Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 88.3% → 99.8%

Time: 7.1s

Alternatives: 9

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: 88.3% 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: 99.8% accurate, 1.0× speedup

Math

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

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(x * Float64(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[(x * N[(N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.4%

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

Alternative 2: 70.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 48000000000:\\ \;\;\;\;x \cdot \frac{x}{y \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+150)
   (/ x y)
   (if (<= x -8.2e+78)
     1.0
     (if (<= x -2.3e+55)
       (/ x y)
       (if (<= x 8.5e-94)
         (/ x (+ x 1.0))
         (if (<= x 48000000000.0) (* x (/ x (* y (+ x 1.0)))) (/ x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8.2e+78) {
		tmp = 1.0;
	} else if (x <= -2.3e+55) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 48000000000.0) {
		tmp = x * (x / (y * (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 <= (-2.9d+150)) then
        tmp = x / y
    else if (x <= (-8.2d+78)) then
        tmp = 1.0d0
    else if (x <= (-2.3d+55)) then
        tmp = x / y
    else if (x <= 8.5d-94) then
        tmp = x / (x + 1.0d0)
    else if (x <= 48000000000.0d0) then
        tmp = x * (x / (y * (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 <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8.2e+78) {
		tmp = 1.0;
	} else if (x <= -2.3e+55) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 48000000000.0) {
		tmp = x * (x / (y * (x + 1.0)));
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+150:
		tmp = x / y
	elif x <= -8.2e+78:
		tmp = 1.0
	elif x <= -2.3e+55:
		tmp = x / y
	elif x <= 8.5e-94:
		tmp = x / (x + 1.0)
	elif x <= 48000000000.0:
		tmp = x * (x / (y * (x + 1.0)))
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+150)
		tmp = Float64(x / y);
	elseif (x <= -8.2e+78)
		tmp = 1.0;
	elseif (x <= -2.3e+55)
		tmp = Float64(x / y);
	elseif (x <= 8.5e-94)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 48000000000.0)
		tmp = Float64(x * Float64(x / Float64(y * 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 <= -2.9e+150)
		tmp = x / y;
	elseif (x <= -8.2e+78)
		tmp = 1.0;
	elseif (x <= -2.3e+55)
		tmp = x / y;
	elseif (x <= 8.5e-94)
		tmp = x / (x + 1.0);
	elseif (x <= 48000000000.0)
		tmp = x * (x / (y * (x + 1.0)));
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -8.2e+78], 1.0, If[LessEqual[x, -2.3e+55], N[(x / y), $MachinePrecision], If[LessEqual[x, 8.5e-94], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 48000000000.0], N[(x * N[(x / N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.90000000000000011e150 or -8.1999999999999994e78 < x < -2.29999999999999987e55 or 4.8e10 < x

   1. Initial program 67.0%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 76.0%

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

   if -2.90000000000000011e150 < x < -8.1999999999999994e78

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -2.29999999999999987e55 < x < 8.50000000000000003e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 82.4%

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

   if 8.50000000000000003e-94 < x < 4.8e10

   1. Initial program 99.7%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 0 66.6%

      \[\leadsto x \cdot \color{blue}{\frac{x}{y \cdot \left(1 + x\right)}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -8.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.3 \cdot 10^{+55}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 48000000000:\\ \;\;\;\;x \cdot \frac{x}{y \cdot \left(x + 1\right)}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 70.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{x}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+150)
   (/ x y)
   (if (<= x -9.2e+78)
     1.0
     (if (<= x -4.5e+51)
       (/ x y)
       (if (<= x 8.5e-94)
         (/ x (+ x 1.0))
         (if (<= x 1.0) (/ x (/ y x)) (/ x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -9.2e+78) {
		tmp = 1.0;
	} else if (x <= -4.5e+51) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.0) {
		tmp = x / (y / 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 <= (-2.9d+150)) then
        tmp = x / y
    else if (x <= (-9.2d+78)) then
        tmp = 1.0d0
    else if (x <= (-4.5d+51)) then
        tmp = x / y
    else if (x <= 8.5d-94) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.0d0) then
        tmp = x / (y / x)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -9.2e+78) {
		tmp = 1.0;
	} else if (x <= -4.5e+51) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.0) {
		tmp = x / (y / x);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+150:
		tmp = x / y
	elif x <= -9.2e+78:
		tmp = 1.0
	elif x <= -4.5e+51:
		tmp = x / y
	elif x <= 8.5e-94:
		tmp = x / (x + 1.0)
	elif x <= 1.0:
		tmp = x / (y / x)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+150)
		tmp = Float64(x / y);
	elseif (x <= -9.2e+78)
		tmp = 1.0;
	elseif (x <= -4.5e+51)
		tmp = Float64(x / y);
	elseif (x <= 8.5e-94)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.0)
		tmp = Float64(x / Float64(y / x));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.9e+150)
		tmp = x / y;
	elseif (x <= -9.2e+78)
		tmp = 1.0;
	elseif (x <= -4.5e+51)
		tmp = x / y;
	elseif (x <= 8.5e-94)
		tmp = x / (x + 1.0);
	elseif (x <= 1.0)
		tmp = x / (y / x);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -9.2e+78], 1.0, If[LessEqual[x, -4.5e+51], N[(x / y), $MachinePrecision], If[LessEqual[x, 8.5e-94], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(x / N[(y / x), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.90000000000000011e150 or -9.2000000000000008e78 < x < -4.5e51 or 1 < x

   1. Initial program 67.6%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 75.2%

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

   if -2.90000000000000011e150 < x < -9.2000000000000008e78

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -4.5e51 < x < 8.50000000000000003e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 82.4%

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

   if 8.50000000000000003e-94 < x < 1

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 64.2%

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

   6. Taylor expanded in x around 0 63.1%

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

      1. clear-num 63.0%

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

      2. un-div-inv 63.1%

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

   8. Applied egg-rr 63.1%

      \[\leadsto \color{blue}{\frac{x}{\frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -9.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;\frac{x}{\frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 70.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+150)
   (/ x y)
   (if (<= x -1.02e+79)
     1.0
     (if (<= x -3.7e+52)
       (/ x y)
       (if (<= x 8.5e-94)
         (/ x (+ x 1.0))
         (if (<= x 1.0) (* x (/ x y)) (/ x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -1.02e+79) {
		tmp = 1.0;
	} else if (x <= -3.7e+52) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.0) {
		tmp = x * (x / y);
	} 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 <= (-2.9d+150)) then
        tmp = x / y
    else if (x <= (-1.02d+79)) then
        tmp = 1.0d0
    else if (x <= (-3.7d+52)) then
        tmp = x / y
    else if (x <= 8.5d-94) then
        tmp = x / (x + 1.0d0)
    else if (x <= 1.0d0) then
        tmp = x * (x / y)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -1.02e+79) {
		tmp = 1.0;
	} else if (x <= -3.7e+52) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else if (x <= 1.0) {
		tmp = x * (x / y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+150:
		tmp = x / y
	elif x <= -1.02e+79:
		tmp = 1.0
	elif x <= -3.7e+52:
		tmp = x / y
	elif x <= 8.5e-94:
		tmp = x / (x + 1.0)
	elif x <= 1.0:
		tmp = x * (x / y)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+150)
		tmp = Float64(x / y);
	elseif (x <= -1.02e+79)
		tmp = 1.0;
	elseif (x <= -3.7e+52)
		tmp = Float64(x / y);
	elseif (x <= 8.5e-94)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 1.0)
		tmp = Float64(x * Float64(x / y));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.9e+150)
		tmp = x / y;
	elseif (x <= -1.02e+79)
		tmp = 1.0;
	elseif (x <= -3.7e+52)
		tmp = x / y;
	elseif (x <= 8.5e-94)
		tmp = x / (x + 1.0);
	elseif (x <= 1.0)
		tmp = x * (x / y);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -1.02e+79], 1.0, If[LessEqual[x, -3.7e+52], N[(x / y), $MachinePrecision], If[LessEqual[x, 8.5e-94], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.0], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.90000000000000011e150 or -1.02000000000000006e79 < x < -3.7e52 or 1 < x

   1. Initial program 67.6%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 75.2%

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

   if -2.90000000000000011e150 < x < -1.02000000000000006e79

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -3.7e52 < x < 8.50000000000000003e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 82.4%

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

   if 8.50000000000000003e-94 < x < 1

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 64.2%

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

   6. Taylor expanded in x around 0 63.1%

      \[\leadsto x \cdot \frac{x}{\color{blue}{y}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 75.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -3.7 \cdot 10^{+52}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 69.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -8.6 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{-94}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+150)
   (/ x y)
   (if (<= x -8.6e+78)
     1.0
     (if (<= x -1.0)
       (/ x y)
       (if (<= x 3.2e-94) x (if (<= x 1.0) (* x (/ x y)) (/ x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8.6e+78) {
		tmp = 1.0;
	} else if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 3.2e-94) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = x * (x / y);
	} 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 <= (-2.9d+150)) then
        tmp = x / y
    else if (x <= (-8.6d+78)) then
        tmp = 1.0d0
    else if (x <= (-1.0d0)) then
        tmp = x / y
    else if (x <= 3.2d-94) then
        tmp = x
    else if (x <= 1.0d0) then
        tmp = x * (x / y)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8.6e+78) {
		tmp = 1.0;
	} else if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 3.2e-94) {
		tmp = x;
	} else if (x <= 1.0) {
		tmp = x * (x / y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+150:
		tmp = x / y
	elif x <= -8.6e+78:
		tmp = 1.0
	elif x <= -1.0:
		tmp = x / y
	elif x <= 3.2e-94:
		tmp = x
	elif x <= 1.0:
		tmp = x * (x / y)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+150)
		tmp = Float64(x / y);
	elseif (x <= -8.6e+78)
		tmp = 1.0;
	elseif (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= 3.2e-94)
		tmp = x;
	elseif (x <= 1.0)
		tmp = Float64(x * Float64(x / y));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.9e+150)
		tmp = x / y;
	elseif (x <= -8.6e+78)
		tmp = 1.0;
	elseif (x <= -1.0)
		tmp = x / y;
	elseif (x <= 3.2e-94)
		tmp = x;
	elseif (x <= 1.0)
		tmp = x * (x / y);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -8.6e+78], 1.0, If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 3.2e-94], x, If[LessEqual[x, 1.0], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.90000000000000011e150 or -8.59999999999999962e78 < x < -1 or 1 < x

   1. Initial program 69.4%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 73.2%

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

   if -2.90000000000000011e150 < x < -8.59999999999999962e78

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -1 < x < 3.19999999999999997e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 83.5%

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

   if 3.19999999999999997e-94 < x < 1

   1. Initial program 99.8%

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

      1. associate-/l* 99.7%

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

   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 0 64.2%

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

   6. Taylor expanded in x around 0 63.1%

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

Alternative 6: 70.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + 1\right) \cdot \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3e+150)
   (/ x y)
   (if (<= x -1.02e+79)
     1.0
     (if (<= x -4.6e+51)
       (/ x y)
       (if (<= x 8.5e-94) (/ x (+ x 1.0)) (/ x (* (+ x 1.0) (/ y x))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3e+150) {
		tmp = x / y;
	} else if (x <= -1.02e+79) {
		tmp = 1.0;
	} else if (x <= -4.6e+51) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / ((x + 1.0) * (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 (x <= (-3d+150)) then
        tmp = x / y
    else if (x <= (-1.02d+79)) then
        tmp = 1.0d0
    else if (x <= (-4.6d+51)) then
        tmp = x / y
    else if (x <= 8.5d-94) then
        tmp = x / (x + 1.0d0)
    else
        tmp = x / ((x + 1.0d0) * (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -3e+150) {
		tmp = x / y;
	} else if (x <= -1.02e+79) {
		tmp = 1.0;
	} else if (x <= -4.6e+51) {
		tmp = x / y;
	} else if (x <= 8.5e-94) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / ((x + 1.0) * (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3e+150:
		tmp = x / y
	elif x <= -1.02e+79:
		tmp = 1.0
	elif x <= -4.6e+51:
		tmp = x / y
	elif x <= 8.5e-94:
		tmp = x / (x + 1.0)
	else:
		tmp = x / ((x + 1.0) * (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3e+150)
		tmp = Float64(x / y);
	elseif (x <= -1.02e+79)
		tmp = 1.0;
	elseif (x <= -4.6e+51)
		tmp = Float64(x / y);
	elseif (x <= 8.5e-94)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(x / Float64(Float64(x + 1.0) * Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3e+150)
		tmp = x / y;
	elseif (x <= -1.02e+79)
		tmp = 1.0;
	elseif (x <= -4.6e+51)
		tmp = x / y;
	elseif (x <= 8.5e-94)
		tmp = x / (x + 1.0);
	else
		tmp = x / ((x + 1.0) * (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -1.02e+79], 1.0, If[LessEqual[x, -4.6e+51], N[(x / y), $MachinePrecision], If[LessEqual[x, 8.5e-94], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / N[(N[(x + 1.0), $MachinePrecision] * N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -3.00000000000000012e150 or -1.02000000000000006e79 < x < -4.6000000000000001e51

   1. Initial program 71.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 78.8%

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

   if -3.00000000000000012e150 < x < -1.02000000000000006e79

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -4.6000000000000001e51 < x < 8.50000000000000003e-94

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf 82.4%

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

   if 8.50000000000000003e-94 < x

   1. Initial program 74.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 0 56.3%

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

      1. clear-num 56.3%

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

      2. un-div-inv 56.4%

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

      3. +-commutative 56.4%

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

      4. *-commutative 56.4%

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

      5. associate-/l* 71.6%

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

   7. Applied egg-rr 71.6%

      \[\leadsto \color{blue}{\frac{x}{\left(x + 1\right) \cdot \frac{y}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 76.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -1.02 \cdot 10^{+79}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -4.6 \cdot 10^{+51}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-94}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{\left(x + 1\right) \cdot \frac{y}{x}}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 71.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1 \lor \neg \left(x \leq 6.2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.9e+150)
   (/ x y)
   (if (<= x -8e+78) 1.0 (if (or (<= x -1.0) (not (<= x 6.2))) (/ x y) x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8e+78) {
		tmp = 1.0;
	} else if ((x <= -1.0) || !(x <= 6.2)) {
		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 <= (-2.9d+150)) then
        tmp = x / y
    else if (x <= (-8d+78)) then
        tmp = 1.0d0
    else if ((x <= (-1.0d0)) .or. (.not. (x <= 6.2d0))) 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 <= -2.9e+150) {
		tmp = x / y;
	} else if (x <= -8e+78) {
		tmp = 1.0;
	} else if ((x <= -1.0) || !(x <= 6.2)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.9e+150:
		tmp = x / y
	elif x <= -8e+78:
		tmp = 1.0
	elif (x <= -1.0) or not (x <= 6.2):
		tmp = x / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.9e+150)
		tmp = Float64(x / y);
	elseif (x <= -8e+78)
		tmp = 1.0;
	elseif ((x <= -1.0) || !(x <= 6.2))
		tmp = Float64(x / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.9e+150)
		tmp = x / y;
	elseif (x <= -8e+78)
		tmp = 1.0;
	elseif ((x <= -1.0) || ~((x <= 6.2)))
		tmp = x / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.9e+150], N[(x / y), $MachinePrecision], If[LessEqual[x, -8e+78], 1.0, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 6.2]], $MachinePrecision]], N[(x / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.90000000000000011e150 or -8.00000000000000007e78 < x < -1 or 6.20000000000000018 < x

   1. Initial program 69.4%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 inf 73.2%

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

   if -2.90000000000000011e150 < x < -8.00000000000000007e78

   1. Initial program 89.1%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 63.3%

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

   6. Taylor expanded in x around inf 63.4%

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

   if -1 < x < 6.20000000000000018

   1. Initial program 99.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 x around 0 72.4%

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

4. Final simplification 72.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.9 \cdot 10^{+150}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -8 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1 \lor \neg \left(x \leq 6.2\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 49.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= x -1.0) 1.0 (if (<= x 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (x <= 1.0d0) 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 <= -1.0) {
		tmp = 1.0;
	} else if (x <= 1.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0
	elif x <= 1.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = 1.0;
	elseif (x <= 1.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], 1.0, If[LessEqual[x, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 71.8%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 30.1%

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

   6. Taylor expanded in x around inf 29.4%

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

   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. 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 0 72.4%

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

Alternative 9: 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 84.4%

   \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
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 49.7%

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

6. Taylor expanded in x around inf 18.1%

   \[\leadsto \color{blue}{1} \]
7. 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 2024100 
(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)))