Linear.Projection:inversePerspective from linear-1.19.1.3, B

Percentage Accurate: 76.6% → 100.0%

Time: 8.5s

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: 76.6% 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 77.2%

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

   1. associate-/l/ N/A

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

   2. div-sub N/A

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

   3. *-inverses N/A

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

   4. sub-div N/A

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

   5. associate-/l/ N/A

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

   6. --lowering--.f64 N/A

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

   7. associate-/r* N/A

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

   8. /-lowering-/.f64 N/A

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

   9. associate-/r* N/A

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

   10. *-inverses N/A

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

   11. metadata-eval N/A

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

   12. *-commutative N/A

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

   13. associate-/r* N/A

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

   14. *-inverses N/A

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

   15. associate-/r* N/A

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

   16. /-lowering-/.f64 N/A

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

   17. associate-/r* N/A

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

   18. *-inverses N/A

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

   19. metadata-eval 100.0

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

4. Applied egg-rr 100.0%

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

Alternative 2: 87.0% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x - y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{if}\;t\_0 \leq -\infty:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;t\_0 \leq -1 \cdot 10^{-126}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;t\_0 \leq 0:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;t\_0 \leq 10^{+308}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- x y) (* y (* x 2.0)))))
   (if (<= t_0 (- INFINITY))
     (/ -0.5 x)
     (if (<= t_0 -1e-126)
       t_0
       (if (<= t_0 0.0) (/ -0.5 x) (if (<= t_0 1e+308) t_0 (/ 0.5 y)))))))

C

double code(double x, double y) {
	double t_0 = (x - y) / (y * (x * 2.0));
	double tmp;
	if (t_0 <= -((double) INFINITY)) {
		tmp = -0.5 / x;
	} else if (t_0 <= -1e-126) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = -0.5 / x;
	} else if (t_0 <= 1e+308) {
		tmp = t_0;
	} else {
		tmp = 0.5 / y;
	}
	return tmp;
}

Java

public static double code(double x, double y) {
	double t_0 = (x - y) / (y * (x * 2.0));
	double tmp;
	if (t_0 <= -Double.POSITIVE_INFINITY) {
		tmp = -0.5 / x;
	} else if (t_0 <= -1e-126) {
		tmp = t_0;
	} else if (t_0 <= 0.0) {
		tmp = -0.5 / x;
	} else if (t_0 <= 1e+308) {
		tmp = t_0;
	} else {
		tmp = 0.5 / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) / (y * (x * 2.0))
	tmp = 0
	if t_0 <= -math.inf:
		tmp = -0.5 / x
	elif t_0 <= -1e-126:
		tmp = t_0
	elif t_0 <= 0.0:
		tmp = -0.5 / x
	elif t_0 <= 1e+308:
		tmp = t_0
	else:
		tmp = 0.5 / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) / Float64(y * Float64(x * 2.0)))
	tmp = 0.0
	if (t_0 <= Float64(-Inf))
		tmp = Float64(-0.5 / x);
	elseif (t_0 <= -1e-126)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = Float64(-0.5 / x);
	elseif (t_0 <= 1e+308)
		tmp = t_0;
	else
		tmp = Float64(0.5 / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) / (y * (x * 2.0));
	tmp = 0.0;
	if (t_0 <= -Inf)
		tmp = -0.5 / x;
	elseif (t_0 <= -1e-126)
		tmp = t_0;
	elseif (t_0 <= 0.0)
		tmp = -0.5 / x;
	elseif (t_0 <= 1e+308)
		tmp = t_0;
	else
		tmp = 0.5 / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] / N[(y * N[(x * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, (-Infinity)], N[(-0.5 / x), $MachinePrecision], If[LessEqual[t$95$0, -1e-126], t$95$0, If[LessEqual[t$95$0, 0.0], N[(-0.5 / x), $MachinePrecision], If[LessEqual[t$95$0, 1e+308], t$95$0, N[(0.5 / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (-.f64 x y) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) < -inf.0 or -9.9999999999999995e-127 < (/.f64 (-.f64 x y) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) < -0.0

   1. Initial program 5.8%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 56.7

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

   5. Simplified 56.7%

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

   if -inf.0 < (/.f64 (-.f64 x y) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) < -9.9999999999999995e-127 or -0.0 < (/.f64 (-.f64 x y) (*.f64 (*.f64 x #s(literal 2 binary64)) y)) < 1e308

   1. Initial program 99.2%

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

   if 1e308 < (/.f64 (-.f64 x y) (*.f64 (*.f64 x #s(literal 2 binary64)) y))

   1. Initial program 9.1%

      \[\frac{x - y}{\left(x \cdot 2\right) \cdot y} \]
   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 62.4

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

   5. Simplified 62.4%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x - y}{y \cdot \left(x \cdot 2\right)} \leq -\infty:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;\frac{x - y}{y \cdot \left(x \cdot 2\right)} \leq -1 \cdot 10^{-126}:\\ \;\;\;\;\frac{x - y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{elif}\;\frac{x - y}{y \cdot \left(x \cdot 2\right)} \leq 0:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;\frac{x - y}{y \cdot \left(x \cdot 2\right)} \leq 10^{+308}:\\ \;\;\;\;\frac{x - y}{y \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{0.5}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x - y\right) \cdot \frac{0.5}{y \cdot x}\\ \mathbf{if}\;y \leq -3.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-140}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-219}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+102}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (- x y) (/ 0.5 (* y x)))))
   (if (<= y -3.5e+130)
     (/ -0.5 x)
     (if (<= y -4.4e-140)
       t_0
       (if (<= y 5.8e-219) (/ 0.5 y) (if (<= y 6.8e+102) t_0 (/ -0.5 x)))))))

C

double code(double x, double y) {
	double t_0 = (x - y) * (0.5 / (y * x));
	double tmp;
	if (y <= -3.5e+130) {
		tmp = -0.5 / x;
	} else if (y <= -4.4e-140) {
		tmp = t_0;
	} else if (y <= 5.8e-219) {
		tmp = 0.5 / y;
	} else if (y <= 6.8e+102) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (x - y) * (0.5d0 / (y * x))
    if (y <= (-3.5d+130)) then
        tmp = (-0.5d0) / x
    else if (y <= (-4.4d-140)) then
        tmp = t_0
    else if (y <= 5.8d-219) then
        tmp = 0.5d0 / y
    else if (y <= 6.8d+102) then
        tmp = t_0
    else
        tmp = (-0.5d0) / x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x - y) * (0.5 / (y * x));
	double tmp;
	if (y <= -3.5e+130) {
		tmp = -0.5 / x;
	} else if (y <= -4.4e-140) {
		tmp = t_0;
	} else if (y <= 5.8e-219) {
		tmp = 0.5 / y;
	} else if (y <= 6.8e+102) {
		tmp = t_0;
	} else {
		tmp = -0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x - y) * (0.5 / (y * x))
	tmp = 0
	if y <= -3.5e+130:
		tmp = -0.5 / x
	elif y <= -4.4e-140:
		tmp = t_0
	elif y <= 5.8e-219:
		tmp = 0.5 / y
	elif y <= 6.8e+102:
		tmp = t_0
	else:
		tmp = -0.5 / x
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x - y) * Float64(0.5 / Float64(y * x)))
	tmp = 0.0
	if (y <= -3.5e+130)
		tmp = Float64(-0.5 / x);
	elseif (y <= -4.4e-140)
		tmp = t_0;
	elseif (y <= 5.8e-219)
		tmp = Float64(0.5 / y);
	elseif (y <= 6.8e+102)
		tmp = t_0;
	else
		tmp = Float64(-0.5 / x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x - y) * (0.5 / (y * x));
	tmp = 0.0;
	if (y <= -3.5e+130)
		tmp = -0.5 / x;
	elseif (y <= -4.4e-140)
		tmp = t_0;
	elseif (y <= 5.8e-219)
		tmp = 0.5 / y;
	elseif (y <= 6.8e+102)
		tmp = t_0;
	else
		tmp = -0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x - y), $MachinePrecision] * N[(0.5 / N[(y * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -3.5e+130], N[(-0.5 / x), $MachinePrecision], If[LessEqual[y, -4.4e-140], t$95$0, If[LessEqual[y, 5.8e-219], N[(0.5 / y), $MachinePrecision], If[LessEqual[y, 6.8e+102], t$95$0, N[(-0.5 / x), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.5000000000000001e130 or 6.8000000000000001e102 < y

   1. Initial program 71.1%

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

   3. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 91.7

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

   5. Simplified 91.7%

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

   if -3.5000000000000001e130 < y < -4.3999999999999998e-140 or 5.79999999999999968e-219 < y < 6.8000000000000001e102

   1. Initial program 87.2%

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

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

      8. associate-/r* N/A

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

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

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

      10. associate-/r* N/A

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

      11. *-inverses N/A

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

      12. metadata-eval N/A

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

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

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

      14. --lowering--.f64 87.2

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

   4. Applied egg-rr 87.2%

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

   if -4.3999999999999998e-140 < y < 5.79999999999999968e-219

   1. Initial program 64.3%

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

   3. Taylor expanded in x around inf

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

      1. /-lowering-/.f64 90.9

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

   5. Simplified 90.9%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+130}:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{-140}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{0.5}{y \cdot x}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-219}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{elif}\;y \leq 6.8 \cdot 10^{+102}:\\ \;\;\;\;\left(x - y\right) \cdot \frac{0.5}{y \cdot x}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7000000000:\\ \;\;\;\;\frac{-0.5}{x}\\ \mathbf{elif}\;y \leq 2.35 \cdot 10^{+69}:\\ \;\;\;\;\frac{0.5}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{-0.5}{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7000000000.0)
   (/ -0.5 x)
   (if (<= y 2.35e+69) (/ 0.5 y) (/ -0.5 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7000000000.0) {
		tmp = -0.5 / x;
	} else if (y <= 2.35e+69) {
		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 <= (-7000000000.0d0)) then
        tmp = (-0.5d0) / x
    else if (y <= 2.35d+69) 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 <= -7000000000.0) {
		tmp = -0.5 / x;
	} else if (y <= 2.35e+69) {
		tmp = 0.5 / y;
	} else {
		tmp = -0.5 / x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7000000000.0:
		tmp = -0.5 / x
	elif y <= 2.35e+69:
		tmp = 0.5 / y
	else:
		tmp = -0.5 / x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7000000000.0)
		tmp = Float64(-0.5 / x);
	elseif (y <= 2.35e+69)
		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 <= -7000000000.0)
		tmp = -0.5 / x;
	elseif (y <= 2.35e+69)
		tmp = 0.5 / y;
	else
		tmp = -0.5 / x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7000000000.0], N[(-0.5 / x), $MachinePrecision], If[LessEqual[y, 2.35e+69], N[(0.5 / y), $MachinePrecision], N[(-0.5 / x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -7e9 or 2.34999999999999998e69 < y

   1. Initial program 76.7%

      \[\frac{x - y}{\left(x \cdot 2\right) \cdot y} \]
   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 80.3

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

   5. Simplified 80.3%

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

   if -7e9 < y < 2.34999999999999998e69

   1. Initial program 77.5%

      \[\frac{x - y}{\left(x \cdot 2\right) \cdot y} \]
   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 77.6

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

   5. Simplified 77.6%

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

Alternative 5: 50.4% 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 77.2%

   \[\frac{x - y}{\left(x \cdot 2\right) \cdot y} \]
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 48.4

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

5. Simplified 48.4%

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

Developer Target 1: 100.0% accurate, 1.0× speedup

Math

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

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]

Reproduce

herbie shell --seed 2024204 
(FPCore (x y)
  :name "Linear.Projection:inversePerspective from linear-1.19.1.3, B"
  :precision binary64

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

  (/ (- x y) (* (* x 2.0) y)))