
(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 (<= y -5.5e+26) (not (<= y 2e-13))) (/ (* x 2.0) (/ (- x y) y)) (* y (/ (* x 2.0) (- x y)))))
double code(double x, double y) {
double tmp;
if ((y <= -5.5e+26) || !(y <= 2e-13)) {
tmp = (x * 2.0) / ((x - y) / y);
} else {
tmp = y * ((x * 2.0) / (x - y));
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-5.5d+26)) .or. (.not. (y <= 2d-13))) then
tmp = (x * 2.0d0) / ((x - y) / y)
else
tmp = y * ((x * 2.0d0) / (x - y))
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -5.5e+26) || !(y <= 2e-13)) {
tmp = (x * 2.0) / ((x - y) / y);
} else {
tmp = y * ((x * 2.0) / (x - y));
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -5.5e+26) or not (y <= 2e-13): tmp = (x * 2.0) / ((x - y) / y) else: tmp = y * ((x * 2.0) / (x - y)) return tmp
function code(x, y) tmp = 0.0 if ((y <= -5.5e+26) || !(y <= 2e-13)) tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y)); else tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y))); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -5.5e+26) || ~((y <= 2e-13))) tmp = (x * 2.0) / ((x - y) / y); else tmp = y * ((x * 2.0) / (x - y)); end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -5.5e+26], N[Not[LessEqual[y, 2e-13]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -5.5 \cdot 10^{+26} \lor \neg \left(y \leq 2 \cdot 10^{-13}\right):\\
\;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\
\mathbf{else}:\\
\;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\
\end{array}
\end{array}
if y < -5.4999999999999997e26 or 2.0000000000000001e-13 < y Initial program 83.5%
associate-/l*99.9%
Simplified99.9%
if -5.4999999999999997e26 < y < 2.0000000000000001e-13Initial program 78.4%
associate-*l/100.0%
Simplified100.0%
Final simplification100.0%
(FPCore (x y) :precision binary64 (if (or (<= y -1.95e+49) (not (<= y 8.6e-46))) (* -2.0 (+ x (/ x (/ y x)))) (* y 2.0)))
double code(double x, double y) {
double tmp;
if ((y <= -1.95e+49) || !(y <= 8.6e-46)) {
tmp = -2.0 * (x + (x / (y / x)));
} else {
tmp = y * 2.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((y <= (-1.95d+49)) .or. (.not. (y <= 8.6d-46))) then
tmp = (-2.0d0) * (x + (x / (y / x)))
else
tmp = y * 2.0d0
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((y <= -1.95e+49) || !(y <= 8.6e-46)) {
tmp = -2.0 * (x + (x / (y / x)));
} else {
tmp = y * 2.0;
}
return tmp;
}
def code(x, y): tmp = 0 if (y <= -1.95e+49) or not (y <= 8.6e-46): tmp = -2.0 * (x + (x / (y / x))) else: tmp = y * 2.0 return tmp
function code(x, y) tmp = 0.0 if ((y <= -1.95e+49) || !(y <= 8.6e-46)) tmp = Float64(-2.0 * Float64(x + Float64(x / Float64(y / x)))); else tmp = Float64(y * 2.0); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((y <= -1.95e+49) || ~((y <= 8.6e-46))) tmp = -2.0 * (x + (x / (y / x))); else tmp = y * 2.0; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[y, -1.95e+49], N[Not[LessEqual[y, 8.6e-46]], $MachinePrecision]], N[(-2.0 * N[(x + N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -1.95 \cdot 10^{+49} \lor \neg \left(y \leq 8.6 \cdot 10^{-46}\right):\\
\;\;\;\;-2 \cdot \left(x + \frac{x}{\frac{y}{x}}\right)\\
\mathbf{else}:\\
\;\;\;\;y \cdot 2\\
\end{array}
\end{array}
if y < -1.95e49 or 8.6000000000000007e-46 < y Initial program 84.2%
associate-*l/76.1%
Simplified76.1%
Taylor expanded in x around 0 71.8%
+-commutative71.8%
distribute-lft-out71.8%
unpow271.8%
associate-/l*79.4%
Simplified79.4%
if -1.95e49 < y < 8.6000000000000007e-46Initial program 77.6%
associate-*l/100.0%
Simplified100.0%
Taylor expanded in x around inf 73.7%
Final simplification76.3%
(FPCore (x y) :precision binary64 (if (or (<= x -1.2e-154) (not (<= x 1.05e-111))) (* y (/ (* x 2.0) (- x y))) (* x -2.0)))
double code(double x, double y) {
double tmp;
if ((x <= -1.2e-154) || !(x <= 1.05e-111)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = x * -2.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if ((x <= (-1.2d-154)) .or. (.not. (x <= 1.05d-111))) then
tmp = y * ((x * 2.0d0) / (x - y))
else
tmp = x * (-2.0d0)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if ((x <= -1.2e-154) || !(x <= 1.05e-111)) {
tmp = y * ((x * 2.0) / (x - y));
} else {
tmp = x * -2.0;
}
return tmp;
}
def code(x, y): tmp = 0 if (x <= -1.2e-154) or not (x <= 1.05e-111): tmp = y * ((x * 2.0) / (x - y)) else: tmp = x * -2.0 return tmp
function code(x, y) tmp = 0.0 if ((x <= -1.2e-154) || !(x <= 1.05e-111)) tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y))); else tmp = Float64(x * -2.0); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if ((x <= -1.2e-154) || ~((x <= 1.05e-111))) tmp = y * ((x * 2.0) / (x - y)); else tmp = x * -2.0; end tmp_2 = tmp; end
code[x_, y_] := If[Or[LessEqual[x, -1.2e-154], N[Not[LessEqual[x, 1.05e-111]], $MachinePrecision]], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;x \leq -1.2 \cdot 10^{-154} \lor \neg \left(x \leq 1.05 \cdot 10^{-111}\right):\\
\;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\
\mathbf{else}:\\
\;\;\;\;x \cdot -2\\
\end{array}
\end{array}
if x < -1.19999999999999993e-154 or 1.0499999999999999e-111 < x Initial program 85.7%
associate-*l/99.2%
Simplified99.2%
if -1.19999999999999993e-154 < x < 1.0499999999999999e-111Initial program 69.3%
associate-*l/67.4%
Simplified67.4%
Taylor expanded in x around 0 90.9%
Final simplification96.6%
(FPCore (x y) :precision binary64 (if (<= y -2.8e+49) (* x -2.0) (if (<= y 8.6e-46) (* y 2.0) (* x -2.0))))
double code(double x, double y) {
double tmp;
if (y <= -2.8e+49) {
tmp = x * -2.0;
} else if (y <= 8.6e-46) {
tmp = y * 2.0;
} else {
tmp = x * -2.0;
}
return tmp;
}
real(8) function code(x, y)
real(8), intent (in) :: x
real(8), intent (in) :: y
real(8) :: tmp
if (y <= (-2.8d+49)) then
tmp = x * (-2.0d0)
else if (y <= 8.6d-46) then
tmp = y * 2.0d0
else
tmp = x * (-2.0d0)
end if
code = tmp
end function
public static double code(double x, double y) {
double tmp;
if (y <= -2.8e+49) {
tmp = x * -2.0;
} else if (y <= 8.6e-46) {
tmp = y * 2.0;
} else {
tmp = x * -2.0;
}
return tmp;
}
def code(x, y): tmp = 0 if y <= -2.8e+49: tmp = x * -2.0 elif y <= 8.6e-46: tmp = y * 2.0 else: tmp = x * -2.0 return tmp
function code(x, y) tmp = 0.0 if (y <= -2.8e+49) tmp = Float64(x * -2.0); elseif (y <= 8.6e-46) tmp = Float64(y * 2.0); else tmp = Float64(x * -2.0); end return tmp end
function tmp_2 = code(x, y) tmp = 0.0; if (y <= -2.8e+49) tmp = x * -2.0; elseif (y <= 8.6e-46) tmp = y * 2.0; else tmp = x * -2.0; end tmp_2 = tmp; end
code[x_, y_] := If[LessEqual[y, -2.8e+49], N[(x * -2.0), $MachinePrecision], If[LessEqual[y, 8.6e-46], N[(y * 2.0), $MachinePrecision], N[(x * -2.0), $MachinePrecision]]]
\begin{array}{l}
\\
\begin{array}{l}
\mathbf{if}\;y \leq -2.8 \cdot 10^{+49}:\\
\;\;\;\;x \cdot -2\\
\mathbf{elif}\;y \leq 8.6 \cdot 10^{-46}:\\
\;\;\;\;y \cdot 2\\
\mathbf{else}:\\
\;\;\;\;x \cdot -2\\
\end{array}
\end{array}
if y < -2.7999999999999998e49 or 8.6000000000000007e-46 < y Initial program 84.2%
associate-*l/76.1%
Simplified76.1%
Taylor expanded in x around 0 79.0%
if -2.7999999999999998e49 < y < 8.6000000000000007e-46Initial program 77.6%
associate-*l/100.0%
Simplified100.0%
Taylor expanded in x around inf 73.7%
Final simplification76.1%
(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 80.6%
associate-*l/89.3%
Simplified89.3%
Taylor expanded in x around 0 51.3%
Final simplification51.3%
(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 2023242
(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)))