Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 88.2% → 99.9%

Time: 9.2s

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: 88.2% 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, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ t\_0 + t\_0 \cdot \frac{x}{y} \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

   1. associate-/r/ 99.9%

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

   2. +-commutative 99.9%

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

   3. un-div-inv 99.8%

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

   4. +-commutative 99.8%

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

   5. distribute-lft-in 99.8%

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

   6. *-commutative 99.8%

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

   7. *-un-lft-identity 99.8%

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

   8. un-div-inv 99.8%

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

   9. +-commutative 99.8%

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

   10. un-div-inv 99.9%

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

   11. +-commutative 99.9%

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

8. Applied egg-rr 99.9%

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

9. Final simplification 99.9%

   \[\leadsto \frac{x}{x + 1} + \frac{x}{x + 1} \cdot \frac{x}{y} \]
10. Add Preprocessing

Alternative 2: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + \frac{y}{x}}\\ \mathbf{if}\;x \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \frac{1}{y}\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y (/ y x)))))
   (if (<= x -6.8e-7)
     t_0
     (if (<= x 2.9e-7)
       (* x (+ 1.0 (* x (/ 1.0 y))))
       (if (or (<= x 5.7e+104) (not (<= x 3.15e+134))) t_0 1.0)))))

C

double code(double x, double y) {
	double t_0 = x / (y + (y / x));
	double tmp;
	if (x <= -6.8e-7) {
		tmp = t_0;
	} else if (x <= 2.9e-7) {
		tmp = x * (1.0 + (x * (1.0 / y)));
	} else if ((x <= 5.7e+104) || !(x <= 3.15e+134)) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	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 + (y / x))
    if (x <= (-6.8d-7)) then
        tmp = t_0
    else if (x <= 2.9d-7) then
        tmp = x * (1.0d0 + (x * (1.0d0 / y)))
    else if ((x <= 5.7d+104) .or. (.not. (x <= 3.15d+134))) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + (y / x));
	double tmp;
	if (x <= -6.8e-7) {
		tmp = t_0;
	} else if (x <= 2.9e-7) {
		tmp = x * (1.0 + (x * (1.0 / y)));
	} else if ((x <= 5.7e+104) || !(x <= 3.15e+134)) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + (y / x))
	tmp = 0
	if x <= -6.8e-7:
		tmp = t_0
	elif x <= 2.9e-7:
		tmp = x * (1.0 + (x * (1.0 / y)))
	elif (x <= 5.7e+104) or not (x <= 3.15e+134):
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + Float64(y / x)))
	tmp = 0.0
	if (x <= -6.8e-7)
		tmp = t_0;
	elseif (x <= 2.9e-7)
		tmp = Float64(x * Float64(1.0 + Float64(x * Float64(1.0 / y))));
	elseif ((x <= 5.7e+104) || !(x <= 3.15e+134))
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + (y / x));
	tmp = 0.0;
	if (x <= -6.8e-7)
		tmp = t_0;
	elseif (x <= 2.9e-7)
		tmp = x * (1.0 + (x * (1.0 / y)));
	elseif ((x <= 5.7e+104) || ~((x <= 3.15e+134)))
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.8e-7], t$95$0, If[LessEqual[x, 2.9e-7], N[(x * N[(1.0 + N[(x * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.7e+104], N[Not[LessEqual[x, 3.15e+134]], $MachinePrecision]], t$95$0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.79999999999999948e-7 or 2.8999999999999998e-7 < x < 5.69999999999999985e104 or 3.1500000000000001e134 < x

   1. Initial program 75.3%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

   7. Taylor expanded in y around 0 66.8%

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

   8. Taylor expanded in x around 0 66.8%

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

      1. distribute-rgt1-in 66.8%

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

      2. *-commutative 66.8%

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

      3. associate-*r/ 83.2%

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

      4. *-lft-identity 83.2%

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

      5. associate-*l/ 83.1%

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

      6. distribute-rgt-in 83.1%

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

      7. rgt-mult-inverse 83.2%

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

      8. *-lft-identity 83.2%

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

      9. distribute-lft-in 83.2%

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

      10. *-rgt-identity 83.2%

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

      11. associate-*r/ 83.2%

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

      12. *-rgt-identity 83.2%

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

   10. Simplified 83.2%

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

   if -6.79999999999999948e-7 < x < 2.8999999999999998e-7

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.2%

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

   6. Taylor expanded in y around 0 98.4%

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

   if 5.69999999999999985e104 < x < 3.1500000000000001e134

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

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

      1. un-div-inv 100.0%

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

      2. +-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.8 \cdot 10^{-7}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-7}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \frac{1}{y}\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 72.1% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (/ x y)
   (if (<= x 0.022)
     x
     (if (or (<= x 4.9e+104) (not (<= x 3.15e+134))) (/ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 0.022) {
		tmp = x;
	} else if ((x <= 4.9e+104) || !(x <= 3.15e+134)) {
		tmp = x / y;
	} else {
		tmp = 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)) then
        tmp = x / y
    else if (x <= 0.022d0) then
        tmp = x
    else if ((x <= 4.9d+104) .or. (.not. (x <= 3.15d+134))) then
        tmp = x / y
    else
        tmp = 1.0d0
    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 <= 0.022) {
		tmp = x;
	} else if ((x <= 4.9e+104) || !(x <= 3.15e+134)) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / y
	elif x <= 0.022:
		tmp = x
	elif (x <= 4.9e+104) or not (x <= 3.15e+134):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= 0.022)
		tmp = x;
	elseif ((x <= 4.9e+104) || !(x <= 3.15e+134))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x / y;
	elseif (x <= 0.022)
		tmp = x;
	elseif ((x <= 4.9e+104) || ~((x <= 3.15e+134)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 0.022], x, If[Or[LessEqual[x, 4.9e+104], N[Not[LessEqual[x, 3.15e+134]], $MachinePrecision]], N[(x / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 0.021999999999999999 < x < 4.89999999999999985e104 or 3.1500000000000001e134 < x

   1. Initial program 75.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.9%

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

   if -1 < x < 0.021999999999999999

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 64.1%

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

   if 4.89999999999999985e104 < x < 3.1500000000000001e134

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

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

      1. un-div-inv 100.0%

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

      2. +-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 73.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.022:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.3 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (/ x y)
   (if (<= x 0.112)
     (* x (- 1.0 x))
     (if (or (<= x 5.7e+104) (not (<= x 3.3e+134))) (/ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 0.112) {
		tmp = x * (1.0 - x);
	} else if ((x <= 5.7e+104) || !(x <= 3.3e+134)) {
		tmp = x / y;
	} else {
		tmp = 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)) then
        tmp = x / y
    else if (x <= 0.112d0) then
        tmp = x * (1.0d0 - x)
    else if ((x <= 5.7d+104) .or. (.not. (x <= 3.3d+134))) then
        tmp = x / y
    else
        tmp = 1.0d0
    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 <= 0.112) {
		tmp = x * (1.0 - x);
	} else if ((x <= 5.7e+104) || !(x <= 3.3e+134)) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / y
	elif x <= 0.112:
		tmp = x * (1.0 - x)
	elif (x <= 5.7e+104) or not (x <= 3.3e+134):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= 0.112)
		tmp = Float64(x * Float64(1.0 - x));
	elseif ((x <= 5.7e+104) || !(x <= 3.3e+134))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = x / y;
	elseif (x <= 0.112)
		tmp = x * (1.0 - x);
	elseif ((x <= 5.7e+104) || ~((x <= 3.3e+134)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 0.112], N[(x * N[(1.0 - x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.7e+104], N[Not[LessEqual[x, 3.3e+134]], $MachinePrecision]], N[(x / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -1 or 0.112000000000000002 < x < 5.69999999999999985e104 or 3.3e134 < x

   1. Initial program 75.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 80.9%

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

   if -1 < x < 0.112000000000000002

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 65.0%

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

   6. Taylor expanded in x around 0 65.0%

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

      1. neg-mul-1 65.0%

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

      2. sub-neg 65.0%

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

   8. Simplified 65.0%

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

   if 5.69999999999999985e104 < x < 3.3e134

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

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

      1. un-div-inv 100.0%

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

      2. +-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.112:\\ \;\;\;\;x \cdot \left(1 - x\right)\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.3 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 72.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.4:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e+29)
   (/ x y)
   (if (<= x 0.4)
     (/ x (+ x 1.0))
     (if (or (<= x 5.7e+104) (not (<= x 3.15e+134))) (/ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+29) {
		tmp = x / y;
	} else if (x <= 0.4) {
		tmp = x / (x + 1.0);
	} else if ((x <= 5.7e+104) || !(x <= 3.15e+134)) {
		tmp = x / y;
	} else {
		tmp = 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 <= (-9.5d+29)) then
        tmp = x / y
    else if (x <= 0.4d0) then
        tmp = x / (x + 1.0d0)
    else if ((x <= 5.7d+104) .or. (.not. (x <= 3.15d+134))) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e+29) {
		tmp = x / y;
	} else if (x <= 0.4) {
		tmp = x / (x + 1.0);
	} else if ((x <= 5.7e+104) || !(x <= 3.15e+134)) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e+29:
		tmp = x / y
	elif x <= 0.4:
		tmp = x / (x + 1.0)
	elif (x <= 5.7e+104) or not (x <= 3.15e+134):
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e+29)
		tmp = Float64(x / y);
	elseif (x <= 0.4)
		tmp = Float64(x / Float64(x + 1.0));
	elseif ((x <= 5.7e+104) || !(x <= 3.15e+134))
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e+29)
		tmp = x / y;
	elseif (x <= 0.4)
		tmp = x / (x + 1.0);
	elseif ((x <= 5.7e+104) || ~((x <= 3.15e+134)))
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e+29], N[(x / y), $MachinePrecision], If[LessEqual[x, 0.4], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 5.7e+104], N[Not[LessEqual[x, 3.15e+134]], $MachinePrecision]], N[(x / y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if x < -9.5000000000000003e29 or 0.40000000000000002 < x < 5.69999999999999985e104 or 3.1500000000000001e134 < x

   1. Initial program 73.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 83.8%

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

   if -9.5000000000000003e29 < x < 0.40000000000000002

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 63.9%

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

   if 5.69999999999999985e104 < x < 3.1500000000000001e134

   1. Initial program 100.0%

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

      1. associate-/l* 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 99.7%

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

      1. un-div-inv 100.0%

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

      2. +-commutative 100.0%

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

   7. Applied egg-rr 100.0%

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

   8. Taylor expanded in x around inf 100.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{+29}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.4:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+104} \lor \neg \left(x \leq 3.15 \cdot 10^{+134}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.027 \lor \neg \left(x \leq 0.41\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \left(\frac{1}{y} + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.027) (not (<= x 0.41)))
   (+ (/ x (+ x 1.0)) (/ x y))
   (* x (+ 1.0 (* x (+ (/ 1.0 y) -1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.027) || !(x <= 0.41)) {
		tmp = (x / (x + 1.0)) + (x / y);
	} else {
		tmp = x * (1.0 + (x * ((1.0 / 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 <= (-0.027d0)) .or. (.not. (x <= 0.41d0))) then
        tmp = (x / (x + 1.0d0)) + (x / y)
    else
        tmp = x * (1.0d0 + (x * ((1.0d0 / y) + (-1.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -0.027) || !(x <= 0.41)) {
		tmp = (x / (x + 1.0)) + (x / y);
	} else {
		tmp = x * (1.0 + (x * ((1.0 / y) + -1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.027) or not (x <= 0.41):
		tmp = (x / (x + 1.0)) + (x / y)
	else:
		tmp = x * (1.0 + (x * ((1.0 / y) + -1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.027) || !(x <= 0.41))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(x / y));
	else
		tmp = Float64(x * Float64(1.0 + Float64(x * Float64(Float64(1.0 / y) + -1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -0.027) || ~((x <= 0.41)))
		tmp = (x / (x + 1.0)) + (x / y);
	else
		tmp = x * (1.0 + (x * ((1.0 / y) + -1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.027], N[Not[LessEqual[x, 0.41]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(x * N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -0.0269999999999999997 or 0.409999999999999976 < x

   1. Initial program 75.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. associate-/r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. un-div-inv 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-in 99.8%

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

      6. *-commutative 99.8%

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

      7. *-un-lft-identity 99.8%

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

      8. un-div-inv 99.9%

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

      9. +-commutative 99.9%

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

      10. un-div-inv 100.0%

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

      11. +-commutative 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around inf 98.5%

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

   if -0.0269999999999999997 < x < 0.409999999999999976

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 98.0%

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

4. Final simplification 98.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.027 \lor \neg \left(x \leq 0.41\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \left(\frac{1}{y} + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-9} \lor \neg \left(x \leq 1.7 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \frac{1}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.15e-9) (not (<= x 1.7e-12)))
   (+ (/ x (+ x 1.0)) (/ x y))
   (* x (+ 1.0 (* x (/ 1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e-9) || !(x <= 1.7e-12)) {
		tmp = (x / (x + 1.0)) + (x / y);
	} else {
		tmp = x * (1.0 + (x * (1.0 / 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 <= (-1.15d-9)) .or. (.not. (x <= 1.7d-12))) then
        tmp = (x / (x + 1.0d0)) + (x / y)
    else
        tmp = x * (1.0d0 + (x * (1.0d0 / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.15e-9) || !(x <= 1.7e-12)) {
		tmp = (x / (x + 1.0)) + (x / y);
	} else {
		tmp = x * (1.0 + (x * (1.0 / y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.15e-9) or not (x <= 1.7e-12):
		tmp = (x / (x + 1.0)) + (x / y)
	else:
		tmp = x * (1.0 + (x * (1.0 / y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.15e-9) || !(x <= 1.7e-12))
		tmp = Float64(Float64(x / Float64(x + 1.0)) + Float64(x / y));
	else
		tmp = Float64(x * Float64(1.0 + Float64(x * Float64(1.0 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.15e-9) || ~((x <= 1.7e-12)))
		tmp = (x / (x + 1.0)) + (x / y);
	else
		tmp = x * (1.0 + (x * (1.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.15e-9], N[Not[LessEqual[x, 1.7e-12]], $MachinePrecision]], N[(N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision] + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 + N[(x * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.15e-9 or 1.7e-12 < x

   1. Initial program 76.7%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

      1. clear-num 99.7%

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

      2. un-div-inv 100.0%

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

   6. Applied egg-rr 100.0%

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

      1. associate-/r/ 100.0%

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

      2. +-commutative 100.0%

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

      3. un-div-inv 99.8%

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

      4. +-commutative 99.8%

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

      5. distribute-lft-in 99.8%

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

      6. *-commutative 99.8%

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

      7. *-un-lft-identity 99.8%

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

      8. un-div-inv 99.8%

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

      9. +-commutative 99.8%

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

      10. un-div-inv 100.0%

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

      11. +-commutative 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around inf 96.9%

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

   if -1.15e-9 < x < 1.7e-12

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 99.2%

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

   6. Taylor expanded in y around 0 99.1%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.15 \cdot 10^{-9} \lor \neg \left(x \leq 1.7 \cdot 10^{-12}\right):\\ \;\;\;\;\frac{x}{x + 1} + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 + x \cdot \frac{1}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 76.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-14} \lor \neg \left(y \leq 8.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.4e-14) (not (<= y 8.5e+71)))
   (/ x (+ x 1.0))
   (/ x (+ y (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.4e-14) || !(y <= 8.5e+71)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / (y + (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 <= (-7.4d-14)) .or. (.not. (y <= 8.5d+71))) then
        tmp = x / (x + 1.0d0)
    else
        tmp = x / (y + (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7.4e-14) || !(y <= 8.5e+71)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / (y + (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.4e-14) or not (y <= 8.5e+71):
		tmp = x / (x + 1.0)
	else:
		tmp = x / (y + (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.4e-14) || !(y <= 8.5e+71))
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(x / Float64(y + Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7.4e-14) || ~((y <= 8.5e+71)))
		tmp = x / (x + 1.0);
	else
		tmp = x / (y + (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.4e-14], N[Not[LessEqual[y, 8.5e+71]], $MachinePrecision]], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7.40000000000000002e-14 or 8.4999999999999996e71 < y

   1. Initial program 84.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 76.7%

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

   if -7.40000000000000002e-14 < y < 8.4999999999999996e71

   1. Initial program 89.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

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

      1. clear-num 99.7%

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

      2. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in y around 0 81.4%

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

   8. Taylor expanded in x around 0 81.4%

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

      1. distribute-rgt1-in 81.4%

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

      2. *-commutative 81.4%

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

      3. associate-*r/ 82.1%

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

      4. *-lft-identity 82.1%

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

      5. associate-*l/ 82.0%

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

      6. distribute-rgt-in 82.0%

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

      7. rgt-mult-inverse 82.1%

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

      8. *-lft-identity 82.1%

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

      9. distribute-lft-in 82.1%

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

      10. *-rgt-identity 82.1%

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

      11. associate-*r/ 82.1%

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

      12. *-rgt-identity 82.1%

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

   10. Simplified 82.1%

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

4. Final simplification 79.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.4 \cdot 10^{-14} \lor \neg \left(y \leq 8.5 \cdot 10^{+71}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 48.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.3) 1.0 (if (<= x 7.5e+17) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = 1.0;
	} else if (x <= 7.5e+17) {
		tmp = x;
	} else {
		tmp = 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 <= (-2.3d0)) then
        tmp = 1.0d0
    else if (x <= 7.5d+17) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.3) {
		tmp = 1.0;
	} else if (x <= 7.5e+17) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.3:
		tmp = 1.0
	elif x <= 7.5e+17:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.3)
		tmp = 1.0;
	elseif (x <= 7.5e+17)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.3)
		tmp = 1.0;
	elseif (x <= 7.5e+17)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.3], 1.0, If[LessEqual[x, 7.5e+17], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -2.2999999999999998 or 7.5e17 < x

   1. Initial program 75.1%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf 23.6%

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

      1. un-div-inv 23.7%

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

      2. +-commutative 23.7%

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

   7. Applied egg-rr 23.7%

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

   8. Taylor expanded in x around inf 23.2%

      \[\leadsto \color{blue}{1} \]

   if -2.2999999999999998 < x < 7.5e17

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0 62.0%

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

4. Final simplification 43.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return x * ((1.0 + (x / y)) / (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)) / (x + 1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto x \cdot \frac{1 + \frac{x}{y}}{x + 1} \]
6. Add Preprocessing

Alternative 11: 99.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

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

   1. clear-num 99.7%

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

   2. un-div-inv 99.9%

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

6. Applied egg-rr 99.9%

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

7. Final simplification 99.9%

   \[\leadsto \frac{x}{\frac{x + 1}{1 + \frac{x}{y}}} \]
8. Add Preprocessing

Alternative 12: 14.8% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 87.7%

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

   1. associate-/l* 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{x \cdot \frac{\frac{x}{y} + 1}{x + 1}} \]
4. Add Preprocessing

5. Taylor expanded in y around inf 43.6%

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

   1. un-div-inv 43.6%

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

   2. +-commutative 43.6%

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

7. Applied egg-rr 43.6%

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

8. Taylor expanded in x around inf 13.2%

   \[\leadsto \color{blue}{1} \]

9. Final simplification 13.2%

   \[\leadsto 1 \]
10. Add Preprocessing

Developer target: 99.8% 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 2024071 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

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

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