Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 75.9% → 100.0%

Time: 3.5s

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: 75.9% 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 82.3%

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

   1. remove-double-neg 82.3%

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

   2. unsub-neg 82.3%

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

   3. div-sub 82.0%

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

   4. remove-double-neg 82.0%

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

   5. distribute-rgt-neg-out 82.0%

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

   6. distribute-neg-frac 82.0%

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

   7. distribute-frac-neg2 82.0%

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

   8. distribute-rgt-neg-out 82.0%

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

   9. sub-neg 82.0%

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

   10. distribute-rgt-neg-out 82.0%

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

   11. remove-double-neg 82.0%

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

   12. associate-/r* 86.4%

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

   13. associate-/r* 86.4%

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

   14. *-inverses 86.4%

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

   15. metadata-eval 86.4%

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

   16. distribute-frac-neg2 86.4%

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

   17. distribute-rgt-neg-out 86.4%

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

   18. remove-double-neg 86.4%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 100.0%

   \[\leadsto \color{blue}{0.5 \cdot \frac{1}{x} + 0.5 \cdot \frac{1}{y}} \]
6. Step-by-step derivation

   1. associate-*r/ 100.0%

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

   2. metadata-eval 100.0%

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

   3. associate-*r/ 100.0%

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

   4. metadata-eval 100.0%

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

   5. +-commutative 100.0%

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

   6. metadata-eval 100.0%

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

   7. distribute-neg-frac 100.0%

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

   8. unsub-neg 100.0%

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

7. Simplified 100.0%

   \[\leadsto \color{blue}{\frac{0.5}{y} - \frac{-0.5}{x}} \]
8. Add Preprocessing

Alternative 2: 60.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3.4 \cdot 10^{-105}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 3.4e-105) (/ 0.5 y) (/ 0.5 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3.4e-105) {
		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 <= 3.4d-105) 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 <= 3.4e-105) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3.4e-105:
		tmp = 0.5 / y
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3.4e-105)
		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 <= 3.4e-105)
		tmp = 0.5 / y;
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3.4e-105], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 3.39999999999999992e-105

   1. Initial program 81.4%

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

      1. remove-double-neg 81.4%

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

      2. unsub-neg 81.4%

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

      3. div-sub 81.2%

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

      4. remove-double-neg 81.2%

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

      5. distribute-rgt-neg-out 81.2%

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

      6. distribute-neg-frac 81.2%

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

      7. distribute-frac-neg2 81.2%

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

      8. distribute-rgt-neg-out 81.2%

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

      9. sub-neg 81.2%

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

      10. distribute-rgt-neg-out 81.2%

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

      11. remove-double-neg 81.2%

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

      12. associate-/r* 85.3%

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

      13. associate-/r* 85.3%

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

      14. *-inverses 85.3%

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

      15. metadata-eval 85.3%

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

      16. distribute-frac-neg2 85.3%

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

      17. distribute-rgt-neg-out 85.3%

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

      18. remove-double-neg 85.3%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 62.0%

      \[\leadsto \color{blue}{\frac{0.5}{y}} \]

   if 3.39999999999999992e-105 < y

   1. Initial program 83.9%

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

      1. remove-double-neg 83.9%

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

      2. unsub-neg 83.9%

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

      3. div-sub 83.6%

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

      4. remove-double-neg 83.6%

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

      5. distribute-rgt-neg-out 83.6%

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

      6. distribute-neg-frac 83.6%

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

      7. distribute-frac-neg2 83.6%

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

      8. distribute-rgt-neg-out 83.6%

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

      9. sub-neg 83.6%

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

      10. distribute-rgt-neg-out 83.6%

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

      11. remove-double-neg 83.6%

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

      12. associate-/r* 88.6%

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

      13. associate-/r* 88.6%

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

      14. *-inverses 88.6%

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

      15. metadata-eval 88.6%

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

      16. distribute-frac-neg2 88.6%

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

      17. distribute-rgt-neg-out 88.6%

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

      18. remove-double-neg 88.6%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 70.6%

      \[\leadsto \color{blue}{\frac{0.5}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 3: 51.3% 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 82.3%

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

   1. remove-double-neg 82.3%

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

   2. unsub-neg 82.3%

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

   3. div-sub 82.0%

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

   4. remove-double-neg 82.0%

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

   5. distribute-rgt-neg-out 82.0%

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

   6. distribute-neg-frac 82.0%

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

   7. distribute-frac-neg2 82.0%

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

   8. distribute-rgt-neg-out 82.0%

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

   9. sub-neg 82.0%

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

   10. distribute-rgt-neg-out 82.0%

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

   11. remove-double-neg 82.0%

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

   12. associate-/r* 86.4%

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

   13. associate-/r* 86.4%

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

   14. *-inverses 86.4%

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

   15. metadata-eval 86.4%

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

   16. distribute-frac-neg2 86.4%

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

   17. distribute-rgt-neg-out 86.4%

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

   18. remove-double-neg 86.4%

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

3. Simplified 100.0%

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

5. Taylor expanded in y around inf 49.9%

   \[\leadsto \color{blue}{\frac{0.5}{x}} \]
6. Add Preprocessing

Developer target: 100.0% accurate, 1.3× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024096 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

  :alt
  (+ (/ 0.5 x) (/ 0.5 y))

  (/ (+ x y) (* (* x 2.0) y)))