Linear.Projection:perspective from linear-1.19.1.3, B

Percentage Accurate: 76.1% → 99.8%

Time: 4.8s

Alternatives: 7

Speedup: 0.7×

Specification

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Initial Program: 76.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\left(x \cdot 2\right) \cdot y}{x - y} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* (* x 2.0) y) (- x y)))

C

double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 2.0d0) * y) / (x - y)
end function

Java

public static double code(double x, double y) {
	return ((x * 2.0) * y) / (x - y);
}

Python

def code(x, y):
	return ((x * 2.0) * y) / (x - y)

Julia

function code(x, y)
	return Float64(Float64(Float64(x * 2.0) * y) / Float64(x - y))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 2.0) * y) / (x - y);
end

Wolfram

code[x_, y_] := N[(N[(N[(x * 2.0), $MachinePrecision] * y), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 10^{+41}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.6e+29) (not (<= y 1e+41)))
   (/ x (fma 0.5 (/ x y) -0.5))
   (/ y (+ 0.5 (* -0.5 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.6e+29) || !(y <= 1e+41)) {
		tmp = x / fma(0.5, (x / y), -0.5);
	} else {
		tmp = y / (0.5 + (-0.5 * (y / x)));
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.6e+29) || !(y <= 1e+41))
		tmp = Float64(x / fma(0.5, Float64(x / y), -0.5));
	else
		tmp = Float64(y / Float64(0.5 + Float64(-0.5 * Float64(y / x))));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.6e+29], N[Not[LessEqual[y, 1e+41]], $MachinePrecision]], N[(x / N[(0.5 * N[(x / y), $MachinePrecision] + -0.5), $MachinePrecision]), $MachinePrecision], N[(y / N[(0.5 + N[(-0.5 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.59999999999999993e29 or 1.00000000000000001e41 < y

   1. Initial program 71.9%

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

      1. associate-*l* 71.9%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. remove-double-neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. *-lft-identity 99.9%

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

      7. *-inverses 99.9%

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

      8. times-frac 99.9%

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

      9. *-inverses 99.9%

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

      10. *-inverses 99.9%

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

      11. associate-/r* 99.9%

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

      12. *-commutative 99.9%

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

      13. fma-neg 99.9%

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

      14. *-commutative 99.9%

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

      15. associate-/r* 99.9%

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

      16. *-inverses 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

      18. *-commutative 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

      19. associate-/r* 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

      20. *-inverses 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

      21. metadata-eval 99.9%

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

      22. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   if -1.59999999999999993e29 < y < 1.00000000000000001e41

   1. Initial program 77.8%

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

      1. *-commutative 77.8%

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

      2. associate-/l* 99.9%

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

      3. div-sub 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. distribute-neg-frac 100.0%

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

      7. neg-mul-1 100.0%

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

      8. *-commutative 100.0%

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

      9. times-frac 100.0%

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

      10. metadata-eval 100.0%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{-0.5} + \frac{x}{x \cdot 2}} \]

      11. metadata-eval 100.0%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{\left(-0.5\right)} + \frac{x}{x \cdot 2}} \]

      12. metadata-eval 100.0%

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

      13. *-inverses 100.0%

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

      14. associate-/r* 100.0%

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

      15. *-commutative 100.0%

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

      16. associate-/r* 100.0%

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

      17. *-inverses 100.0%

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

      18. *-inverses 100.0%

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

      19. associate-/r* 100.0%

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

      20. *-commutative 100.0%

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

      21. fma-def 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{y}{x} + 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.6 \cdot 10^{+29} \lor \neg \left(y \leq 10^{+41}\right):\\ \;\;\;\;\frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -0.5\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+76} \lor \neg \left(y \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8e+76) (not (<= y 2.5e+18)))
   (/ (* x 2.0) (/ (- x y) y))
   (/ y (+ 0.5 (* -0.5 (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8e+76) || !(y <= 2.5e+18)) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = y / (0.5 + (-0.5 * (y / 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+76)) .or. (.not. (y <= 2.5d+18))) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = y / (0.5d0 + ((-0.5d0) * (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8e+76) || !(y <= 2.5e+18)) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = y / (0.5 + (-0.5 * (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8e+76) or not (y <= 2.5e+18):
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = y / (0.5 + (-0.5 * (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8e+76) || !(y <= 2.5e+18))
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = Float64(y / Float64(0.5 + Float64(-0.5 * Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8e+76) || ~((y <= 2.5e+18)))
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = y / (0.5 + (-0.5 * (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8e+76], N[Not[LessEqual[y, 2.5e+18]], $MachinePrecision]], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(y / N[(0.5 + N[(-0.5 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.0000000000000004e76 or 2.5e18 < y

   1. Initial program 69.8%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   if -8.0000000000000004e76 < y < 2.5e18

   1. Initial program 79.0%

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

      1. *-commutative 79.0%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-frac 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. times-frac 99.9%

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

      10. metadata-eval 99.9%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{-0.5} + \frac{x}{x \cdot 2}} \]

      11. metadata-eval 99.9%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{\left(-0.5\right)} + \frac{x}{x \cdot 2}} \]

      12. metadata-eval 99.9%

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

      13. *-inverses 99.9%

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

      14. associate-/r* 99.9%

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

      15. *-commutative 99.9%

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

      16. associate-/r* 99.9%

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

      17. *-inverses 99.9%

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

      18. *-inverses 99.9%

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

      19. associate-/r* 99.9%

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

      20. *-commutative 99.9%

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

      21. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{y}{x} + 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8 \cdot 10^{+76} \lor \neg \left(y \leq 2.5 \cdot 10^{+18}\right):\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \end{array} \]

Alternative 3: 74.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(y + \frac{y}{\frac{x}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+38)
   (/ x -0.5)
   (if (<= y 1.65e+58) (* 2.0 (+ y (/ y (/ x y)))) (/ x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+38) {
		tmp = x / -0.5;
	} else if (y <= 1.65e+58) {
		tmp = 2.0 * (y + (y / (x / y)));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.8d+38)) then
        tmp = x / (-0.5d0)
    else if (y <= 1.65d+58) then
        tmp = 2.0d0 * (y + (y / (x / y)))
    else
        tmp = x / (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+38) {
		tmp = x / -0.5;
	} else if (y <= 1.65e+58) {
		tmp = 2.0 * (y + (y / (x / y)));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+38:
		tmp = x / -0.5
	elif y <= 1.65e+58:
		tmp = 2.0 * (y + (y / (x / y)))
	else:
		tmp = x / -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+38)
		tmp = Float64(x / -0.5);
	elseif (y <= 1.65e+58)
		tmp = Float64(2.0 * Float64(y + Float64(y / Float64(x / y))));
	else
		tmp = Float64(x / -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e+38)
		tmp = x / -0.5;
	elseif (y <= 1.65e+58)
		tmp = 2.0 * (y + (y / (x / y)));
	else
		tmp = x / -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+38], N[(x / -0.5), $MachinePrecision], If[LessEqual[y, 1.65e+58], N[(2.0 * N[(y + N[(y / N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / -0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.79999999999999985e38 or 1.64999999999999991e58 < y

   1. Initial program 69.6%

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

      1. associate-*l* 69.6%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. remove-double-neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. *-lft-identity 99.9%

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

      7. *-inverses 99.9%

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

      8. times-frac 99.9%

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

      9. *-inverses 99.9%

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

      10. *-inverses 99.9%

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

      11. associate-/r* 99.9%

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

      12. *-commutative 99.9%

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

      13. fma-neg 99.9%

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

      14. *-commutative 99.9%

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

      15. associate-/r* 99.9%

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

      16. *-inverses 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

      18. *-commutative 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

      19. associate-/r* 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

      20. *-inverses 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

      21. metadata-eval 99.9%

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

      22. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 76.8%

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

   if -1.79999999999999985e38 < y < 1.64999999999999991e58

   1. Initial program 79.2%

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

      1. associate-*l/ 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around inf 76.0%

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

      1. distribute-lft-out 76.0%

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

      2. unpow2 76.0%

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

      3. associate-/l* 76.1%

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

   6. Simplified 76.1%

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

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+58}:\\ \;\;\;\;2 \cdot \left(y + \frac{y}{\frac{x}{y}}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \]

Alternative 4: 93.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e+203)
   (/ x -0.5)
   (if (<= y 3.1e+228) (* y (/ (* x 2.0) (- x y))) (/ x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+203) {
		tmp = x / -0.5;
	} else if (y <= 3.1e+228) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.7d+203)) then
        tmp = x / (-0.5d0)
    else if (y <= 3.1d+228) then
        tmp = y * ((x * 2.0d0) / (x - y))
    else
        tmp = x / (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+203) {
		tmp = x / -0.5;
	} else if (y <= 3.1e+228) {
		tmp = y * ((x * 2.0) / (x - y));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e+203:
		tmp = x / -0.5
	elif y <= 3.1e+228:
		tmp = y * ((x * 2.0) / (x - y))
	else:
		tmp = x / -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e+203)
		tmp = Float64(x / -0.5);
	elseif (y <= 3.1e+228)
		tmp = Float64(y * Float64(Float64(x * 2.0) / Float64(x - y)));
	else
		tmp = Float64(x / -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e+203)
		tmp = x / -0.5;
	elseif (y <= 3.1e+228)
		tmp = y * ((x * 2.0) / (x - y));
	else
		tmp = x / -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e+203], N[(x / -0.5), $MachinePrecision], If[LessEqual[y, 3.1e+228], N[(y * N[(N[(x * 2.0), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / -0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7000000000000001e203 or 3.0999999999999999e228 < y

   1. Initial program 57.2%

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

      1. associate-*l* 57.2%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. remove-double-neg 100.0%

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

      5. remove-double-neg 100.0%

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

      6. *-lft-identity 100.0%

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

      7. *-inverses 100.0%

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

      8. times-frac 100.0%

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

      9. *-inverses 100.0%

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

      10. *-inverses 100.0%

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

      11. associate-/r* 100.0%

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

      12. *-commutative 100.0%

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

      13. fma-neg 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/r* 100.0%

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

      16. *-inverses 100.0%

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

      17. metadata-eval 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

      18. *-commutative 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

      19. associate-/r* 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

      20. *-inverses 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

      21. metadata-eval 100.0%

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

      22. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.0%

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

   if -1.7000000000000001e203 < y < 3.0999999999999999e228

   1. Initial program 78.3%

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

      1. associate-*l/ 96.3%

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

   3. Simplified 96.3%

      \[\leadsto \color{blue}{\frac{x \cdot 2}{x - y} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+203}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+228}:\\ \;\;\;\;y \cdot \frac{x \cdot 2}{x - y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \]

Alternative 5: 93.4% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+204}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e+204)
   (/ x -0.5)
   (if (<= y 4.2e+228) (/ y (+ 0.5 (* -0.5 (/ y x)))) (/ x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+204) {
		tmp = x / -0.5;
	} else if (y <= 4.2e+228) {
		tmp = y / (0.5 + (-0.5 * (y / x)));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.7d+204)) then
        tmp = x / (-0.5d0)
    else if (y <= 4.2d+228) then
        tmp = y / (0.5d0 + ((-0.5d0) * (y / x)))
    else
        tmp = x / (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+204) {
		tmp = x / -0.5;
	} else if (y <= 4.2e+228) {
		tmp = y / (0.5 + (-0.5 * (y / x)));
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e+204:
		tmp = x / -0.5
	elif y <= 4.2e+228:
		tmp = y / (0.5 + (-0.5 * (y / x)))
	else:
		tmp = x / -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e+204)
		tmp = Float64(x / -0.5);
	elseif (y <= 4.2e+228)
		tmp = Float64(y / Float64(0.5 + Float64(-0.5 * Float64(y / x))));
	else
		tmp = Float64(x / -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e+204)
		tmp = x / -0.5;
	elseif (y <= 4.2e+228)
		tmp = y / (0.5 + (-0.5 * (y / x)));
	else
		tmp = x / -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e+204], N[(x / -0.5), $MachinePrecision], If[LessEqual[y, 4.2e+228], N[(y / N[(0.5 + N[(-0.5 * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / -0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.70000000000000005e204 or 4.19999999999999988e228 < y

   1. Initial program 57.2%

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

      1. associate-*l* 57.2%

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

      2. associate-/l* 100.0%

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

      3. div-sub 100.0%

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

      4. remove-double-neg 100.0%

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

      5. remove-double-neg 100.0%

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

      6. *-lft-identity 100.0%

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

      7. *-inverses 100.0%

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

      8. times-frac 100.0%

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

      9. *-inverses 100.0%

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

      10. *-inverses 100.0%

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

      11. associate-/r* 100.0%

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

      12. *-commutative 100.0%

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

      13. fma-neg 100.0%

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

      14. *-commutative 100.0%

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

      15. associate-/r* 100.0%

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

      16. *-inverses 100.0%

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

      17. metadata-eval 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

      18. *-commutative 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

      19. associate-/r* 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

      20. *-inverses 100.0%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

      21. metadata-eval 100.0%

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

      22. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around 0 92.0%

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

   if -1.70000000000000005e204 < y < 4.19999999999999988e228

   1. Initial program 78.3%

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

      1. *-commutative 78.3%

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

      2. associate-/l* 96.4%

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

      3. div-sub 96.4%

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

      4. sub-neg 96.4%

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

      5. +-commutative 96.4%

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

      6. distribute-neg-frac 96.4%

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

      7. neg-mul-1 96.4%

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

      8. *-commutative 96.4%

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

      9. times-frac 96.4%

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

      10. metadata-eval 96.4%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{-0.5} + \frac{x}{x \cdot 2}} \]

      11. metadata-eval 96.4%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{\left(-0.5\right)} + \frac{x}{x \cdot 2}} \]

      12. metadata-eval 96.4%

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

      13. *-inverses 96.4%

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

      14. associate-/r* 96.4%

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

      15. *-commutative 96.4%

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

      16. associate-/r* 96.4%

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

      17. *-inverses 96.4%

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

      18. *-inverses 96.4%

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

      19. associate-/r* 96.4%

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

      20. *-commutative 96.4%

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

      21. fma-def 96.4%

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

   3. Simplified 96.4%

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

   4. Taylor expanded in y around 0 96.4%

      \[\leadsto \frac{y}{\color{blue}{-0.5 \cdot \frac{y}{x} + 0.5}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 95.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+204}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 4.2 \cdot 10^{+228}:\\ \;\;\;\;\frac{y}{0.5 + -0.5 \cdot \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \]

Alternative 6: 74.9% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.95e+32) (/ x -0.5) (if (<= y 5.2e+57) (/ y 0.5) (/ x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.95e+32) {
		tmp = x / -0.5;
	} else if (y <= 5.2e+57) {
		tmp = y / 0.5;
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-2.95d+32)) then
        tmp = x / (-0.5d0)
    else if (y <= 5.2d+57) then
        tmp = y / 0.5d0
    else
        tmp = x / (-0.5d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.95e+32) {
		tmp = x / -0.5;
	} else if (y <= 5.2e+57) {
		tmp = y / 0.5;
	} else {
		tmp = x / -0.5;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.95e+32:
		tmp = x / -0.5
	elif y <= 5.2e+57:
		tmp = y / 0.5
	else:
		tmp = x / -0.5
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.95e+32)
		tmp = Float64(x / -0.5);
	elseif (y <= 5.2e+57)
		tmp = Float64(y / 0.5);
	else
		tmp = Float64(x / -0.5);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.95e+32)
		tmp = x / -0.5;
	elseif (y <= 5.2e+57)
		tmp = y / 0.5;
	else
		tmp = x / -0.5;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.95e+32], N[(x / -0.5), $MachinePrecision], If[LessEqual[y, 5.2e+57], N[(y / 0.5), $MachinePrecision], N[(x / -0.5), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.94999999999999983e32 or 5.2e57 < y

   1. Initial program 70.6%

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

      1. associate-*l* 70.6%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. remove-double-neg 99.9%

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

      5. remove-double-neg 99.9%

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

      6. *-lft-identity 99.9%

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

      7. *-inverses 99.9%

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

      8. times-frac 99.9%

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

      9. *-inverses 99.9%

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

      10. *-inverses 99.9%

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

      11. associate-/r* 99.9%

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

      12. *-commutative 99.9%

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

      13. fma-neg 99.9%

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

      14. *-commutative 99.9%

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

      15. associate-/r* 99.9%

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

      16. *-inverses 99.9%

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

      17. metadata-eval 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

      18. *-commutative 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

      19. associate-/r* 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

      20. *-inverses 99.9%

          \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

      21. metadata-eval 99.9%

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

      22. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 75.9%

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

   if -2.94999999999999983e32 < y < 5.2e57

   1. Initial program 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-/l* 99.9%

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

      3. div-sub 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. distribute-neg-frac 99.9%

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

      7. neg-mul-1 99.9%

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

      8. *-commutative 99.9%

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

      9. times-frac 99.9%

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

      10. metadata-eval 99.9%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{-0.5} + \frac{x}{x \cdot 2}} \]

      11. metadata-eval 99.9%

          \[\leadsto \frac{y}{\frac{y}{x} \cdot \color{blue}{\left(-0.5\right)} + \frac{x}{x \cdot 2}} \]

      12. metadata-eval 99.9%

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

      13. *-inverses 99.9%

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

      14. associate-/r* 99.9%

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

      15. *-commutative 99.9%

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

      16. associate-/r* 99.9%

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

      17. *-inverses 99.9%

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

      18. *-inverses 99.9%

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

      19. associate-/r* 99.9%

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

      20. *-commutative 99.9%

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

      21. fma-def 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 76.2%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.95 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{-0.5}\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{+57}:\\ \;\;\;\;\frac{y}{0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{-0.5}\\ \end{array} \]

Alternative 7: 50.9% accurate, 3.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 (/ x -0.5))

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x / (-0.5d0)
end function

Java

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

Python

def code(x, y):
	return x / -0.5

Julia

function code(x, y)
	return Float64(x / -0.5)
end

MATLAB

function tmp = code(x, y)
	tmp = x / -0.5;
end

Wolfram

code[x_, y_] := N[(x / -0.5), $MachinePrecision]

Derivation

1. Initial program 74.8%

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

   1. associate-*l* 74.8%

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

   2. associate-/l* 90.8%

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

   3. div-sub 90.8%

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

   4. remove-double-neg 90.8%

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

   5. remove-double-neg 90.8%

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

   6. *-lft-identity 90.8%

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

   7. *-inverses 90.8%

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

   8. times-frac 90.8%

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

   9. *-inverses 90.8%

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

   10. *-inverses 90.8%

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

   11. associate-/r* 90.8%

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

   12. *-commutative 90.8%

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

   13. fma-neg 90.8%

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

   14. *-commutative 90.8%

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

   15. associate-/r* 90.8%

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

   16. *-inverses 90.8%

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

   17. metadata-eval 90.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(\color{blue}{0.5}, \frac{x}{y}, -\frac{y}{2 \cdot y}\right)} \]

   18. *-commutative 90.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{y}{\color{blue}{y \cdot 2}}\right)} \]

   19. associate-/r* 90.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\color{blue}{\frac{\frac{y}{y}}{2}}\right)} \]

   20. *-inverses 90.8%

       \[\leadsto \frac{x}{\mathsf{fma}\left(0.5, \frac{x}{y}, -\frac{\color{blue}{1}}{2}\right)} \]

   21. metadata-eval 90.8%

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

   22. metadata-eval 90.8%

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

3. Simplified 90.8%

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

4. Taylor expanded in x around 0 48.7%

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

5. Final simplification 48.7%

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

Developer target: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{if}\;x < -1.7210442634149447 \cdot 10^{+81}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x < 83645045635564430:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (/ (* 2.0 x) (- x y)) y)))
   (if (< x -1.7210442634149447e+81)
     t_0
     (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	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 = ((2.0d0 * x) / (x - y)) * y
    if (x < (-1.7210442634149447d+81)) then
        tmp = t_0
    else if (x < 83645045635564430.0d0) then
        tmp = (x * 2.0d0) / ((x - y) / y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((2.0 * x) / (x - y)) * y;
	double tmp;
	if (x < -1.7210442634149447e+81) {
		tmp = t_0;
	} else if (x < 83645045635564430.0) {
		tmp = (x * 2.0) / ((x - y) / y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((2.0 * x) / (x - y)) * y
	tmp = 0
	if x < -1.7210442634149447e+81:
		tmp = t_0
	elif x < 83645045635564430.0:
		tmp = (x * 2.0) / ((x - y) / y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(2.0 * x) / Float64(x - y)) * y)
	tmp = 0.0
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = Float64(Float64(x * 2.0) / Float64(Float64(x - y) / y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((2.0 * x) / (x - y)) * y;
	tmp = 0.0;
	if (x < -1.7210442634149447e+81)
		tmp = t_0;
	elseif (x < 83645045635564430.0)
		tmp = (x * 2.0) / ((x - y) / y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(2.0 * x), $MachinePrecision] / N[(x - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]}, If[Less[x, -1.7210442634149447e+81], t$95$0, If[Less[x, 83645045635564430.0], N[(N[(x * 2.0), $MachinePrecision] / N[(N[(x - y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2023224 
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2.0 x) (- x y)) y) (if (< x 83645045635564430.0) (/ (* x 2.0) (/ (- x y) y)) (* (/ (* 2.0 x) (- x y)) y)))

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