Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 76.8% → 100.0%

Time: 5.9s

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: 76.8% 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

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

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]

Derivation

1. Initial program 74.1%

   \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
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. lift-*.f64 N/A

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

   3. lift-*.f64 N/A

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

   4. associate-*l* N/A

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

   5. *-commutative N/A

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

   6. associate-/r* N/A

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

   7. lower-/.f64 N/A

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

   8. lower-/.f64 N/A

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

   9. *-commutative N/A

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

   10. lower-*.f64 92.1

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

4. Applied rewrites 92.1%

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

5. Taylor expanded in x around 0

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

   1. metadata-eval N/A

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

   2. distribute-lft-out N/A

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

   3. *-rgt-identity N/A

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

   4. times-frac N/A

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

   5. +-commutative N/A

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

   6. *-lft-identity N/A

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

   7. associate-*l/ N/A

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

   8. lft-mult-inverse N/A

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

   9. distribute-rgt-in N/A

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

   10. *-commutative N/A

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

   11. times-frac N/A

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

   12. associate-*l* N/A

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

   13. distribute-lft-out N/A

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

   14. *-rgt-identity N/A

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

   15. associate-/l* N/A

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

   16. *-rgt-identity N/A

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

   17. associate-*r/ N/A

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

   18. rgt-mult-inverse N/A

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

   19. *-rgt-identity N/A

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

   20. +-commutative N/A

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

   21. lower-+.f64 N/A

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

7. Applied rewrites 100.0%

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

Alternative 2: 68.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 7.5e-196)
   (/ 0.5 y)
   (if (<= y 3.5e+122) (/ (+ x y) (* y (* x 2.0))) (/ 0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 7.5e-196) {
		tmp = 0.5 / y;
	} else if (y <= 3.5e+122) {
		tmp = (x + y) / (y * (x * 2.0));
	} 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 <= 7.5d-196) then
        tmp = 0.5d0 / y
    else if (y <= 3.5d+122) then
        tmp = (x + y) / (y * (x * 2.0d0))
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= 7.5e-196) {
		tmp = 0.5 / y;
	} else if (y <= 3.5e+122) {
		tmp = (x + y) / (y * (x * 2.0));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 7.5e-196:
		tmp = 0.5 / y
	elif y <= 3.5e+122:
		tmp = (x + y) / (y * (x * 2.0))
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 7.5e-196)
		tmp = Float64(0.5 / y);
	elseif (y <= 3.5e+122)
		tmp = Float64(Float64(x + y) / Float64(y * Float64(x * 2.0)));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 7.5e-196)
		tmp = 0.5 / y;
	elseif (y <= 3.5e+122)
		tmp = (x + y) / (y * (x * 2.0));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 7.5e-196], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 3.5e+122], N[(N[(x + y), $MachinePrecision] / N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 7.5e-196

   1. Initial program 69.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 53.7

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

   5. Applied rewrites 53.7%

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

   if 7.5e-196 < y < 3.50000000000000014e122

   1. Initial program 86.3%

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

   if 3.50000000000000014e122 < y

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 7.5 \cdot 10^{-196}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 68.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-189}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y 3e-189)
   (/ 0.5 y)
   (if (<= y 3.5e+122) (* (+ x y) (/ 0.5 (* x y))) (/ 0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= 3e-189) {
		tmp = 0.5 / y;
	} else if (y <= 3.5e+122) {
		tmp = (x + y) * (0.5 / (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 <= 3d-189) then
        tmp = 0.5d0 / y
    else if (y <= 3.5d+122) then
        tmp = (x + y) * (0.5d0 / (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 <= 3e-189) {
		tmp = 0.5 / y;
	} else if (y <= 3.5e+122) {
		tmp = (x + y) * (0.5 / (x * y));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 3e-189:
		tmp = 0.5 / y
	elif y <= 3.5e+122:
		tmp = (x + y) * (0.5 / (x * y))
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 3e-189)
		tmp = Float64(0.5 / y);
	elseif (y <= 3.5e+122)
		tmp = Float64(Float64(x + y) * Float64(0.5 / Float64(x * y)));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 3e-189)
		tmp = 0.5 / y;
	elseif (y <= 3.5e+122)
		tmp = (x + y) * (0.5 / (x * y));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 3e-189], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 3.5e+122], N[(N[(x + y), $MachinePrecision] * N[(0.5 / N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < 3e-189

   1. Initial program 70.4%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 54.4

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

   5. Applied rewrites 54.4%

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

   if 3e-189 < y < 3.50000000000000014e122

   1. Initial program 85.9%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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. lower-*.f64 85.2

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

   4. Applied rewrites 85.2%

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

   if 3.50000000000000014e122 < y

   1. Initial program 68.8%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 94.1

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

   5. Applied rewrites 94.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 3 \cdot 10^{-189}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+122}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 60.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 2.4 \cdot 10^{-123}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y 2.4e-123) (/ 0.5 y) (/ 0.5 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= 2.4e-123) {
		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 <= 2.4d-123) 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 <= 2.4e-123) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= 2.4e-123:
		tmp = 0.5 / y
	else:
		tmp = 0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= 2.4e-123)
		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 <= 2.4e-123)
		tmp = 0.5 / y;
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, 2.4e-123], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 2.4e-123

   1. Initial program 71.9%

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

   3. Taylor expanded in x around inf

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

      1. lower-/.f64 57.1

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

   5. Applied rewrites 57.1%

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

   if 2.4e-123 < y

   1. Initial program 77.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 73.6

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

   5. Applied rewrites 73.6%

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

Alternative 5: 50.8% 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 74.1%

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

3. Taylor expanded in x around 0

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

   1. lower-/.f64 54.5

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

5. Applied rewrites 54.5%

   \[\leadsto \color{blue}{\frac{0.5}{x}} \]
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 2024238 
(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)))