Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.7% → 94.1%

Time: 5.5s

Alternatives: 4

Speedup: 0.7×

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: 76.7% 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: 94.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{x}, y, 2\right) \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+137}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.04e+155)
   (* (fma (/ 2.0 x) y 2.0) y)
   (if (<= x 1.05e+137) (* (* 2.0 x) (/ y (- x y))) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.04e+155) {
		tmp = fma((2.0 / x), y, 2.0) * y;
	} else if (x <= 1.05e+137) {
		tmp = (2.0 * x) * (y / (x - y));
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.04e+155)
		tmp = Float64(fma(Float64(2.0 / x), y, 2.0) * y);
	elseif (x <= 1.05e+137)
		tmp = Float64(Float64(2.0 * x) * Float64(y / Float64(x - y)));
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.04e+155], N[(N[(N[(2.0 / x), $MachinePrecision] * y + 2.0), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[x, 1.05e+137], N[(N[(2.0 * x), $MachinePrecision] * N[(y / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.03999999999999996e155

   1. Initial program 58.0%

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

   3. Taylor expanded in y around 0

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

      1. *-commutative N/A

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

      2. +-commutative N/A

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

      3. *-lft-identity N/A

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

      4. associate-*l/ N/A

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

      5. associate-*l* N/A

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

      6. *-commutative N/A

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

      7. lower-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-fma.f64 N/A

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

      10. associate-*r/ N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 94.1

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

   5. Applied rewrites 94.1%

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

   if -1.03999999999999996e155 < x < 1.05e137

   1. Initial program 79.8%

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

      1. lift-/.f64 N/A

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

      2. lift-*.f64 N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. lower-*.f64 N/A

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

      6. lower-/.f64 98.1

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

      7. lift-*.f64 N/A

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

      8. *-commutative N/A

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

      9. lower-*.f64 98.1

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

   4. Applied rewrites 98.1%

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

   if 1.05e137 < x

   1. Initial program 69.3%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 90.6

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

   5. Applied rewrites 90.6%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.04 \cdot 10^{+155}:\\ \;\;\;\;\mathsf{fma}\left(\frac{2}{x}, y, 2\right) \cdot y\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+137}:\\ \;\;\;\;\left(2 \cdot x\right) \cdot \frac{y}{x - y}\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.3 \cdot 10^{-9}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+80}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x}{y}, -2, -2\right) \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.3e-9)
   (* y 2.0)
   (if (<= x 4e+80) (* (fma (/ x y) -2.0 -2.0) x) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.3e-9) {
		tmp = y * 2.0;
	} else if (x <= 4e+80) {
		tmp = fma((x / y), -2.0, -2.0) * x;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.3e-9)
		tmp = Float64(y * 2.0);
	elseif (x <= 4e+80)
		tmp = Float64(fma(Float64(x / y), -2.0, -2.0) * x);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.3e-9], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 4e+80], N[(N[(N[(x / y), $MachinePrecision] * -2.0 + -2.0), $MachinePrecision] * x), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.3000000000000001e-9 or 4e80 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if -1.3000000000000001e-9 < x < 4e80

   1. Initial program 78.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-2 \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

   6. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-2 \cdot x + -2 \cdot \frac{{x}^{2}}{y}} \]
   7. Step-by-step derivation

      1. associate-*r/ N/A

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

      2. unpow2 N/A

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

      3. associate-*r* N/A

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

      4. associate-*l/ N/A

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

      5. associate-*r/ N/A

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

      6. distribute-rgt-in N/A

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

      7. +-commutative N/A

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

      8. metadata-eval N/A

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

      9. sub-neg N/A

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

      10. *-commutative N/A

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

      11. lower-*.f64 N/A

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

      12. sub-neg N/A

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

      13. *-commutative N/A

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

      14. metadata-eval N/A

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

      15. lower-fma.f64 N/A

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

      16. lower-/.f64 75.7

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

   8. Applied rewrites 75.7%

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

Alternative 3: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -7.8 \cdot 10^{-8}:\\ \;\;\;\;y \cdot 2\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+80}:\\ \;\;\;\;-2 \cdot x\\ \mathbf{else}:\\ \;\;\;\;y \cdot 2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -7.8e-8) (* y 2.0) (if (<= x 4e+80) (* -2.0 x) (* y 2.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -7.8e-8) {
		tmp = y * 2.0;
	} else if (x <= 4e+80) {
		tmp = -2.0 * x;
	} 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 (x <= (-7.8d-8)) then
        tmp = y * 2.0d0
    else if (x <= 4d+80) then
        tmp = (-2.0d0) * x
    else
        tmp = y * 2.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -7.8e-8) {
		tmp = y * 2.0;
	} else if (x <= 4e+80) {
		tmp = -2.0 * x;
	} else {
		tmp = y * 2.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -7.8e-8:
		tmp = y * 2.0
	elif x <= 4e+80:
		tmp = -2.0 * x
	else:
		tmp = y * 2.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -7.8e-8)
		tmp = Float64(y * 2.0);
	elseif (x <= 4e+80)
		tmp = Float64(-2.0 * x);
	else
		tmp = Float64(y * 2.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -7.8e-8)
		tmp = y * 2.0;
	elseif (x <= 4e+80)
		tmp = -2.0 * x;
	else
		tmp = y * 2.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -7.8e-8], N[(y * 2.0), $MachinePrecision], If[LessEqual[x, 4e+80], N[(-2.0 * x), $MachinePrecision], N[(y * 2.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -7.7999999999999997e-8 or 4e80 < x

   1. Initial program 72.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{2 \cdot y} \]
   4. Step-by-step derivation

      1. *-commutative N/A

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

      2. lower-*.f64 80.6

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

   5. Applied rewrites 80.6%

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

   if -7.7999999999999997e-8 < x < 4e80

   1. Initial program 78.1%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{-2 \cdot x} \]
   4. Step-by-step derivation

      1. lower-*.f64 75.4

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

   5. Applied rewrites 75.4%

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

Alternative 4: 50.0% accurate, 4.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 75.6%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{-2 \cdot x} \]
4. Step-by-step derivation

   1. lower-*.f64 51.3

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

5. Applied rewrites 51.3%

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

Developer Target 1: 99.4% accurate, 0.6× 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 2024270 
(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)))