Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 87.7% → 99.9%

Time: 6.4s

Alternatives: 12

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))

C

double code(double x, double y) {
	return (x * ((x / y) + 1.0)) / (x + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * ((x / y) + 1.0d0)) / (x + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x * ((x / y) + 1.0)) / (x + 1.0);
}

Python

def code(x, y):
	return (x * ((x / y) + 1.0)) / (x + 1.0)

Julia

function code(x, y)
	return Float64(Float64(x * Float64(Float64(x / y) + 1.0)) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * ((x / y) + 1.0)) / (x + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 87.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))

C

double code(double x, double y) {
	return (x * ((x / y) + 1.0)) / (x + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x * ((x / y) + 1.0d0)) / (x + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x * ((x / y) + 1.0)) / (x + 1.0);
}

Python

def code(x, y):
	return (x * ((x / y) + 1.0)) / (x + 1.0)

Julia

function code(x, y)
	return Float64(Float64(x * Float64(Float64(x / y) + 1.0)) / Float64(x + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x * ((x / y) + 1.0)) / (x + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \mathbf{elif}\;t_0 \leq 5 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* x (+ (/ x y) 1.0)) (+ x 1.0))))
   (if (<= t_0 -5e+24)
     (/ x (+ y (/ y x)))
     (if (<= t_0 5e+95) t_0 (/ x (* y (+ 1.0 (/ 1.0 x))))))))

C

double code(double x, double y) {
	double t_0 = (x * ((x / y) + 1.0)) / (x + 1.0);
	double tmp;
	if (t_0 <= -5e+24) {
		tmp = x / (y + (y / x));
	} else if (t_0 <= 5e+95) {
		tmp = t_0;
	} else {
		tmp = x / (y * (1.0 + (1.0 / 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 * ((x / y) + 1.0d0)) / (x + 1.0d0)
    if (t_0 <= (-5d+24)) then
        tmp = x / (y + (y / x))
    else if (t_0 <= 5d+95) then
        tmp = t_0
    else
        tmp = x / (y * (1.0d0 + (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x * ((x / y) + 1.0)) / (x + 1.0);
	double tmp;
	if (t_0 <= -5e+24) {
		tmp = x / (y + (y / x));
	} else if (t_0 <= 5e+95) {
		tmp = t_0;
	} else {
		tmp = x / (y * (1.0 + (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * ((x / y) + 1.0)) / (x + 1.0)
	tmp = 0
	if t_0 <= -5e+24:
		tmp = x / (y + (y / x))
	elif t_0 <= 5e+95:
		tmp = t_0
	else:
		tmp = x / (y * (1.0 + (1.0 / x)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * Float64(Float64(x / y) + 1.0)) / Float64(x + 1.0))
	tmp = 0.0
	if (t_0 <= -5e+24)
		tmp = Float64(x / Float64(y + Float64(y / x)));
	elseif (t_0 <= 5e+95)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(y * Float64(1.0 + Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * ((x / y) + 1.0)) / (x + 1.0);
	tmp = 0.0;
	if (t_0 <= -5e+24)
		tmp = x / (y + (y / x));
	elseif (t_0 <= 5e+95)
		tmp = t_0;
	else
		tmp = x / (y * (1.0 + (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+24], N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 5e+95], t$95$0, N[(x / N[(y * N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1)) < -5.00000000000000045e24

   1. Initial program 78.3%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 78.3%

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

      2. associate-/l* 99.9%

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

      3. remove-double-neg 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-/r* 99.9%

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

      7. +-commutative 99.9%

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

      8. remove-double-neg 99.9%

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

      9. unsub-neg 99.9%

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

      10. div-sub 99.9%

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

      11. *-inverses 99.9%

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

      12. div-sub 99.9%

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

      13. associate-/r* 99.9%

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

      14. *-commutative 99.9%

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

      15. neg-mul-1 99.9%

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

      16. remove-double-neg 99.9%

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

      17. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 99.9%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. distribute-lft-in 99.9%

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

      2. *-rgt-identity 99.9%

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

      3. associate-*r/ 100.0%

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

      4. *-rgt-identity 100.0%

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

   6. Simplified 100.0%

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

   if -5.00000000000000045e24 < (/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1)) < 5.00000000000000025e95

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   if 5.00000000000000025e95 < (/.f64 (*.f64 x (+.f64 (/.f64 x y) 1)) (+.f64 x 1))

   1. Initial program 70.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 70.1%

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

      2. associate-/l* 99.9%

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

      3. remove-double-neg 99.9%

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

      4. neg-mul-1 99.9%

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

      5. *-commutative 99.9%

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

      6. associate-/r* 99.9%

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

      7. +-commutative 99.9%

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

      8. remove-double-neg 99.9%

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

      9. unsub-neg 99.9%

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

      10. div-sub 100.0%

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

      11. *-inverses 100.0%

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

      12. div-sub 100.0%

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

      13. associate-/r* 100.0%

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

      14. *-commutative 100.0%

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

      15. neg-mul-1 100.0%

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

      16. remove-double-neg 100.0%

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

      17. metadata-eval 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 100.0%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \leq -5 \cdot 10^{+24}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \mathbf{elif}\;\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \leq 5 \cdot 10^{+95}:\\ \;\;\;\;\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}\\ \end{array} \]

Alternative 2: 99.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{1}{x}\\ \frac{\frac{x}{y}}{t_0} + \frac{1}{t_0} \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ 1.0 x)))) (+ (/ (/ x y) t_0) (/ 1.0 t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (1.0 / x);
	return ((x / y) / t_0) + (1.0 / t_0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    t_0 = 1.0d0 + (1.0d0 / x)
    code = ((x / y) / t_0) + (1.0d0 / t_0)
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (1.0 / x);
	return ((x / y) / t_0) + (1.0 / t_0);
}

Python

def code(x, y):
	t_0 = 1.0 + (1.0 / x)
	return ((x / y) / t_0) + (1.0 / t_0)

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(1.0 / x))
	return Float64(Float64(Float64(x / y) / t_0) + Float64(1.0 / t_0))
end

MATLAB

function tmp = code(x, y)
	t_0 = 1.0 + (1.0 / x);
	tmp = ((x / y) / t_0) + (1.0 / t_0);
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]}, N[(N[(N[(x / y), $MachinePrecision] / t$95$0), $MachinePrecision] + N[(1.0 / t$95$0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 89.7%

   \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 89.7%

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

   2. associate-/l* 99.8%

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

   3. remove-double-neg 99.8%

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

   4. neg-mul-1 99.8%

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

   5. *-commutative 99.8%

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

   6. associate-/r* 99.8%

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

   7. +-commutative 99.8%

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

   8. remove-double-neg 99.8%

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

   9. unsub-neg 99.8%

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

   10. div-sub 99.8%

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

   11. *-inverses 99.8%

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

   12. div-sub 99.8%

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

   13. associate-/r* 99.8%

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

   14. *-commutative 99.8%

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

   15. neg-mul-1 99.8%

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

   16. remove-double-neg 99.8%

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

   17. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Taylor expanded in y around 0 99.8%

   \[\leadsto \color{blue}{\frac{1}{1 + \frac{1}{x}} + \frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
5. Step-by-step derivation

   1. +-commutative 99.8%

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

   2. associate-/r* 99.8%

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

6. Simplified 99.8%

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

7. Final simplification 99.8%

   \[\leadsto \frac{\frac{x}{y}}{1 + \frac{1}{x}} + \frac{1}{1 + \frac{1}{x}} \]

Alternative 3: 98.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -80000 \lor \neg \left(x \leq 1900000\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{x}{y}}{1 + \frac{1}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -80000.0) (not (<= x 1900000.0)))
   (+ 1.0 (/ (+ x -1.0) y))
   (+ x (/ (/ x y) (+ 1.0 (/ 1.0 x))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -80000.0) || !(x <= 1900000.0)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x + ((x / y) / (1.0 + (1.0 / x)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-80000.0d0)) .or. (.not. (x <= 1900000.0d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) / y)
    else
        tmp = x + ((x / y) / (1.0d0 + (1.0d0 / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -80000.0) || !(x <= 1900000.0)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x + ((x / y) / (1.0 + (1.0 / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -80000.0) or not (x <= 1900000.0):
		tmp = 1.0 + ((x + -1.0) / y)
	else:
		tmp = x + ((x / y) / (1.0 + (1.0 / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -80000.0) || !(x <= 1900000.0))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(x + Float64(Float64(x / y) / Float64(1.0 + Float64(1.0 / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -80000.0) || ~((x <= 1900000.0)))
		tmp = 1.0 + ((x + -1.0) / y);
	else
		tmp = x + ((x / y) / (1.0 + (1.0 / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -80000.0], N[Not[LessEqual[x, 1900000.0]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(x / y), $MachinePrecision] / N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -8e4 or 1.9e6 < x

   1. Initial program 79.4%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 99.7%

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

   3. Taylor expanded in y around -inf 99.7%

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

      1. mul-1-neg 99.7%

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

      2. unsub-neg 99.7%

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

      3. neg-mul-1 99.7%

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

      4. unsub-neg 99.7%

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

   5. Simplified 99.7%

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

   if -8e4 < x < 1.9e6

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. remove-double-neg 99.7%

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

      4. neg-mul-1 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.7%

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

      7. +-commutative 99.7%

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

      8. remove-double-neg 99.7%

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

      9. unsub-neg 99.7%

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

      10. div-sub 99.7%

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

      11. *-inverses 99.7%

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

      12. div-sub 99.7%

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

      13. associate-/r* 99.7%

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

      14. *-commutative 99.7%

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

      15. neg-mul-1 99.7%

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

      16. remove-double-neg 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 99.6%

      \[\leadsto \color{blue}{\frac{1}{1 + \frac{1}{x}} + \frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. +-commutative 99.6%

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

      2. associate-/r* 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in x around 0 98.3%

      \[\leadsto \frac{\frac{x}{y}}{1 + \frac{1}{x}} + \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -80000 \lor \neg \left(x \leq 1900000\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{x}{y}}{1 + \frac{1}{x}}\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (/ x y)
   (if (<= x -4.3e-66)
     (* x (/ x y))
     (if (<= x 4.1e+30) (/ x (+ x 1.0)) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= -4.3e-66) {
		tmp = x * (x / y);
	} else if (x <= 4.1e+30) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = x / y
    else if (x <= (-4.3d-66)) then
        tmp = x * (x / y)
    else if (x <= 4.1d+30) then
        tmp = x / (x + 1.0d0)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= -4.3e-66) {
		tmp = x * (x / y);
	} else if (x <= 4.1e+30) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / y
	elif x <= -4.3e-66:
		tmp = x * (x / y)
	elif x <= 4.1e+30:
		tmp = x / (x + 1.0)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= -4.3e-66)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 4.1e+30)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x / y;
	elseif (x <= -4.3e-66)
		tmp = x * (x / y);
	elseif (x <= 4.1e+30)
		tmp = x / (x + 1.0);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, -4.3e-66], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.1e+30], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 4.10000000000000005e30 < x

   1. Initial program 78.2%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 83.2%

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

   if -1 < x < -4.30000000000000013e-66

   1. Initial program 99.7%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-/l* 99.1%

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

      3. remove-double-neg 99.1%

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

      4. neg-mul-1 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. +-commutative 99.1%

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

      8. remove-double-neg 99.1%

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

      9. unsub-neg 99.1%

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

      10. div-sub 99.1%

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

      11. *-inverses 99.1%

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

      12. div-sub 99.1%

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

      13. associate-/r* 99.1%

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

      14. *-commutative 99.1%

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

      15. neg-mul-1 99.1%

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

      16. remove-double-neg 99.1%

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

      17. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. associate-/r* 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-/r/ 64.7%

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

      2. /-rgt-identity 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -4.30000000000000013e-66 < x < 4.10000000000000005e30

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in y around inf 74.4%

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

      1. +-commutative 74.4%

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

   4. Simplified 74.4%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -4.3 \cdot 10^{-66}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 5: 74.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -1}{y}\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) y)))
   (if (<= x -1.0)
     t_0
     (if (<= x -1.2e-64) (* x (/ x y)) (if (<= x 30.0) (/ x (+ x 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = (x + -1.0) / y;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= -1.2e-64) {
		tmp = x * (x / y);
	} else if (x <= 30.0) {
		tmp = x / (x + 1.0);
	} 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 = (x + (-1.0d0)) / y
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= (-1.2d-64)) then
        tmp = x * (x / y)
    else if (x <= 30.0d0) then
        tmp = x / (x + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + -1.0) / y;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= -1.2e-64) {
		tmp = x * (x / y);
	} else if (x <= 30.0) {
		tmp = x / (x + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + -1.0) / y
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= -1.2e-64:
		tmp = x * (x / y)
	elif x <= 30.0:
		tmp = x / (x + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -1.0) / y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= -1.2e-64)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 30.0)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + -1.0) / y;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= -1.2e-64)
		tmp = x * (x / y);
	elseif (x <= 30.0)
		tmp = x / (x + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, -1.2e-64], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 30.0], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 30 < x

   1. Initial program 79.8%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 98.6%

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

   3. Taylor expanded in y around 0 80.8%

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

   if -1 < x < -1.19999999999999999e-64

   1. Initial program 99.7%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-/l* 99.1%

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

      3. remove-double-neg 99.1%

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

      4. neg-mul-1 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. +-commutative 99.1%

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

      8. remove-double-neg 99.1%

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

      9. unsub-neg 99.1%

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

      10. div-sub 99.1%

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

      11. *-inverses 99.1%

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

      12. div-sub 99.1%

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

      13. associate-/r* 99.1%

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

      14. *-commutative 99.1%

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

      15. neg-mul-1 99.1%

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

      16. remove-double-neg 99.1%

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

      17. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. associate-/r* 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-/r/ 64.7%

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

      2. /-rgt-identity 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -1.19999999999999999e-64 < x < 30

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in y around inf 77.0%

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

      1. +-commutative 77.0%

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

   4. Simplified 77.0%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x + -1}{y}\\ \mathbf{elif}\;x \leq -1.2 \cdot 10^{-64}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 30:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -1}{y}\\ \end{array} \]

Alternative 6: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} + 1\\ \mathbf{if}\;x \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ x y) 1.0)))
   (if (<= x -1.0)
     t_0
     (if (<= x -2.7e-67) (* x (/ x y)) (if (<= x 0.6) (/ x (+ x 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = (x / y) + 1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= -2.7e-67) {
		tmp = x * (x / y);
	} else if (x <= 0.6) {
		tmp = x / (x + 1.0);
	} 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 = (x / y) + 1.0d0
    if (x <= (-1.0d0)) then
        tmp = t_0
    else if (x <= (-2.7d-67)) then
        tmp = x * (x / y)
    else if (x <= 0.6d0) then
        tmp = x / (x + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) + 1.0;
	double tmp;
	if (x <= -1.0) {
		tmp = t_0;
	} else if (x <= -2.7e-67) {
		tmp = x * (x / y);
	} else if (x <= 0.6) {
		tmp = x / (x + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) + 1.0
	tmp = 0
	if x <= -1.0:
		tmp = t_0
	elif x <= -2.7e-67:
		tmp = x * (x / y)
	elif x <= 0.6:
		tmp = x / (x + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) + 1.0)
	tmp = 0.0
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= -2.7e-67)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 0.6)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) + 1.0;
	tmp = 0.0;
	if (x <= -1.0)
		tmp = t_0;
	elseif (x <= -2.7e-67)
		tmp = x * (x / y);
	elseif (x <= 0.6)
		tmp = x / (x + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[LessEqual[x, -1.0], t$95$0, If[LessEqual[x, -2.7e-67], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.6], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 0.599999999999999978 < x

   1. Initial program 80.0%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 97.8%

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

   3. Taylor expanded in y around -inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. unsub-neg 97.8%

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

      3. neg-mul-1 97.8%

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

      4. unsub-neg 97.8%

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

   5. Simplified 97.8%

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

   6. Taylor expanded in x around inf 96.8%

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

      1. neg-mul-1 96.8%

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

      2. distribute-neg-frac 96.8%

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

   8. Simplified 96.8%

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

   if -1 < x < -2.70000000000000016e-67

   1. Initial program 99.7%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-/l* 99.1%

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

      3. remove-double-neg 99.1%

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

      4. neg-mul-1 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. +-commutative 99.1%

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

      8. remove-double-neg 99.1%

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

      9. unsub-neg 99.1%

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

      10. div-sub 99.1%

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

      11. *-inverses 99.1%

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

      12. div-sub 99.1%

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

      13. associate-/r* 99.1%

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

      14. *-commutative 99.1%

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

      15. neg-mul-1 99.1%

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

      16. remove-double-neg 99.1%

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

      17. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. associate-/r* 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-/r/ 64.7%

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

      2. /-rgt-identity 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -2.70000000000000016e-67 < x < 0.599999999999999978

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in y around inf 77.7%

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

      1. +-commutative 77.7%

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

   4. Simplified 77.7%

      \[\leadsto \color{blue}{\frac{x}{x + 1}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{-67}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.6:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} + 1\\ \end{array} \]

Alternative 7: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y} + 1\\ \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ (/ x y) 1.0)))
   (if (or (<= x -1.0) (not (<= x 1.0))) t_0 (* x t_0))))

C

double code(double x, double y) {
	double t_0 = (x / y) + 1.0;
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = t_0;
	} else {
		tmp = x * 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 = (x / y) + 1.0d0
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = t_0
    else
        tmp = x * t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x / y) + 1.0;
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = t_0;
	} else {
		tmp = x * t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x / y) + 1.0
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = t_0
	else:
		tmp = x * t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x / y) + 1.0)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = t_0;
	else
		tmp = Float64(x * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x / y) + 1.0;
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = t_0;
	else
		tmp = x * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]}, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], t$95$0, N[(x * t$95$0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 79.8%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 98.6%

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

   3. Taylor expanded in y around -inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. unsub-neg 98.6%

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

      3. neg-mul-1 98.6%

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

      4. unsub-neg 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around inf 97.5%

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

      1. neg-mul-1 97.5%

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

      2. distribute-neg-frac 97.5%

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

   8. Simplified 97.5%

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

   if -1 < x < 1

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. remove-double-neg 99.7%

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

      4. neg-mul-1 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.7%

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

      7. +-commutative 99.7%

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

      8. remove-double-neg 99.7%

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

      9. unsub-neg 99.7%

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

      10. div-sub 99.7%

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

      11. *-inverses 99.7%

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

      12. div-sub 99.7%

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

      13. associate-/r* 99.7%

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

      14. *-commutative 99.7%

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

      15. neg-mul-1 99.7%

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

      16. remove-double-neg 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 95.9%

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

      1. associate-/r/ 96.2%

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

      2. /-rgt-identity 96.2%

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

      3. +-commutative 96.2%

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

   6. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\left(1 + \frac{x}{y}\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 96.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{x}{y} + 1\right)\\ \end{array} \]

Alternative 8: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.22\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{x}{y} + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.22)))
   (+ 1.0 (/ (+ x -1.0) y))
   (* x (+ (/ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.22)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x * ((x / y) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.22d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) / y)
    else
        tmp = x * ((x / y) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.22)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x * ((x / y) + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.22):
		tmp = 1.0 + ((x + -1.0) / y)
	else:
		tmp = x * ((x / y) + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.22))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(x * Float64(Float64(x / y) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.22)))
		tmp = 1.0 + ((x + -1.0) / y);
	else
		tmp = x * ((x / y) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.22]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.21999999999999997 < x

   1. Initial program 79.8%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 98.6%

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

   3. Taylor expanded in y around -inf 98.6%

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

      1. mul-1-neg 98.6%

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

      2. unsub-neg 98.6%

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

      3. neg-mul-1 98.6%

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

      4. unsub-neg 98.6%

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

   5. Simplified 98.6%

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

   if -1 < x < 1.21999999999999997

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.9%

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

      2. associate-/l* 99.7%

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

      3. remove-double-neg 99.7%

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

      4. neg-mul-1 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.7%

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

      7. +-commutative 99.7%

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

      8. remove-double-neg 99.7%

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

      9. unsub-neg 99.7%

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

      10. div-sub 99.7%

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

      11. *-inverses 99.7%

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

      12. div-sub 99.7%

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

      13. associate-/r* 99.7%

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

      14. *-commutative 99.7%

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

      15. neg-mul-1 99.7%

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

      16. remove-double-neg 99.7%

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

      17. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in x around 0 95.9%

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

      1. associate-/r/ 96.2%

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

      2. /-rgt-identity 96.2%

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

      3. +-commutative 96.2%

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

   6. Applied egg-rr 96.2%

      \[\leadsto \color{blue}{\left(1 + \frac{x}{y}\right) \cdot x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 97.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.22\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{x}{y} + 1\right)\\ \end{array} \]

Alternative 9: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{\frac{x}{y} + 1}{\frac{1}{x} - -1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ (/ x y) 1.0) (- (/ 1.0 x) -1.0)))

C

double code(double x, double y) {
	return ((x / y) + 1.0) / ((1.0 / x) - -1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x / y) + 1.0d0) / ((1.0d0 / x) - (-1.0d0))
end function

Java

public static double code(double x, double y) {
	return ((x / y) + 1.0) / ((1.0 / x) - -1.0);
}

Python

def code(x, y):
	return ((x / y) + 1.0) / ((1.0 / x) - -1.0)

Julia

function code(x, y)
	return Float64(Float64(Float64(x / y) + 1.0) / Float64(Float64(1.0 / x) - -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x / y) + 1.0) / ((1.0 / x) - -1.0);
end

Wolfram

code[x_, y_] := N[(N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision] / N[(N[(1.0 / x), $MachinePrecision] - -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 89.7%

   \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
2. Step-by-step derivation

   1. *-commutative 89.7%

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

   2. associate-/l* 99.8%

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

   3. remove-double-neg 99.8%

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

   4. neg-mul-1 99.8%

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

   5. *-commutative 99.8%

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

   6. associate-/r* 99.8%

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

   7. +-commutative 99.8%

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

   8. remove-double-neg 99.8%

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

   9. unsub-neg 99.8%

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

   10. div-sub 99.8%

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

   11. *-inverses 99.8%

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

   12. div-sub 99.8%

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

   13. associate-/r* 99.8%

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

   14. *-commutative 99.8%

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

   15. neg-mul-1 99.8%

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

   16. remove-double-neg 99.8%

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

   17. metadata-eval 99.8%

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

3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \frac{\frac{x}{y} + 1}{\frac{1}{x} - -1} \]

Alternative 10: 74.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (/ x y)
   (if (<= x -7.2e-65) (* x (/ x y)) (if (<= x 0.4) x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= -7.2e-65) {
		tmp = x * (x / y);
	} else if (x <= 0.4) {
		tmp = x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = x / y
    else if (x <= (-7.2d-65)) then
        tmp = x * (x / y)
    else if (x <= 0.4d0) then
        tmp = x
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= -7.2e-65) {
		tmp = x * (x / y);
	} else if (x <= 0.4) {
		tmp = x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / y
	elif x <= -7.2e-65:
		tmp = x * (x / y)
	elif x <= 0.4:
		tmp = x
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= -7.2e-65)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 0.4)
		tmp = x;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x / y;
	elseif (x <= -7.2e-65)
		tmp = x * (x / y);
	elseif (x <= 0.4)
		tmp = x;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, -7.2e-65], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.4], x, N[(x / y), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 0.40000000000000002 < x

   1. Initial program 80.0%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 79.2%

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

   if -1 < x < -7.1999999999999996e-65

   1. Initial program 99.7%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   2. Step-by-step derivation

      1. *-commutative 99.7%

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

      2. associate-/l* 99.1%

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

      3. remove-double-neg 99.1%

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

      4. neg-mul-1 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.1%

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

      7. +-commutative 99.1%

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

      8. remove-double-neg 99.1%

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

      9. unsub-neg 99.1%

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

      10. div-sub 99.1%

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

      11. *-inverses 99.1%

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

      12. div-sub 99.1%

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

      13. associate-/r* 99.1%

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

      14. *-commutative 99.1%

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

      15. neg-mul-1 99.1%

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

      16. remove-double-neg 99.1%

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

      17. metadata-eval 99.1%

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

   3. Simplified 99.1%

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

   4. Taylor expanded in y around 0 77.8%

      \[\leadsto \color{blue}{\frac{x}{y \cdot \left(1 + \frac{1}{x}\right)}} \]
   5. Step-by-step derivation

      1. associate-/r* 77.3%

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

   6. Simplified 77.3%

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

   7. Taylor expanded in x around 0 64.3%

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

      1. associate-/r/ 64.7%

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

      2. /-rgt-identity 64.7%

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

   9. Applied egg-rr 64.7%

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

   if -7.1999999999999996e-65 < x < 0.40000000000000002

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around 0 76.6%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -7.2 \cdot 10^{-65}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 11: 74.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.48\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.48))) (/ x y) x))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.48)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 0.48d0))) then
        tmp = x / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.48)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.48):
		tmp = x / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.48))
		tmp = Float64(x / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 0.48)))
		tmp = x / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 0.48]], $MachinePrecision]], N[(x / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 0.47999999999999998 < x

   1. Initial program 80.0%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around inf 79.2%

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

   if -1 < x < 0.47999999999999998

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

   2. Taylor expanded in x around 0 70.6%

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

4. Final simplification 75.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.48\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 38.9% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 x)

C

double code(double x, double y) {
	return x;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x
end function

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

function tmp = code(x, y)
	tmp = x;
end

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 89.7%

   \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]

2. Taylor expanded in x around 0 36.7%

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

3. Final simplification 36.7%

   \[\leadsto x \]

Developer target: 99.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \frac{x}{1} \cdot \frac{\frac{x}{y} + 1}{x + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0))))

C

double code(double x, double y) {
	return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x / 1.0d0) * (((x / y) + 1.0d0) / (x + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0));
}

Python

def code(x, y):
	return (x / 1.0) * (((x / y) + 1.0) / (x + 1.0))

Julia

function code(x, y)
	return Float64(Float64(x / 1.0) * Float64(Float64(Float64(x / y) + 1.0) / Float64(x + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = (x / 1.0) * (((x / y) + 1.0) / (x + 1.0));
end

Wolfram

code[x_, y_] := N[(N[(x / 1.0), $MachinePrecision] * N[(N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023322 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* (/ x 1.0) (/ (+ (/ x y) 1.0) (+ x 1.0)))

  (/ (* x (+ (/ x y) 1.0)) (+ x 1.0)))