Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.3% → 99.2%
Time: 5.7s
Alternatives: 4
Speedup: 0.5×

Specification

?
\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]
(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:

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Accuracy vs Speed?

Herbie found 4 alternatives:

AlternativeAccuracySpeedup
The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Initial Program: 77.3% accurate, 1.0× speedup?

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]
(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}

Alternative 1: 99.2% accurate, 0.1× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\ t_1 := \frac{x \cdot 2}{\frac{x}{y} + -1}\\ \mathbf{if}\;t\_0 \leq -1 \cdot 10^{-9}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-305}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-22}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (* x 2.0) y) (- x y))) (t_1 (/ (* x 2.0) (+ (/ x y) -1.0))))
   (if (<= t_0 -1e-9)
     t_1
     (if (<= t_0 -2e-305)
       t_0
       (if (<= t_0 0.0)
         t_1
         (if (<= t_0 2e-22) t_0 (* x (* 2.0 (/ y (- x y))))))))))
double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = (x * 2.0) / ((x / y) + -1.0);
	double tmp;
	if (t_0 <= -1e-9) {
		tmp = t_1;
	} else if (t_0 <= -2e-305) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-22) {
		tmp = t_0;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = ((x * 2.0d0) * y) / (x - y)
    t_1 = (x * 2.0d0) / ((x / y) + (-1.0d0))
    if (t_0 <= (-1d-9)) then
        tmp = t_1
    else if (t_0 <= (-2d-305)) then
        tmp = t_0
    else if (t_0 <= 0.0d0) then
        tmp = t_1
    else if (t_0 <= 2d-22) then
        tmp = t_0
    else
        tmp = x * (2.0d0 * (y / (x - y)))
    end if
    code = tmp
end function
public static double code(double x, double y) {
	double t_0 = ((x * 2.0) * y) / (x - y);
	double t_1 = (x * 2.0) / ((x / y) + -1.0);
	double tmp;
	if (t_0 <= -1e-9) {
		tmp = t_1;
	} else if (t_0 <= -2e-305) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = t_1;
	} else if (t_0 <= 2e-22) {
		tmp = t_0;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}
def code(x, y):
	t_0 = ((x * 2.0) * y) / (x - y)
	t_1 = (x * 2.0) / ((x / y) + -1.0)
	tmp = 0
	if t_0 <= -1e-9:
		tmp = t_1
	elif t_0 <= -2e-305:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = t_1
	elif t_0 <= 2e-22:
		tmp = t_0
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp
function code(x, y)
	t_0 = Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
	t_1 = Float64(Float64(x * 2.0) / Float64(Float64(x / y) + -1.0))
	tmp = 0.0
	if (t_0 <= -1e-9)
		tmp = t_1;
	elseif (t_0 <= -2e-305)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-22)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	end
	return tmp
end
function tmp_2 = code(x, y)
	t_0 = ((x * 2.0) * y) / (x - y);
	t_1 = (x * 2.0) / ((x / y) + -1.0);
	tmp = 0.0;
	if (t_0 <= -1e-9)
		tmp = t_1;
	elseif (t_0 <= -2e-305)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = t_1;
	elseif (t_0 <= 2e-22)
		tmp = t_0;
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end
code[x_, y_] := Block[{t$95$0 = N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -1e-9], t$95$1, If[LessEqual[t$95$0, -2e-305], t$95$0, If[LessEqual[t$95$0, 0.0], t$95$1, If[LessEqual[t$95$0, 2e-22], t$95$0, N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]
\begin{array}{l}

\\
\begin{array}{l}
t_0 := \frac{\left(x \cdot 2\right) \cdot y}{x - y}\\
t_1 := \frac{x \cdot 2}{\frac{x}{y} + -1}\\
\mathbf{if}\;t\_0 \leq -1 \cdot 10^{-9}:\\
\;\;\;\;t\_1\\

\mathbf{elif}\;t\_0 \leq -2 \cdot 10^{-305}:\\
\;\;\;\;t\_0\\

\mathbf{elif}\;t\_0 \leq 0:\\
\;\;\;\;t\_1\\

\mathbf{elif}\;t\_0 \leq 2 \cdot 10^{-22}:\\
\;\;\;\;t\_0\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\


\end{array}
\end{array}
Derivation
  1. Split input into 3 regimes
  2. if (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -1.00000000000000006e-9 or -1.99999999999999999e-305 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -0.0

    1. Initial program 33.9%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*99.8%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*99.8%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified99.8%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
    5. Step-by-step derivation
      1. associate-*r*99.8%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. clear-num99.7%

        \[\leadsto \left(x \cdot 2\right) \cdot \color{blue}{\frac{1}{\frac{x - y}{y}}} \]
      3. un-div-inv99.9%

        \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
    6. Applied egg-rr99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x - y}{y}}} \]
    7. Step-by-step derivation
      1. div-sub99.9%

        \[\leadsto \frac{x \cdot 2}{\color{blue}{\frac{x}{y} - \frac{y}{y}}} \]
      2. sub-neg99.9%

        \[\leadsto \frac{x \cdot 2}{\color{blue}{\frac{x}{y} + \left(-\frac{y}{y}\right)}} \]
      3. *-inverses99.9%

        \[\leadsto \frac{x \cdot 2}{\frac{x}{y} + \left(-\color{blue}{1}\right)} \]
      4. metadata-eval99.9%

        \[\leadsto \frac{x \cdot 2}{\frac{x}{y} + \color{blue}{-1}} \]
    8. Simplified99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{\frac{x}{y} + -1}} \]

    if -1.00000000000000006e-9 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < -1.99999999999999999e-305 or -0.0 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y)) < 2.0000000000000001e-22

    1. Initial program 98.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Add Preprocessing

    if 2.0000000000000001e-22 < (/.f64 (*.f64 (*.f64 x #s(literal 2 binary64)) y) (-.f64 x y))

    1. Initial program 50.2%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*100.0%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*100.0%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified100.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
  3. Recombined 3 regimes into one program.
  4. Add Preprocessing

Alternative 2: 94.0% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+163} \lor \neg \left(x \leq 1.65 \cdot 10^{+189}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= x -9e+163) (not (<= x 1.65e+189)))
   (* 2.0 y)
   (* x (* 2.0 (/ y (- x y))))))
double code(double x, double y) {
	double tmp;
	if ((x <= -9e+163) || !(x <= 1.65e+189)) {
		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 <= (-9d+163)) .or. (.not. (x <= 1.65d+189))) 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 <= -9e+163) || !(x <= 1.65e+189)) {
		tmp = 2.0 * y;
	} else {
		tmp = x * (2.0 * (y / (x - y)));
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (x <= -9e+163) or not (x <= 1.65e+189):
		tmp = 2.0 * y
	else:
		tmp = x * (2.0 * (y / (x - y)))
	return tmp
function code(x, y)
	tmp = 0.0
	if ((x <= -9e+163) || !(x <= 1.65e+189))
		tmp = Float64(2.0 * y);
	else
		tmp = Float64(x * Float64(2.0 * Float64(y / Float64(x - y))));
	end
	return tmp
end
function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -9e+163) || ~((x <= 1.65e+189)))
		tmp = 2.0 * y;
	else
		tmp = x * (2.0 * (y / (x - y)));
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[x, -9e+163], N[Not[LessEqual[x, 1.65e+189]], $MachinePrecision]], N[(2.0 * y), $MachinePrecision], N[(x * N[(2.0 * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;x \leq -9 \cdot 10^{+163} \lor \neg \left(x \leq 1.65 \cdot 10^{+189}\right):\\
\;\;\;\;2 \cdot y\\

\mathbf{else}:\\
\;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if x < -8.99999999999999976e163 or 1.6500000000000001e189 < x

    1. Initial program 75.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*58.6%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*58.6%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified58.6%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
    5. Taylor expanded in x around inf 97.5%

      \[\leadsto \color{blue}{2 \cdot y} \]
    6. Step-by-step derivation
      1. *-commutative97.5%

        \[\leadsto \color{blue}{y \cdot 2} \]
    7. Simplified97.5%

      \[\leadsto \color{blue}{y \cdot 2} \]

    if -8.99999999999999976e163 < x < 1.6500000000000001e189

    1. Initial program 75.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*94.2%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*94.2%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified94.2%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
  3. Recombined 2 regimes into one program.
  4. Final simplification94.8%

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9 \cdot 10^{+163} \lor \neg \left(x \leq 1.65 \cdot 10^{+189}\right):\\ \;\;\;\;2 \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(2 \cdot \frac{y}{x - y}\right)\\ \end{array} \]
  5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.7× speedup?

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+83} \lor \neg \left(y \leq 52\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \end{array} \]
(FPCore (x y)
 :precision binary64
 (if (or (<= y -4.4e+83) (not (<= y 52.0))) (* x -2.0) (* 2.0 y)))
double code(double x, double y) {
	double tmp;
	if ((y <= -4.4e+83) || !(y <= 52.0)) {
		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 <= (-4.4d+83)) .or. (.not. (y <= 52.0d0))) 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 <= -4.4e+83) || !(y <= 52.0)) {
		tmp = x * -2.0;
	} else {
		tmp = 2.0 * y;
	}
	return tmp;
}
def code(x, y):
	tmp = 0
	if (y <= -4.4e+83) or not (y <= 52.0):
		tmp = x * -2.0
	else:
		tmp = 2.0 * y
	return tmp
function code(x, y)
	tmp = 0.0
	if ((y <= -4.4e+83) || !(y <= 52.0))
		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 <= -4.4e+83) || ~((y <= 52.0)))
		tmp = x * -2.0;
	else
		tmp = 2.0 * y;
	end
	tmp_2 = tmp;
end
code[x_, y_] := If[Or[LessEqual[y, -4.4e+83], N[Not[LessEqual[y, 52.0]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(2.0 * y), $MachinePrecision]]
\begin{array}{l}

\\
\begin{array}{l}
\mathbf{if}\;y \leq -4.4 \cdot 10^{+83} \lor \neg \left(y \leq 52\right):\\
\;\;\;\;x \cdot -2\\

\mathbf{else}:\\
\;\;\;\;2 \cdot y\\


\end{array}
\end{array}
Derivation
  1. Split input into 2 regimes
  2. if y < -4.39999999999999997e83 or 52 < y

    1. Initial program 72.5%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*100.0%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*100.0%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified100.0%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
    5. Taylor expanded in y around inf 87.2%

      \[\leadsto x \cdot \color{blue}{-2} \]

    if -4.39999999999999997e83 < y < 52

    1. Initial program 78.1%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
    2. Step-by-step derivation
      1. associate-/l*78.7%

        \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
      2. associate-*l*78.7%

        \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    3. Simplified78.7%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
    4. Add Preprocessing
    5. Taylor expanded in x around inf 76.9%

      \[\leadsto \color{blue}{2 \cdot y} \]
    6. Step-by-step derivation
      1. *-commutative76.9%

        \[\leadsto \color{blue}{y \cdot 2} \]
    7. Simplified76.9%

      \[\leadsto \color{blue}{y \cdot 2} \]
  3. Recombined 2 regimes into one program.
  4. Final simplification81.3%

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.4 \cdot 10^{+83} \lor \neg \left(y \leq 52\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;2 \cdot y\\ \end{array} \]
  5. Add Preprocessing

Alternative 4: 51.2% accurate, 3.0× speedup?

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]
(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}
Derivation
  1. Initial program 75.8%

    \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
  2. Step-by-step derivation
    1. associate-/l*87.6%

      \[\leadsto \color{blue}{\left(x \cdot 2\right) \cdot \frac{y}{x - y}} \]
    2. associate-*l*87.6%

      \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
  3. Simplified87.6%

    \[\leadsto \color{blue}{x \cdot \left(2 \cdot \frac{y}{x - y}\right)} \]
  4. Add Preprocessing
  5. Taylor expanded in y around inf 51.4%

    \[\leadsto x \cdot \color{blue}{-2} \]
  6. Add Preprocessing

Developer Target 1: 99.6% accurate, 0.5× speedup?

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]
(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}

Reproduce

?
herbie shell --seed 2024135 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< x -1721044263414944700000000000000000000000000000000000000000000000000000000000000000) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564430) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y))))

  (/ (* (* x 2.0) y) (- x y)))