Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 77.4% → 100.0%

Time: 4.0s

Alternatives: 5

Speedup: 1.0×

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, 1.0× 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 74.9%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \frac{1}{x} + \frac{1}{2} \cdot \frac{1}{y}} \]
4. Step-by-step derivation

   1. +-commutative N/A

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

   2. remove-double-neg N/A

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

   3. associate-*r/ N/A

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

   4. metadata-eval N/A

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

   5. distribute-frac-neg2 N/A

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

   6. mul-1-neg N/A

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

   7. unsub-neg N/A

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

   8. lower--.f64 N/A

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

   9. associate-*r/ N/A

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

   10. metadata-eval N/A

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

   11. lower-/.f64 N/A

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

   12. mul-1-neg N/A

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

   13. distribute-frac-neg2 N/A

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

   14. distribute-neg-frac N/A

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

   15. metadata-eval N/A

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

   16. metadata-eval N/A

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

   17. lower-/.f64 N/A

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

   18. metadata-eval 100.0

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

5. Applied rewrites 100.0%

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

Alternative 2: 66.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-206}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y + x}{\left(2 \cdot x\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8e-206)
   (/ 0.5 y)
   (if (<= y 5.8e-175)
     (/ 0.5 x)
     (if (<= y 5e+70) (/ (+ y x) (* (* 2.0 x) y)) (/ 0.5 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8e-206) {
		tmp = 0.5 / y;
	} else if (y <= 5.8e-175) {
		tmp = 0.5 / x;
	} else if (y <= 5e+70) {
		tmp = (y + x) / ((2.0 * x) * 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 <= 8d-206) then
        tmp = 0.5d0 / y
    else if (y <= 5.8d-175) then
        tmp = 0.5d0 / x
    else if (y <= 5d+70) then
        tmp = (y + x) / ((2.0d0 * x) * 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 <= 8e-206) {
		tmp = 0.5 / y;
	} else if (y <= 5.8e-175) {
		tmp = 0.5 / x;
	} else if (y <= 5e+70) {
		tmp = (y + x) / ((2.0 * x) * y);
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8e-206:
		tmp = 0.5 / y
	elif y <= 5.8e-175:
		tmp = 0.5 / x
	elif y <= 5e+70:
		tmp = (y + x) / ((2.0 * x) * y)
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8e-206)
		tmp = Float64(0.5 / y);
	elseif (y <= 5.8e-175)
		tmp = Float64(0.5 / x);
	elseif (y <= 5e+70)
		tmp = Float64(Float64(y + x) / Float64(Float64(2.0 * x) * y));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8e-206)
		tmp = 0.5 / y;
	elseif (y <= 5.8e-175)
		tmp = 0.5 / x;
	elseif (y <= 5e+70)
		tmp = (y + x) / ((2.0 * x) * y);
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8e-206], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 5.8e-175], N[(0.5 / x), $MachinePrecision], If[LessEqual[y, 5e+70], N[(N[(y + x), $MachinePrecision] / N[(N[(2.0 * x), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.00000000000000023e-206

   1. Initial program 72.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if 8.00000000000000023e-206 < y < 5.79999999999999998e-175 or 5.0000000000000002e70 < y

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 81.1

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

   5. Applied rewrites 81.1%

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

   if 5.79999999999999998e-175 < y < 5.0000000000000002e70

   1. Initial program 91.2%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   2. Add Preprocessing
3. Recombined 3 regimes into one program.

4. Final simplification 71.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-206}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;\frac{y + x}{\left(2 \cdot x\right) \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 66.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-206}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{0.5}{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 8e-206)
   (/ 0.5 y)
   (if (<= y 5.8e-175)
     (/ 0.5 x)
     (if (<= y 5e+70) (* (+ y x) (/ 0.5 (* y x))) (/ 0.5 x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 8e-206) {
		tmp = 0.5 / y;
	} else if (y <= 5.8e-175) {
		tmp = 0.5 / x;
	} else if (y <= 5e+70) {
		tmp = (y + x) * (0.5 / (y * x));
	} 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 <= 8d-206) then
        tmp = 0.5d0 / y
    else if (y <= 5.8d-175) then
        tmp = 0.5d0 / x
    else if (y <= 5d+70) then
        tmp = (y + x) * (0.5d0 / (y * x))
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 8e-206) {
		tmp = 0.5 / y;
	} else if (y <= 5.8e-175) {
		tmp = 0.5 / x;
	} else if (y <= 5e+70) {
		tmp = (y + x) * (0.5 / (y * x));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 8e-206:
		tmp = 0.5 / y
	elif y <= 5.8e-175:
		tmp = 0.5 / x
	elif y <= 5e+70:
		tmp = (y + x) * (0.5 / (y * x))
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 8e-206)
		tmp = Float64(0.5 / y);
	elseif (y <= 5.8e-175)
		tmp = Float64(0.5 / x);
	elseif (y <= 5e+70)
		tmp = Float64(Float64(y + x) * Float64(0.5 / Float64(y * x)));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 8e-206)
		tmp = 0.5 / y;
	elseif (y <= 5.8e-175)
		tmp = 0.5 / x;
	elseif (y <= 5e+70)
		tmp = (y + x) * (0.5 / (y * x));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 8e-206], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 5.8e-175], N[(0.5 / x), $MachinePrecision], If[LessEqual[y, 5e+70], N[(N[(y + x), $MachinePrecision] * N[(0.5 / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < 8.00000000000000023e-206

   1. Initial program 72.6%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 61.0

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

   5. Applied rewrites 61.0%

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

   if 8.00000000000000023e-206 < y < 5.79999999999999998e-175 or 5.0000000000000002e70 < y

   1. Initial program 65.3%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 81.1

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

   5. Applied rewrites 81.1%

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

   if 5.79999999999999998e-175 < y < 5.0000000000000002e70

   1. Initial program 91.2%

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

      1. lift-/.f64 N/A

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

      2. clear-num N/A

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

      3. associate-/r/ N/A

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

      4. lower-*.f64 N/A

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

      5. lift-*.f64 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-*l* N/A

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

      9. associate-/r* N/A

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

      10. metadata-eval N/A

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

      11. metadata-eval N/A

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

      12. lower-/.f64 N/A

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

      13. metadata-eval N/A

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

      14. *-commutative N/A

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

      15. lower-*.f64 89.2

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

      16. lift-+.f64 N/A

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

      17. +-commutative N/A

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

      18. lower-+.f64 89.2

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

   4. Applied rewrites 89.2%

      \[\leadsto \color{blue}{\frac{0.5}{y \cdot x} \cdot \left(y + x\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 71.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-206}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-175}:\\ \;\;\;\;\frac{0.5}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+70}:\\ \;\;\;\;\left(y + x\right) \cdot \frac{0.5}{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.9% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 6.4 \cdot 10^{-97}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 6.4e-97) (/ 0.5 y) (/ 0.5 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 6.4e-97) {
		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 <= 6.4d-97) 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 <= 6.4e-97) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 6.4e-97:
		tmp = 0.5 / y
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 6.4e-97)
		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 <= 6.4e-97)
		tmp = 0.5 / y;
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 6.4e-97], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 6.39999999999999961e-97

   1. Initial program 73.9%

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

   3. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{y}} \]
   4. Step-by-step derivation

      1. lower-/.f64 63.8

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

   5. Applied rewrites 63.8%

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

   if 6.39999999999999961e-97 < y

   1. Initial program 76.9%

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

   3. Taylor expanded in y around inf

      \[\leadsto \color{blue}{\frac{\frac{1}{2}}{x}} \]
   4. Step-by-step derivation

      1. lower-/.f64 68.3

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

   5. Applied rewrites 68.3%

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

Alternative 5: 50.6% accurate, 2.1× 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 74.9%

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

3. Taylor expanded in y around inf

   \[\leadsto \color{blue}{\frac{\frac{1}{2}}{x}} \]
4. Step-by-step derivation

   1. lower-/.f64 47.7

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

5. Applied rewrites 47.7%

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

Developer Target 1: 100.0% accurate, 1.0× 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 2024255 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, C"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (/ 1/2 x) (/ 1/2 y)))

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