Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 88.7% → 99.8%

Time: 5.7s

Alternatives: 6

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: 88.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% 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 88.2%

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

Alternative 2: 85.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -500000000 \lor \neg \left(x \leq 380000\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -500000000.0) (not (<= x 380000.0)))
   (+ (/ x y) 1.0)
   (/ x (+ x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -500000000.0) || !(x <= 380000.0)) {
		tmp = (x / y) + 1.0;
	} else {
		tmp = x / (x + 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 <= (-500000000.0d0)) .or. (.not. (x <= 380000.0d0))) then
        tmp = (x / y) + 1.0d0
    else
        tmp = x / (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -500000000.0) || !(x <= 380000.0)) {
		tmp = (x / y) + 1.0;
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -500000000.0) or not (x <= 380000.0):
		tmp = (x / y) + 1.0
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -500000000.0) || !(x <= 380000.0))
		tmp = Float64(Float64(x / y) + 1.0);
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -500000000.0) || ~((x <= 380000.0)))
		tmp = (x / y) + 1.0;
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -500000000.0], N[Not[LessEqual[x, 380000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -5e8 or 3.8e5 < x

   1. Initial program 76.3%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 68.2%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{1 + x} + \frac{{x}^{2}}{1 + x}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 68.2%

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

      2. +-commutative 68.2%

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

      3. associate-/l* 71.4%

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

      4. +-commutative 71.4%

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

      5. unpow2 71.4%

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

      6. +-commutative 71.4%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-out 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 99.5%

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

   9. Taylor expanded in y around 0 99.5%

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

       1. +-commutative 99.5%

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

       2. *-lft-identity 99.5%

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

       3. associate-*l/ 99.1%

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

       4. +-commutative 99.1%

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

       5. distribute-lft-in 99.2%

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

       6. associate-*l/ 99.5%

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

       7. *-lft-identity 99.5%

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

       8. lft-mult-inverse 99.5%

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

   11. Simplified 99.5%

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

   if -5e8 < x < 3.8e5

   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 y around inf 76.9%

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

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -500000000 \lor \neg \left(x \leq 380000\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 4.1e-8))) (+ (/ x y) 1.0) x))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4.1e-8)) {
		tmp = (x / y) + 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 4.1d-8))) then
        tmp = (x / y) + 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4.1e-8)) {
		tmp = (x / y) + 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 4.1e-8):
		tmp = (x / y) + 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 4.1e-8))
		tmp = Float64(Float64(x / y) + 1.0);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 4.1e-8)))
		tmp = (x / y) + 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 4.1e-8]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 4.10000000000000032e-8 < x

   1. Initial program 77.5%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 69.8%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{1 + x} + \frac{{x}^{2}}{1 + x}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 69.8%

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

      2. +-commutative 69.8%

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

      3. associate-/l* 72.9%

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

      4. +-commutative 72.9%

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

      5. unpow2 72.9%

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

      6. +-commutative 72.9%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-out 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 95.8%

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

   9. Taylor expanded in y around 0 95.8%

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

       1. +-commutative 95.8%

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

       2. *-lft-identity 95.8%

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

       3. associate-*l/ 95.5%

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

       4. +-commutative 95.5%

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

       5. distribute-lft-in 95.5%

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

       6. associate-*l/ 95.8%

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

       7. *-lft-identity 95.8%

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

       8. lft-mult-inverse 95.8%

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

   11. Simplified 95.8%

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

   if -1 < x < 4.10000000000000032e-8

   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 77.8%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 72.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 4.1e-8))) (/ x y) x))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4.1e-8)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-1.0d0)) .or. (.not. (x <= 4.1d-8))) then
        tmp = x / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4.1e-8)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 4.1e-8):
		tmp = x / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 4.1e-8))
		tmp = Float64(x / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 4.1e-8)))
		tmp = x / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 4.1e-8]], $MachinePrecision]], N[(x / y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 4.10000000000000032e-8 < x

   1. Initial program 77.5%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 75.9%

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

   if -1 < x < 4.10000000000000032e-8

   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 77.8%

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

4. Final simplification 76.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.1 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.8 \cdot 10^{-5}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.8e-5) 1.0 (if (<= x 4.1e-8) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.8e-5) {
		tmp = 1.0;
	} else if (x <= 4.1e-8) {
		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 <= (-3.8d-5)) then
        tmp = 1.0d0
    else if (x <= 4.1d-8) 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 <= -3.8e-5) {
		tmp = 1.0;
	} else if (x <= 4.1e-8) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.8e-5:
		tmp = 1.0
	elif x <= 4.1e-8:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.8e-5)
		tmp = 1.0;
	elseif (x <= 4.1e-8)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -3.8e-5)
		tmp = 1.0;
	elseif (x <= 4.1e-8)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.8e-5], 1.0, If[LessEqual[x, 4.1e-8], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -3.8000000000000002e-5 or 4.10000000000000032e-8 < x

   1. Initial program 77.9%

      \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
   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 70.3%

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{1 + x} + \frac{{x}^{2}}{1 + x}}{y}} \]
   6. Step-by-step derivation

      1. *-commutative 70.3%

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

      2. +-commutative 70.3%

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

      3. associate-/l* 73.3%

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

      4. +-commutative 73.3%

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

      5. unpow2 73.3%

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

      6. +-commutative 73.3%

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

      7. associate-/l* 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-rgt-out 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf 94.4%

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

   9. Taylor expanded in y around inf 21.2%

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

   if -3.8000000000000002e-5 < x < 4.10000000000000032e-8

   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 79.0%

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

Alternative 6: 15.2% 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 88.2%

   \[\frac{x \cdot \left(\frac{x}{y} + 1\right)}{x + 1} \]
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 75.6%

   \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{1 + x} + \frac{{x}^{2}}{1 + x}}{y}} \]
6. Step-by-step derivation

   1. *-commutative 75.6%

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

   2. +-commutative 75.6%

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

   3. associate-/l* 77.2%

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

   4. +-commutative 77.2%

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

   5. unpow2 77.2%

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

   6. +-commutative 77.2%

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

   7. associate-/l* 91.4%

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

   8. +-commutative 91.4%

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

   9. distribute-rgt-out 91.4%

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

7. Simplified 91.4%

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

8. Taylor expanded in x around inf 51.8%

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

9. Taylor expanded in y around inf 12.9%

   \[\leadsto \color{blue}{1} \]
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 2024096 
(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)))