y) y))))
double code(double x, double y) {
double tmp;
if ((x <= -4.4e+135) || !(x <= 1.55e-81)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = (x * 2.0) / ((x - y) / y);
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= (-4.4d+135)) .or. (.not. (x <= 1.55d-81))) then
tmp = y * ((x * 2.0d0) / (x - y))
else
tmp = (x * 2.0d0) / ((x - y) / y)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -4.4e+135) || !(x <= 1.55e-81)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = (x * 2.0) / ((x - y) / y);
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -4.4e+135) or not (x <= 1.55e-81): tmp = y * ((x * 2.0) / (x - y)) else: tmp = (x * 2.0) / ((x - y) / y) return tmp
function code(x, y) tmp = 0.0 if ((x <= -4.4e+135) || !(x <= 1.55e-81)) tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y))); else tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y)); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -4.4e+135) || ~((x <= 1.55e-81))) tmp = y * ((x * 2.0) / (x - y)); else tmp = (x * 2.0) / ((x - y) / y); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -4.4e+135], N[Not[LessEqual[x, 1.55e-81]], $MachinePrecision]], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.4 \cdot 10^{+135} \lor \neg \left(x \leq 1.55 \cdot 10^{-81}\right):\\
\;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\
\mathbf{else}:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\
\end{array}
\end{array}
if x < -4.3999999999999999e135 or 1.54999999999999994e-81 < x Initial program 80.3%
associate-*l/99.9%
Simplified99.9%
if -4.3999999999999999e135 < x < 1.54999999999999994e-81Initial program 75.9%
associate-/l*100.0%
Simplified100.0%
Final simplification100.0%
(FPCore (x y) :precision binary64 (if (or (<= x -1.3e+193) (not (<= x 2.25e+115))) (* 2.0 y) (* (* x 2.0) (/ y (- x y)))))
double code(double x, double y) {
double tmp;
if ((x <= -1.3e+193) || !(x <= 2.25e+115)) {
tmp = 2.0 * y;
} else {
tmp = (x * 2.0) * (y / (x - y));
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= (-1.3d+193)) .or. (.not. (x <= 2.25d+115))) then
tmp = 2.0d0 * y
else
tmp = (x * 2.0d0) * (y / (x - y))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -1.3e+193) || !(x <= 2.25e+115)) {
tmp = 2.0 * y;
} else {
tmp = (x * 2.0) * (y / (x - y));
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -1.3e+193) or not (x <= 2.25e+115): tmp = 2.0 * y else: tmp = (x * 2.0) * (y / (x - y)) return tmp
function code(x, y) tmp = 0.0 if ((x <= -1.3e+193) || !(x <= 2.25e+115)) tmp = Float64(2.0 * y); else tmp = Float64(Float64(x * 2.0) * Float64(y / Float64(x - y))); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -1.3e+193) || ~((x <= 2.25e+115))) tmp = 2.0 * y; else tmp = (x * 2.0) * (y / (x - y)); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -1.3e+193], N[Not[LessEqual[x, 2.25e+115]], $MachinePrecision]], N[(2.0 * y), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.3 \cdot 10^{+193} \lor \neg \left(x \leq 2.25 \cdot 10^{+115}\right):\\
\;\;\;\;2 \cdot y\\
\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\
\end{array}
\end{array}
if x < -1.30000000000000007e193 or 2.24999999999999982e115 < x Initial program 76.2%
associate-*l/100.0%
Simplified100.0%
Taylor expanded in x around inf 94.2%
if -1.30000000000000007e193 < x < 2.24999999999999982e115Initial program 78.4%
associate-/l*99.0%
Simplified99.0%
clear-num98.8%
associate-/r/98.9%
clear-num99.0%
Applied egg-rr99.0%
Final simplification97.8%
(FPCore (x y) :precision binary64 (if (or (<= x -4.4e+135) (not (<= x 4e-45))) (* y (/ (* x 2.0) (- x y))) (* (* x 2.0) (/ y (- x y)))))
double code(double x, double y) {
double tmp;
if ((x <= -4.4e+135) || !(x <= 4e-45)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = (x * 2.0) * (y / (x - y));
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= (-4.4d+135)) .or. (.not. (x <= 4d-45))) then
tmp = y * ((x * 2.0d0) / (x - y))
else
tmp = (x * 2.0d0) * (y / (x - y))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -4.4e+135) || !(x <= 4e-45)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = (x * 2.0) * (y / (x - y));
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -4.4e+135) or not (x <= 4e-45): tmp = y * ((x * 2.0) / (x - y)) else: tmp = (x * 2.0) * (y / (x - y)) return tmp
function code(x, y) tmp = 0.0 if ((x <= -4.4e+135) || !(x <= 4e-45)) tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y))); else tmp = Float64(Float64(x * 2.0) * Float64(y / Float64(x - y))); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -4.4e+135) || ~((x <= 4e-45))) tmp = y * ((x * 2.0) / (x - y)); else tmp = (x * 2.0) * (y / (x - y)); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -4.4e+135], N[Not[LessEqual[x, 4e-45]], $MachinePrecision]], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x * 2.0), $MachinePrecision] * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -4.4 \cdot 10^{+135} \lor \neg \left(x \leq 4 \cdot 10^{-45}\right):\\
\;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\
\mathbf{else}:\\
\;\;\;\;\left(x \cdot 2\right) \cdot \frac{y}{x - y}\\
\end{array}
\end{array}
if x < -4.3999999999999999e135 or 3.99999999999999994e-45 < x Initial program 79.7%
associate-*l/99.9%
Simplified99.9%
if -4.3999999999999999e135 < x < 3.99999999999999994e-45Initial program 76.6%
associate-/l*100.0%
Simplified100.0%
clear-num99.7%
associate-/r/99.9%
clear-num99.9%
Applied egg-rr99.9%
Final simplification99.9%
(FPCore (x y) :precision binary64 (if (or (<= y -6.5e+16) (not (<= y 1.55e-21))) (* x -2.0) (* 2.0 y)))
double code(double x, double y) {
double tmp;
if ((y <= -6.5e+16) || !(y <= 1.55e-21)) {
tmp = x * -2.0;
} else {
tmp = 2.0 * y;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-6.5d+16)) .or. (.not. (y <= 1.55d-21))) then
tmp = x * (-2.0d0)
else
tmp = 2.0d0 * y
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -6.5e+16) || !(y <= 1.55e-21)) {
tmp = x * -2.0;
} else {
tmp = 2.0 * y;
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -6.5e+16) or not (y <= 1.55e-21): tmp = x * -2.0 else: tmp = 2.0 * y return tmp
function code(x, y) tmp = 0.0 if ((y <= -6.5e+16) || !(y <= 1.55e-21)) tmp = Float64(x * -2.0); else tmp = Float64(2.0 * y); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -6.5e+16) || ~((y <= 1.55e-21))) tmp = x * -2.0; else tmp = 2.0 * y; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -6.5e+16], N[Not[LessEqual[y, 1.55e-21]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -6.5 \cdot 10^{+16} \lor \neg \left(y \leq 1.55 \cdot 10^{-21}\right):\\
\;\;\;\;x \cdot -2\\
\mathbf{else}:\\
\;\;\;\;2 \cdot y\\
\end{array}
\end{array}
if y < -6.5e16 or 1.5499999999999999e-21 < y Initial program 80.0%
associate-*l/73.5%
Simplified73.5%
Taylor expanded in x around 0 81.6%
if -6.5e16 < y < 1.5499999999999999e-21Initial program 75.9%
associate-*l/99.9%
Simplified99.9%
Taylor expanded in x around inf 78.6%
Final simplification80.0%
(FPCore (x y) :precision binary64 (* x -2.0))
double code(double x, double y) {
return x * -2.0;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
code = x * (-2.0d0)
end function
public static double code(double x, double y) {
return x * -2.0;
}
def code(x, y): return x * -2.0
function code(x, y) return Float64(x * -2.0) end
function tmp = code(x, y) tmp = x * -2.0; end
code[x_, y_] := N[(x * -2.0), $MachinePrecision]
\begin{array}{l}
\\
x \cdot -2
\end{array}
Initial program 77.9%
associate-*l/87.1%
Simplified87.1%
Taylor expanded in x around 0 51.7%
Final simplification51.7%
(FPCore (x y)
:precision binary64
(let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
(if (< x -1.7210442634149447e+81)
t_0
(if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))
double code(double x, double y) {
double t_0 = ((2.0 * x) / (x - y)) * y;
double tmp;
if (x < -1.7210442634149447e+81) {
tmp = t_0;
} else if (x < 83645045635564430.0) {
tmp = (x * 2.0) / ((x - y) / y);
} else {
tmp = t_0;
}
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 = ((2.0d0 * x) / (x - y)) * y
if (x < (-1.7210442634149447d+81)) then
tmp = t_0
else if (x < 83645045635564430.0d0) then
tmp = (x * 2.0d0) / ((x - y) / y)
else
tmp = t_0
end if
code = tmp
end function
public static double code(double x, double y) {
double t_0 = ((2.0 * x) / (x - y)) * y;
double tmp;
if (x < -1.7210442634149447e+81) {
tmp = t_0;
} else if (x < 83645045635564430.0) {
tmp = (x * 2.0) / ((x - y) / y);
} else {
tmp = t_0;
}
return tmp;
}
def code(x, y): t_0 = ((2.0 * x) / (x - y)) * y tmp = 0 if x < -1.7210442634149447e+81: tmp = t_0 elif x < 83645045635564430.0: tmp = (x * 2.0) / ((x - y) / y) else: tmp = t_0 return tmp
function code(x, y) t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y) tmp = 0.0 if (x < -1.7210442634149447e+81) tmp = t_0; elseif (x < 83645045635564430.0) tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y)); else tmp = t_0; end return tmp end
function tmp_2 = code(x, y) t_0 = ((2.0 * x) / (x - y)) * y; tmp = 0.0; if (x < -1.7210442634149447e+81) tmp = t_0; elseif (x < 83645045635564430.0) tmp = (x * 2.0) / ((x - y) / y); else tmp = t_0; end tmp_2 = tmp; end
code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]
\begin{array}{l}
\\
\begin{array}{l}
t_0 := \frac{2 \cdot x}{x - y} \cdot y\\
\mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\
\;\;\;\;t\_0\\
\mathbf{elif}\;x < 83645045635564430:\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\
\mathbf{else}:\\
\;\;\;\;t\_0\\
\end{array}
\end{array}
herbie shell --seed 2024040
(FPCore (x y)
:name "Linear.Projection:perspective from linear-1.19.1.3, B"
:precision binary64
:herbie-target
(if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))
(/ (* (* x 2.0) y) (- x y)))