Linear.Projection:inversePerspective from linear-1.19.1.3, C

Percentage Accurate: 77.3% → 99.7%

Time: 5.9s

Alternatives: 5

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: 77.3% 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: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -4.5 \cdot 10^{+39}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{y}{x}, 0.5\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -4.5e+39) (/ (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 <= -4.5e+39) {
		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 <= -4.5e+39)
		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, -4.5e+39], 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 < -4.49999999999999996e39

   1. Initial program 73.4%

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

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

      4. /-lowering-/.f64 100.0

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

   5. Simplified 100.0%

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

   if -4.49999999999999996e39 < x

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 93.3

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

   5. Simplified 93.3%

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

Alternative 2: 96.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+165}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= x -1.75e+165)
   (/ 0.5 y)
   (if (<= x -9e+39) (/ (+ x y) (* y (* x 2.0))) (/ (fma 0.5 (/ x y) 0.5) x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (x <= -1.75e+165) {
		tmp = 0.5 / y;
	} else if (x <= -9e+39) {
		tmp = (x + y) / (y * (x * 2.0));
	} 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 <= -1.75e+165)
		tmp = Float64(0.5 / y);
	elseif (x <= -9e+39)
		tmp = Float64(Float64(x + y) / Float64(y * Float64(x * 2.0)));
	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, -1.75e+165], N[(0.5 / y), $MachinePrecision], If[LessEqual[x, -9e+39], N[(N[(x + y), $MachinePrecision] / N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(0.5 * N[(x / y), $MachinePrecision] + 0.5), $MachinePrecision] / x), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.74999999999999998e165

   1. Initial program 63.0%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 87.9

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

   5. Simplified 87.9%

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

   if -1.74999999999999998e165 < x < -8.99999999999999991e39

   1. Initial program 87.4%

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

   if -8.99999999999999991e39 < x

   1. Initial program 83.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.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. accelerator-lowering-fma.f64 N/A

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

      4. /-lowering-/.f64 93.3

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

   5. Simplified 93.3%

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

4. Final simplification 92.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{+165}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;x \leq -9 \cdot 10^{+39}:\\ \;\;\;\;\frac{x + y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{\mathsf{fma}\left(0.5, \frac{x}{y}, 0.5\right)}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 90.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-161}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+156}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y)
 :precision binary64
 (if (<= y 5e-161)
   (/ 0.5 y)
   (if (<= y 1.6e+156) (* (+ x y) (/ 0.5 (* x y))) (/ 0.5 x))))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 5e-161) {
		tmp = 0.5 / y;
	} else if (y <= 1.6e+156) {
		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 <= 5d-161) then
        tmp = 0.5d0 / y
    else if (y <= 1.6d+156) 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 <= 5e-161) {
		tmp = 0.5 / y;
	} else if (y <= 1.6e+156) {
		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 <= 5e-161:
		tmp = 0.5 / y
	elif y <= 1.6e+156:
		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 <= 5e-161)
		tmp = Float64(0.5 / y);
	elseif (y <= 1.6e+156)
		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 <= 5e-161)
		tmp = 0.5 / y;
	elseif (y <= 1.6e+156)
		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, 5e-161], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 1.6e+156], 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 < 4.9999999999999999e-161

   1. Initial program 78.2%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 59.6

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

   5. Simplified 59.6%

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

   if 4.9999999999999999e-161 < y < 1.60000000000000001e156

   1. Initial program 90.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

      3. *-lowering-*.f64 N/A

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

      4. *-commutative N/A

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

      5. associate-*l* N/A

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

      6. associate-/r* N/A

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

      7. metadata-eval N/A

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

      8. metadata-eval N/A

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

      9. /-lowering-/.f64 N/A

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

      10. metadata-eval N/A

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

      11. *-lowering-*.f64 N/A

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

      12. +-lowering-+.f64 91.4

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

   4. Applied egg-rr 91.4%

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

   if 1.60000000000000001e156 < y

   1. Initial program 68.2%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 89.5

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

   5. Simplified 89.5%

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

4. Final simplification 72.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 5 \cdot 10^{-161}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 1.6 \cdot 10^{+156}:\\ \;\;\;\;\left(x + y\right) \cdot \frac{0.5}{x \cdot y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 82.1% accurate, 1.4× speedup

Math

\[\begin{array}{l} [x, y] = \mathsf{sort}([x, y])\\ \\ \begin{array}{l} \mathbf{if}\;y \leq 1.25 \cdot 10^{-85}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{x}\\ \end{array} \end{array} \]

FPCore

NOTE: x and y should be sorted in increasing order before calling this function.
(FPCore (x y) :precision binary64 (if (<= y 1.25e-85) (/ 0.5 y) (/ 0.5 x)))

C

assert(x < y);
double code(double x, double y) {
	double tmp;
	if (y <= 1.25e-85) {
		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 <= 1.25d-85) 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 <= 1.25e-85) {
		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 <= 1.25e-85:
		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 <= 1.25e-85)
		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 <= 1.25e-85)
		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, 1.25e-85], N[(0.5 / y), $MachinePrecision], N[(0.5 / x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 1.25e-85

   1. Initial program 79.1%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 60.9

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

   5. Simplified 60.9%

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

   if 1.25e-85 < y

   1. Initial program 84.7%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 73.2

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

   5. Simplified 73.2%

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

Alternative 5: 51.0% 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 81.0%

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

3. Taylor expanded in x around 0

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

   1. /-lowering-/.f64 50.7

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

5. Simplified 50.7%

   \[\leadsto \color{blue}{\frac{0.5}{x}} \]
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 2024199 
(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)))