Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 77.1% → 99.8%

Time: 4.7s

Alternatives: 6

Speedup: 1.4×

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: 77.1% 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: 99.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-54}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{y}{x}, 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -5e-54) (/ (fma 0.5 (/ y x) 0.5) y) (/ (fma 0.5 (/ x y) 0.5) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -5e-54) {
		tmp = fma(0.5, (y / x), 0.5) / y;
	} else {
		tmp = fma(0.5, (x / y), 0.5) / x;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (x <= -5e-54)
		tmp = Float64(fma(0.5, Float64(y / x), 0.5) / y);
	else
		tmp = Float64(fma(0.5, Float64(x / y), 0.5) / x);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[x, -5e-54], N[(N[(0.5 * N[(y / x), $MachinePrecision] + 0.5), $MachinePrecision] / y), $MachinePrecision], N[(N[(0.5 * N[(x / y), $MachinePrecision] + 0.5), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5.00000000000000015e-54

   1. Initial program 89.9%

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

   3. Taylor expanded in y around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 99.9

         \[\leadsto \frac{\mathsf{fma}\left(0.5, \color{blue}{\frac{y}{x}}, 0.5\right)}{y} \]

   5. Applied rewrites 99.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.5, \frac{y}{x}, 0.5\right)}{y}} \]

   if -5.00000000000000015e-54 < x

   1. Initial program 78.9%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 93.4

         \[\leadsto \frac{\mathsf{fma}\left(0.5, \color{blue}{\frac{x}{y}}, 0.5\right)}{x} \]

   5. Applied rewrites 93.4%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 2: 90.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-154}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 5e-154)
   (/ 0.5 y)
   (if (<= y 3e+112) (/ (+ x y) (* y (* x 2.0))) (/ 0.5 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5e-154) {
		tmp = 0.5 / y;
	} else if (y <= 3e+112) {
		tmp = (x + y) / (y * (x * 2.0));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 5d-154) then
        tmp = 0.5d0 / y
    else if (y <= 3d+112) then
        tmp = (x + y) / (y * (x * 2.0d0))
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 5e-154) {
		tmp = 0.5 / y;
	} else if (y <= 3e+112) {
		tmp = (x + y) / (y * (x * 2.0));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 5e-154:
		tmp = 0.5 / y
	elif y <= 3e+112:
		tmp = (x + y) / (y * (x * 2.0))
	else:
		tmp = 0.5 / x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5e-154)
		tmp = Float64(0.5 / y);
	elseif (y <= 3e+112)
		tmp = Float64(Float64(x + y) / Float64(y * Float64(x * 2.0)));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5e-154)
		tmp = 0.5 / y;
	elseif (y <= 3e+112)
		tmp = (x + y) / (y * (x * 2.0));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 5e-154], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 3e+112], 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 < 5.0000000000000002e-154

   1. Initial program 77.2%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 57.2

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

   5. Applied rewrites 57.2%

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

   if 5.0000000000000002e-154 < y < 2.99999999999999979e112

   1. Initial program 96.4%

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

   if 2.99999999999999979e112 < y

   1. Initial program 79.6%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 95.1

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

   5. Applied rewrites 95.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-154}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 5.6e-154)
   (/ 0.5 y)
   (if (<= y 3e+112) (* (+ x y) (/ 0.5 (* x y))) (/ 0.5 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5.6e-154) {
		tmp = 0.5 / y;
	} else if (y <= 3e+112) {
		tmp = (x + y) * (0.5 / (x * y));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 5.6d-154) then
        tmp = 0.5d0 / y
    else if (y <= 3d+112) then
        tmp = (x + y) * (0.5d0 / (x * y))
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 5.6e-154) {
		tmp = 0.5 / y;
	} else if (y <= 3e+112) {
		tmp = (x + y) * (0.5 / (x * y));
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 5.6e-154:
		tmp = 0.5 / y
	elif y <= 3e+112:
		tmp = (x + y) * (0.5 / (x * y))
	else:
		tmp = 0.5 / x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5.6e-154)
		tmp = Float64(0.5 / y);
	elseif (y <= 3e+112)
		tmp = Float64(Float64(x + y) * Float64(0.5 / Float64(x * y)));
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.6e-154)
		tmp = 0.5 / y;
	elseif (y <= 3e+112)
		tmp = (x + y) * (0.5 / (x * y));
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 5.6e-154], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 3e+112], 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 < 5.60000000000000025e-154

   1. Initial program 77.2%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 57.2

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

   5. Applied rewrites 57.2%

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

   if 5.60000000000000025e-154 < y < 2.99999999999999979e112

   1. Initial program 96.4%

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

      1. lift-+.f64 N/A

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

      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. div-inv N/A

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

      5. *-commutative N/A

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

      6. lower-*.f64 N/A

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

      7. lift-*.f64 N/A

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

      8. lift-*.f64 N/A

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

      9. *-commutative N/A

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

      10. associate-*l* N/A

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

      11. associate-/r* N/A

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

      12. metadata-eval N/A

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

      13. metadata-eval N/A

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

      14. lower-/.f64 N/A

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

      15. metadata-eval N/A

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

      16. lower-*.f64 96.3

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

   4. Applied rewrites 96.3%

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

   if 2.99999999999999979e112 < y

   1. Initial program 79.6%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 95.1

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

   5. Applied rewrites 95.1%

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

4. Final simplification 71.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5.6 \cdot 10^{-154}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+112}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-171}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 5e-171) (/ 0.5 y) (/ (fma 0.5 (/ x y) 0.5) x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5e-171) {
		tmp = 0.5 / y;
	} else {
		tmp = fma(0.5, (x / y), 0.5) / x;
	}
	return tmp;
}

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5e-171)
		tmp = Float64(0.5 / y);
	else
		tmp = Float64(fma(0.5, Float64(x / y), 0.5) / x);
	end
	return tmp
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 5e-171], N[(0.5 / y), $MachinePrecision], N[(N[(0.5 * N[(x / y), $MachinePrecision] + 0.5), $MachinePrecision] / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 4.99999999999999992e-171

   1. Initial program 78.1%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 57.5

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

   5. Applied rewrites 57.5%

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

   if 4.99999999999999992e-171 < y

   1. Initial program 88.0%

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

   3. Taylor expanded in x around 0

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

      1. lower-/.f64 N/A

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

      2. +-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower-/.f64 95.9

         \[\leadsto \frac{\mathsf{fma}\left(0.5, \color{blue}{\frac{x}{y}}, 0.5\right)}{x} \]

   5. Applied rewrites 95.9%

      \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 5: 83.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5.8 \cdot 10^{-90}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y 5.8e-90) (/ 0.5 y) (/ 0.5 x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5.8e-90) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= 5.8d-90) then
        tmp = 0.5d0 / y
    else
        tmp = 0.5d0 / x
    end if
    code = tmp
end function

Java

assert x < y;
public static double code(double x, double y) {
	double tmp;
	if (y <= 5.8e-90) {
		tmp = 0.5 / y;
	} else {
		tmp = 0.5 / x;
	}
	return tmp;
}

Python

[x, y] = sort([x, y])
def code(x, y):
	tmp = 0
	if y <= 5.8e-90:
		tmp = 0.5 / y
	else:
		tmp = 0.5 / x
	return tmp

Julia

x, y = sort([x, y])
function code(x, y)
	tmp = 0.0
	if (y <= 5.8e-90)
		tmp = Float64(0.5 / y);
	else
		tmp = Float64(0.5 / x);
	end
	return tmp
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= 5.8e-90)
		tmp = 0.5 / y;
	else
		tmp = 0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := If[LessEqual[y, 5.8e-90], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 5.79999999999999967e-90

   1. Initial program 78.3%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 58.7

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

   5. Applied rewrites 58.7%

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

   if 5.79999999999999967e-90 < y

   1. Initial program 88.7%

      \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
   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 70.8

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

   5. Applied rewrites 70.8%

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

Alternative 6: 50.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \frac{0.5}{x} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (/ 0.5 x))

C

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

Fortran

NOTE: x and y should be sorted in increasing order before calling this function.
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.5d0 / x
end function

Java

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

Python

[x, y] = sort([x, y])
def code(x, y):
	return 0.5 / x

Julia

x, y = sort([x, y])
function code(x, y)
	return Float64(0.5 / x)
end

MATLAB

x, y = num2cell(sort([x, y])){:}
function tmp = code(x, y)
	tmp = 0.5 / x;
end

Wolfram

NOTE: x and y should be sorted in increasing order before calling this function.
code[x_, y_] := N[(0.5 / x), $MachinePrecision]

Derivation

1. Initial program 81.8%

   \[\frac{x + y}{\left(x \cdot 2\right) \cdot y} \]
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 52.0

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

5. Applied rewrites 52.0%

   \[\leadsto \color{blue}{\frac{0.5}{x}} \]
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 2024219 
(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)))