Linear.Projection:perspective from linear-1.19.1.3, A

Percentage Accurate: 100.0% → 100.0%

Time: 6.6s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (x - y)
end function

Java

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

Python

def code(x, y):
	return (x + y) / (x - y)

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (- x y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (x - y)
end function

Java

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

Python

def code(x, y):
	return (x + y) / (x - y)

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \log \left(e^{\frac{-y}{y - x}}\right) - \frac{x}{y - x} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (- (log (exp (/ (- y) (- y x)))) (/ x (- y x))))

C

double code(double x, double y) {
	return log(exp((-y / (y - x)))) - (x / (y - x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = log(exp((-y / (y - x)))) - (x / (y - x))
end function

Java

public static double code(double x, double y) {
	return Math.log(Math.exp((-y / (y - x)))) - (x / (y - x));
}

Python

def code(x, y):
	return math.log(math.exp((-y / (y - x)))) - (x / (y - x))

Julia

function code(x, y)
	return Float64(log(exp(Float64(Float64(-y) / Float64(y - x)))) - Float64(x / Float64(y - x)))
end

MATLAB

function tmp = code(x, y)
	tmp = log(exp((-y / (y - x)))) - (x / (y - x));
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]
2. Step-by-step derivation

   1. frac-2neg 100.0%

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

   2. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(x + y\right)}}{-\left(x - y\right)} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{0 - \color{blue}{\left(y + x\right)}}{-\left(x - y\right)} \]

   4. associate--r+ 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - y\right) - x}}{-\left(x - y\right)} \]

   5. neg-sub0 100.0%

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

   6. div-sub 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-neg-in 100.0%

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

   9. +-commutative 100.0%

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

   10. remove-double-neg 100.0%

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

   11. sub-neg 100.0%

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

   12. sub-neg 100.0%

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

   13. distribute-neg-in 100.0%

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

   14. +-commutative 100.0%

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

   15. remove-double-neg 100.0%

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

   16. sub-neg 100.0%

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

3. Applied egg-rr 100.0%

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

   1. add-log-exp_binary64 100.0%

      \[\leadsto \color{blue}{\log \left(e^{\frac{-y}{y - x}}\right) - \frac{x}{y - x}} \]

5. Applied rewrite-once 100.0%

   \[\leadsto \color{blue}{\log \left(e^{\frac{-y}{y - x}}\right)} - \frac{x}{y - x} \]

6. Final simplification 100.0%

   \[\leadsto \log \left(e^{\frac{-y}{y - x}}\right) - \frac{x}{y - x} \]

Alternative 2: 73.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-29}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.06e-29) -1.0 (if (<= y 2.4e+82) (+ 1.0 (* 2.0 (/ y x))) -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.06e-29) {
		tmp = -1.0;
	} else if (y <= 2.4e+82) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.06d-29)) then
        tmp = -1.0d0
    else if (y <= 2.4d+82) then
        tmp = 1.0d0 + (2.0d0 * (y / x))
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.06e-29) {
		tmp = -1.0;
	} else if (y <= 2.4e+82) {
		tmp = 1.0 + (2.0 * (y / x));
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.06e-29:
		tmp = -1.0
	elif y <= 2.4e+82:
		tmp = 1.0 + (2.0 * (y / x))
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.06e-29)
		tmp = -1.0;
	elseif (y <= 2.4e+82)
		tmp = Float64(1.0 + Float64(2.0 * Float64(y / x)));
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.06e-29)
		tmp = -1.0;
	elseif (y <= 2.4e+82)
		tmp = 1.0 + (2.0 * (y / x));
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.06e-29], -1.0, If[LessEqual[y, 2.4e+82], N[(1.0 + N[(2.0 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1.05999999999999995e-29 or 2.39999999999999998e82 < y

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]

   2. Taylor expanded in x around 0 80.5%

      \[\leadsto \color{blue}{-1} \]

   if -1.05999999999999995e-29 < y < 2.39999999999999998e82

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]

   2. Taylor expanded in y around 0 81.3%

      \[\leadsto \color{blue}{1 + 2 \cdot \frac{y}{x}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.06 \cdot 10^{-29}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+82}:\\ \;\;\;\;1 + 2 \cdot \frac{y}{x}\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 3: 100.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \frac{y}{x - y} - \frac{x}{y - x} \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y / (x - y)) - (x / (y - x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]
2. Step-by-step derivation

   1. frac-2neg 100.0%

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

   2. neg-sub0 100.0%

      \[\leadsto \frac{\color{blue}{0 - \left(x + y\right)}}{-\left(x - y\right)} \]

   3. +-commutative 100.0%

      \[\leadsto \frac{0 - \color{blue}{\left(y + x\right)}}{-\left(x - y\right)} \]

   4. associate--r+ 100.0%

      \[\leadsto \frac{\color{blue}{\left(0 - y\right) - x}}{-\left(x - y\right)} \]

   5. neg-sub0 100.0%

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

   6. div-sub 100.0%

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

   7. sub-neg 100.0%

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

   8. distribute-neg-in 100.0%

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

   9. +-commutative 100.0%

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

   10. remove-double-neg 100.0%

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

   11. sub-neg 100.0%

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

   12. sub-neg 100.0%

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

   13. distribute-neg-in 100.0%

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

   14. +-commutative 100.0%

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

   15. remove-double-neg 100.0%

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

   16. sub-neg 100.0%

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

3. Applied egg-rr 100.0%

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

   1. add-log-exp_binary64 100.0%

      \[\leadsto \color{blue}{\log \left(e^{\frac{-y}{y - x}}\right) - \frac{x}{y - x}} \]

5. Applied rewrite-once 100.0%

   \[\leadsto \color{blue}{\log \left(e^{\frac{-y}{y - x}}\right)} - \frac{x}{y - x} \]
6. Step-by-step derivation

   1. rem-log-exp 100.0%

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

   2. distribute-frac-neg 100.0%

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

   3. neg-sub0 100.0%

      \[\leadsto \color{blue}{\left(0 - \frac{y}{y - x}\right)} - \frac{x}{y - x} \]

   4. div-inv 99.9%

      \[\leadsto \left(0 - \color{blue}{y \cdot \frac{1}{y - x}}\right) - \frac{x}{y - x} \]

   5. cancel-sign-sub-inv 99.9%

      \[\leadsto \color{blue}{\left(0 + \left(-y\right) \cdot \frac{1}{y - x}\right)} - \frac{x}{y - x} \]

   6. div-inv 100.0%

      \[\leadsto \left(0 + \color{blue}{\frac{-y}{y - x}}\right) - \frac{x}{y - x} \]

   7. frac-2neg 100.0%

      \[\leadsto \left(0 + \color{blue}{\frac{-\left(-y\right)}{-\left(y - x\right)}}\right) - \frac{x}{y - x} \]

   8. remove-double-neg 100.0%

      \[\leadsto \left(0 + \frac{\color{blue}{y}}{-\left(y - x\right)}\right) - \frac{x}{y - x} \]

7. Applied egg-rr 100.0%

   \[\leadsto \color{blue}{\left(0 + \frac{y}{-\left(y - x\right)}\right)} - \frac{x}{y - x} \]
8. Step-by-step derivation

   1. +-lft-identity 100.0%

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

   2. neg-sub0 100.0%

      \[\leadsto \frac{y}{\color{blue}{0 - \left(y - x\right)}} - \frac{x}{y - x} \]

   3. associate-+l- 100.0%

      \[\leadsto \frac{y}{\color{blue}{\left(0 - y\right) + x}} - \frac{x}{y - x} \]

   4. neg-sub0 100.0%

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

   5. +-commutative 100.0%

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

   6. sub-neg 100.0%

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

9. Simplified 100.0%

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

10. Final simplification 100.0%

    \[\leadsto \frac{y}{x - y} - \frac{x}{y - x} \]

Alternative 4: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y + x}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ y x) (- x y)))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + x) / (x - y)
end function

Java

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

Python

def code(x, y):
	return (y + x) / (x - y)

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]

2. Final simplification 100.0%

   \[\leadsto \frac{y + x}{x - y} \]

Alternative 5: 73.4% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.6e-28) -1.0 (if (<= y 2.1e+77) 1.0 -1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-28) {
		tmp = -1.0;
	} else if (y <= 2.1e+77) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.6d-28)) then
        tmp = -1.0d0
    else if (y <= 2.1d+77) then
        tmp = 1.0d0
    else
        tmp = -1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.6e-28) {
		tmp = -1.0;
	} else if (y <= 2.1e+77) {
		tmp = 1.0;
	} else {
		tmp = -1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.6e-28:
		tmp = -1.0
	elif y <= 2.1e+77:
		tmp = 1.0
	else:
		tmp = -1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.6e-28)
		tmp = -1.0;
	elseif (y <= 2.1e+77)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.6e-28)
		tmp = -1.0;
	elseif (y <= 2.1e+77)
		tmp = 1.0;
	else
		tmp = -1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.6e-28], -1.0, If[LessEqual[y, 2.1e+77], 1.0, -1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -4.59999999999999971e-28 or 2.0999999999999999e77 < y

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]

   2. Taylor expanded in x around 0 79.5%

      \[\leadsto \color{blue}{-1} \]

   if -4.59999999999999971e-28 < y < 2.0999999999999999e77

   1. Initial program 100.0%

      \[\frac{x + y}{x - y} \]

   2. Taylor expanded in x around inf 81.3%

      \[\leadsto \color{blue}{1} \]
3. Recombined 2 regimes into one program.

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.6 \cdot 10^{-28}:\\ \;\;\;\;-1\\ \mathbf{elif}\;y \leq 2.1 \cdot 10^{+77}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;-1\\ \end{array} \]

Alternative 6: 48.8% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ -1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 -1.0)

C

double code(double x, double y) {
	return -1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = -1.0d0
end function

Java

public static double code(double x, double y) {
	return -1.0;
}

Python

def code(x, y):
	return -1.0

Julia

function code(x, y)
	return -1.0
end

MATLAB

function tmp = code(x, y)
	tmp = -1.0;
end

Wolfram

code[x_, y_] := -1.0

Derivation

1. Initial program 100.0%

   \[\frac{x + y}{x - y} \]

2. Taylor expanded in x around 0 48.0%

   \[\leadsto \color{blue}{-1} \]

3. Final simplification 48.0%

   \[\leadsto -1 \]

Developer target: 100.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \frac{1}{\frac{x}{x + y} - \frac{y}{x + y}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y)))))

C

double code(double x, double y) {
	return 1.0 / ((x / (x + y)) - (y / (x + y)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 / ((x / (x + y)) - (y / (x + y)))
end function

Java

public static double code(double x, double y) {
	return 1.0 / ((x / (x + y)) - (y / (x + y)));
}

Python

def code(x, y):
	return 1.0 / ((x / (x + y)) - (y / (x + y)))

Julia

function code(x, y)
	return Float64(1.0 / Float64(Float64(x / Float64(x + y)) - Float64(y / Float64(x + y))))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 / ((x / (x + y)) - (y / (x + y)));
end

Wolfram

code[x_, y_] := N[(1.0 / N[(N[(x / N[(x + y), $MachinePrecision]), $MachinePrecision] - N[(y / N[(x + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023297 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (/ 1.0 (- (/ x (+ x y)) (/ y (+ x y))))

  (/ (+ x y) (- x y)))