Linear.Projection:inversePerspective from linear-1.19.1.3, B

Percentage Accurate: 77.4% → 100.0%

Time: 2.6s

Alternatives: 3

Speedup: 1.3×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 77.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{y} + \frac{-0.5}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (+ (/ 0.5 y) (/ -0.5 x)))

C

double code(double x, double y) {
	return (0.5 / y) + (-0.5 / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (0.5d0 / y) + ((-0.5d0) / x)
end function

Java

public static double code(double x, double y) {
	return (0.5 / y) + (-0.5 / x);
}

Python

def code(x, y):
	return (0.5 / y) + (-0.5 / x)

Julia

function code(x, y)
	return Float64(Float64(0.5 / y) + Float64(-0.5 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = (0.5 / y) + (-0.5 / x);
end

Wolfram

code[x_, y_] := N[(N[(0.5 / y), $MachinePrecision] + N[(-0.5 / x), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 76.5%

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

   1. div-sub 75.8%

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

   2. sub-neg 75.8%

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

   3. associate-/r* 80.1%

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

   4. associate-/r* 80.1%

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

   5. *-inverses 80.1%

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

   6. metadata-eval 80.1%

      \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(-\frac{y}{\left(x \cdot 2\right) \cdot y}\right) \]

   7. neg-mul-1 80.1%

      \[\leadsto \frac{0.5}{y} + \color{blue}{-1 \cdot \frac{y}{\left(x \cdot 2\right) \cdot y}} \]

   8. metadata-eval 80.1%

      \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{1}{-1}} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

   9. metadata-eval 80.1%

      \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1}}{-1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

   10. times-frac 80.1%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\left(--1\right) \cdot y}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}} \]

   11. distribute-lft-neg-in 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1 \cdot y}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

   12. distribute-rgt-neg-in 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1 \cdot \left(-y\right)}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

   13. neg-mul-1 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

   14. distribute-rgt-neg-out 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

   15. times-frac 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1}{x \cdot 2} \cdot \frac{-y}{-y}} \]

   16. *-inverses 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{1} \]

   17. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{\left(--1\right)} \]

   18. associate-*l/ 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1 \cdot \left(--1\right)}{x \cdot 2}} \]

   19. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \color{blue}{1}}{x \cdot 2} \]

   20. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1}}{x \cdot 2} \]

   21. *-commutative 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{\color{blue}{2 \cdot x}} \]

   22. associate-/r* 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\frac{-1}{2}}{x}} \]

   23. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \frac{0.5}{y} + \frac{-0.5}{x} \]

Alternative 2: 75.1% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-14}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65e-14) (/ -0.5 x) (if (<= y 5.5e-14) (/ 0.5 y) (/ -0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65e-14) {
		tmp = -0.5 / x;
	} else if (y <= 5.5e-14) {
		tmp = 0.5 / y;
	} else {
		tmp = -0.5 / 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 <= (-1.65d-14)) then
        tmp = (-0.5d0) / x
    else if (y <= 5.5d-14) then
        tmp = 0.5d0 / y
    else
        tmp = (-0.5d0) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.65e-14) {
		tmp = -0.5 / x;
	} else if (y <= 5.5e-14) {
		tmp = 0.5 / y;
	} else {
		tmp = -0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65e-14:
		tmp = -0.5 / x
	elif y <= 5.5e-14:
		tmp = 0.5 / y
	else:
		tmp = -0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65e-14)
		tmp = Float64(-0.5 / x);
	elseif (y <= 5.5e-14)
		tmp = Float64(0.5 / y);
	else
		tmp = Float64(-0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65e-14)
		tmp = -0.5 / x;
	elseif (y <= 5.5e-14)
		tmp = 0.5 / y;
	else
		tmp = -0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65e-14], N[(-0.5 / x), $MachinePrecision], If[LessEqual[y, 5.5e-14], N[(0.5 / y), $MachinePrecision], N[(-0.5 / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e-14 or 5.49999999999999991e-14 < y

   1. Initial program 83.9%

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

      1. div-sub 83.8%

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

      2. sub-neg 83.8%

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

      3. associate-/r* 90.4%

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

      4. associate-/r* 90.4%

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

      5. *-inverses 90.4%

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

      6. metadata-eval 90.4%

         \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(-\frac{y}{\left(x \cdot 2\right) \cdot y}\right) \]

      7. neg-mul-1 90.4%

         \[\leadsto \frac{0.5}{y} + \color{blue}{-1 \cdot \frac{y}{\left(x \cdot 2\right) \cdot y}} \]

      8. metadata-eval 90.4%

         \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{1}{-1}} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

      9. metadata-eval 90.4%

         \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1}}{-1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

      10. times-frac 90.4%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\left(--1\right) \cdot y}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}} \]

      11. distribute-lft-neg-in 90.4%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1 \cdot y}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

      12. distribute-rgt-neg-in 90.4%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1 \cdot \left(-y\right)}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

      13. neg-mul-1 90.4%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

      14. distribute-rgt-neg-out 90.4%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

      15. times-frac 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1}{x \cdot 2} \cdot \frac{-y}{-y}} \]

      16. *-inverses 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{1} \]

      17. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{\left(--1\right)} \]

      18. associate-*l/ 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1 \cdot \left(--1\right)}{x \cdot 2}} \]

      19. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \color{blue}{1}}{x \cdot 2} \]

      20. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1}}{x \cdot 2} \]

      21. *-commutative 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{\color{blue}{2 \cdot x}} \]

      22. associate-/r* 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\frac{-1}{2}}{x}} \]

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 78.4%

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

   if -1.6499999999999999e-14 < y < 5.49999999999999991e-14

   1. Initial program 67.9%

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

      1. div-sub 66.4%

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

      2. sub-neg 66.4%

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

      3. associate-/r* 67.9%

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

      4. associate-/r* 67.9%

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

      5. *-inverses 67.9%

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

      6. metadata-eval 67.9%

         \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(-\frac{y}{\left(x \cdot 2\right) \cdot y}\right) \]

      7. neg-mul-1 67.9%

         \[\leadsto \frac{0.5}{y} + \color{blue}{-1 \cdot \frac{y}{\left(x \cdot 2\right) \cdot y}} \]

      8. metadata-eval 67.9%

         \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{1}{-1}} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

      9. metadata-eval 67.9%

         \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1}}{-1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

      10. times-frac 67.9%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\left(--1\right) \cdot y}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}} \]

      11. distribute-lft-neg-in 67.9%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1 \cdot y}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

      12. distribute-rgt-neg-in 67.9%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1 \cdot \left(-y\right)}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

      13. neg-mul-1 67.9%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

      14. distribute-rgt-neg-out 67.9%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

      15. times-frac 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1}{x \cdot 2} \cdot \frac{-y}{-y}} \]

      16. *-inverses 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{1} \]

      17. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{\left(--1\right)} \]

      18. associate-*l/ 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1 \cdot \left(--1\right)}{x \cdot 2}} \]

      19. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \color{blue}{1}}{x \cdot 2} \]

      20. metadata-eval 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1}}{x \cdot 2} \]

      21. *-commutative 100.0%

          \[\leadsto \frac{0.5}{y} + \frac{-1}{\color{blue}{2 \cdot x}} \]

      22. associate-/r* 100.0%

          \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\frac{-1}{2}}{x}} \]

      23. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 74.5%

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

4. Final simplification 76.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{-14}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-14}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \]

Alternative 3: 51.1% accurate, 3.0× speedup

Math

\[\begin{array}{l} \\ \frac{-0.5}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ -0.5 x))

C

double code(double x, double y) {
	return -0.5 / x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-0.5d0) / x
end function

Java

public static double code(double x, double y) {
	return -0.5 / x;
}

Python

def code(x, y):
	return -0.5 / x

Julia

function code(x, y)
	return Float64(-0.5 / x)
end

MATLAB

function tmp = code(x, y)
	tmp = -0.5 / x;
end

Wolfram

code[x_, y_] := N[(-0.5 / x), $MachinePrecision]

Derivation

1. Initial program 76.5%

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

   1. div-sub 75.8%

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

   2. sub-neg 75.8%

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

   3. associate-/r* 80.1%

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

   4. associate-/r* 80.1%

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

   5. *-inverses 80.1%

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

   6. metadata-eval 80.1%

      \[\leadsto \frac{\color{blue}{0.5}}{y} + \left(-\frac{y}{\left(x \cdot 2\right) \cdot y}\right) \]

   7. neg-mul-1 80.1%

      \[\leadsto \frac{0.5}{y} + \color{blue}{-1 \cdot \frac{y}{\left(x \cdot 2\right) \cdot y}} \]

   8. metadata-eval 80.1%

      \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{1}{-1}} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

   9. metadata-eval 80.1%

      \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1}}{-1} \cdot \frac{y}{\left(x \cdot 2\right) \cdot y} \]

   10. times-frac 80.1%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\left(--1\right) \cdot y}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)}} \]

   11. distribute-lft-neg-in 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{--1 \cdot y}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

   12. distribute-rgt-neg-in 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1 \cdot \left(-y\right)}}{-1 \cdot \left(\left(x \cdot 2\right) \cdot y\right)} \]

   13. neg-mul-1 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{-\left(x \cdot 2\right) \cdot y}} \]

   14. distribute-rgt-neg-out 80.1%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \left(-y\right)}{\color{blue}{\left(x \cdot 2\right) \cdot \left(-y\right)}} \]

   15. times-frac 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1}{x \cdot 2} \cdot \frac{-y}{-y}} \]

   16. *-inverses 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{1} \]

   17. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{x \cdot 2} \cdot \color{blue}{\left(--1\right)} \]

   18. associate-*l/ 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{-1 \cdot \left(--1\right)}{x \cdot 2}} \]

   19. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1 \cdot \color{blue}{1}}{x \cdot 2} \]

   20. metadata-eval 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{\color{blue}{-1}}{x \cdot 2} \]

   21. *-commutative 100.0%

       \[\leadsto \frac{0.5}{y} + \frac{-1}{\color{blue}{2 \cdot x}} \]

   22. associate-/r* 100.0%

       \[\leadsto \frac{0.5}{y} + \color{blue}{\frac{\frac{-1}{2}}{x}} \]

   23. metadata-eval 100.0%

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

3. Simplified 100.0%

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

4. Taylor expanded in y around inf 54.2%

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

5. Final simplification 54.2%

   \[\leadsto \frac{-0.5}{x} \]

Developer target: 100.0% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \frac{0.5}{y} - \frac{0.5}{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (/ 0.5 y) (/ 0.5 x)))

C

double code(double x, double y) {
	return (0.5 / y) - (0.5 / x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (0.5d0 / y) - (0.5d0 / x)
end function

Java

public static double code(double x, double y) {
	return (0.5 / y) - (0.5 / x);
}

Python

def code(x, y):
	return (0.5 / y) - (0.5 / x)

Julia

function code(x, y)
	return Float64(Float64(0.5 / y) - Float64(0.5 / x))
end

MATLAB

function tmp = code(x, y)
	tmp = (0.5 / y) - (0.5 / x);
end

Wolfram

code[x_, y_] := N[(N[(0.5 / y), $MachinePrecision] - N[(0.5 / x), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023268 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (- (/ 0.5 y) (/ 0.5 x))

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