Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 77.8% → 99.8%

Time: 3.9s

Alternatives: 4

Speedup: 0.5×

Specification

Math

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

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

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

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 77.8% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

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

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+37} \lor \neg \left(y \leq 5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x \cdot -2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 \cdot \frac{x - y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2e+37) (not (<= y 5e-16)))
   (/ (* x -2.0) (- 1.0 (/ x y)))
   (/ y (* 0.5 (/ (- x y) x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2e+37) || !(y <= 5e-16)) {
		tmp = (x * -2.0) / (1.0 - (x / y));
	} else {
		tmp = y / (0.5 * ((x - y) / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2d+37)) .or. (.not. (y <= 5d-16))) then
        tmp = (x * (-2.0d0)) / (1.0d0 - (x / y))
    else
        tmp = y / (0.5d0 * ((x - y) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2e+37) || !(y <= 5e-16)) {
		tmp = (x * -2.0) / (1.0 - (x / y));
	} else {
		tmp = y / (0.5 * ((x - y) / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2e+37) or not (y <= 5e-16):
		tmp = (x * -2.0) / (1.0 - (x / y))
	else:
		tmp = y / (0.5 * ((x - y) / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2e+37) || !(y <= 5e-16))
		tmp = Float64(Float64(x * -2.0) / Float64(1.0 - Float64(x / y)));
	else
		tmp = Float64(y / Float64(0.5 * Float64(Float64(x - y) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2e+37) || ~((y <= 5e-16)))
		tmp = (x * -2.0) / (1.0 - (x / y));
	else
		tmp = y / (0.5 * ((x - y) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2e+37], N[Not[LessEqual[y, 5e-16]], $MachinePrecision]], N[(N[(x * -2.0), $MachinePrecision] / N[(1.0 - N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y / N[(0.5 * N[(N[(x - y), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.99999999999999991e37 or 5.0000000000000004e-16 < y

   1. Initial program 73.6%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. *-lft-identity 73.6%

         \[\leadsto \color{blue}{1 \cdot \frac{\left(x \cdot 2\right) \cdot y}{x - y}} \]

      2. metadata-eval 73.6%

         \[\leadsto \color{blue}{\frac{-1}{-1}} \cdot \frac{\left(x \cdot 2\right) \cdot y}{x - y} \]

      3. times-frac 73.6%

         \[\leadsto \color{blue}{\frac{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}{-1 \cdot \left(x - y\right)}} \]

      4. neg-mul-1 73.6%

         \[\leadsto \frac{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}{\color{blue}{-\left(x - y\right)}} \]

      5. sub-neg 73.6%

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

      6. +-commutative 73.6%

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

      7. distribute-neg-out 73.6%

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

      8. remove-double-neg 73.6%

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

      9. sub-neg 73.6%

         \[\leadsto \frac{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}{\color{blue}{y - x}} \]

      10. associate-*r* 73.6%

          \[\leadsto \frac{\color{blue}{\left(-1 \cdot \left(x \cdot 2\right)\right) \cdot y}}{y - x} \]

      11. neg-mul-1 73.6%

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

      12. distribute-lft-neg-out 73.6%

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

      13. associate-/l* 100.0%

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

      14. distribute-lft-neg-out 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. metadata-eval 100.0%

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

      17. div-sub 100.0%

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

      18. *-inverses 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\frac{x \cdot -2}{1 - \frac{x}{y}}} \]
   4. Add Preprocessing

   if -1.99999999999999991e37 < y < 5.0000000000000004e-16

   1. Initial program 77.9%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 100.0%

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

      4. *-un-lft-identity 100.0%

         \[\leadsto \frac{y}{\frac{\color{blue}{1 \cdot \left(x - y\right)}}{x \cdot 2}} \]

      5. *-commutative 100.0%

         \[\leadsto \frac{y}{\frac{1 \cdot \left(x - y\right)}{\color{blue}{2 \cdot x}}} \]

      6. times-frac 100.0%

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

      7. metadata-eval 100.0%

         \[\leadsto \frac{y}{\color{blue}{0.5} \cdot \frac{x - y}{x}} \]

   6. Applied egg-rr 100.0%

      \[\leadsto \color{blue}{\frac{y}{0.5 \cdot \frac{x - y}{x}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2 \cdot 10^{+37} \lor \neg \left(y \leq 5 \cdot 10^{-16}\right):\\ \;\;\;\;\frac{x \cdot -2}{1 - \frac{x}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 \cdot \frac{x - y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 93.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+221} \lor \neg \left(y \leq 1.62 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5e+221) (not (<= y 1.62e+122)))
   (* x -2.0)
   (* y (/ (* x 2.0) (- x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5e+221) || !(y <= 1.62e+122)) {
		tmp = x * -2.0;
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5d+221)) .or. (.not. (y <= 1.62d+122))) then
        tmp = x * (-2.0d0)
    else
        tmp = y * ((x * 2.0d0) / (x - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5e+221) || !(y <= 1.62e+122)) {
		tmp = x * -2.0;
	} else {
		tmp = y * ((x * 2.0) / (x - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5e+221) or not (y <= 1.62e+122):
		tmp = x * -2.0
	else:
		tmp = y * ((x * 2.0) / (x - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5e+221) || !(y <= 1.62e+122))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5e+221) || ~((y <= 1.62e+122)))
		tmp = x * -2.0;
	else
		tmp = y * ((x * 2.0) / (x - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5e+221], N[Not[LessEqual[y, 1.62e+122]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.0000000000000002e221 or 1.61999999999999994e122 < y

   1. Initial program 69.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 60.4%

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

   3. Simplified 60.4%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 93.5%

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

   if -5.0000000000000002e221 < y < 1.61999999999999994e122

   1. Initial program 77.7%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 96.0%

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

   3. Simplified 96.0%

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

4. Final simplification 95.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+221} \lor \neg \left(y \leq 1.62 \cdot 10^{+122}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 74.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+30} \lor \neg \left(y \leq 2.8 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2.35e+30) (not (<= y 2.8e+36))) (* x -2.0) (* y 2.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+30) || !(y <= 2.8e+36)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-2.35d+30)) .or. (.not. (y <= 2.8d+36))) then
        tmp = x * (-2.0d0)
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2.35e+30) || !(y <= 2.8e+36)) {
		tmp = x * -2.0;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2.35e+30) or not (y <= 2.8e+36):
		tmp = x * -2.0
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2.35e+30) || !(y <= 2.8e+36))
		tmp = Float64(x * -2.0);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2.35e+30) || ~((y <= 2.8e+36)))
		tmp = x * -2.0;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2.35e+30], N[Not[LessEqual[y, 2.8e+36]], $MachinePrecision]], N[(x * -2.0), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.34999999999999995e30 or 2.8000000000000001e36 < y

   1. Initial program 72.8%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 72.9%

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

   3. Simplified 72.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 81.3%

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

   if -2.34999999999999995e30 < y < 2.8000000000000001e36

   1. Initial program 78.3%

      \[\frac{\left(x \cdot 2\right) \cdot y}{x - y} \]
   2. Step-by-step derivation

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 76.1%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.35 \cdot 10^{+30} \lor \neg \left(y \leq 2.8 \cdot 10^{+36}\right):\\ \;\;\;\;x \cdot -2\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 51.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ x \cdot -2 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* x -2.0))

C

double code(double x, double y) {
	return x * -2.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * (-2.0d0)
end function

Java

public static double code(double x, double y) {
	return x * -2.0;
}

Python

def code(x, y):
	return x * -2.0

Julia

function code(x, y)
	return Float64(x * -2.0)
end

MATLAB

function tmp = code(x, y)
	tmp = x * -2.0;
end

Wolfram

code[x_, y_] := N[(x * -2.0), $MachinePrecision]

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%

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

3. Simplified 87.6%

   \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
4. Add Preprocessing

5. Taylor expanded in x around 0 50.6%

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

6. Final simplification 50.6%

   \[\leadsto x \cdot -2 \]
7. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

(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))))

C

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;
}

Fortran

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

Java

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;
}

Python

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

Julia

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

MATLAB

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

Wolfram

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]]]

Reproduce

herbie shell --seed 2024021 
(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)))