Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 88.2% → 99.9%

Time: 5.4s

Alternatives: 8

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, 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 86.1%

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

   1. associate-/l* 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 95.2% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1 < x

   1. Initial program 74.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.2%

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

   if -1 < x < 1

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 95.9%

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

      1. unpow2 95.9%

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

      2. sub-neg 95.9%

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

      3. metadata-eval 95.9%

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

   6. Simplified 95.9%

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

4. Final simplification 97.7%

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

Alternative 3: 74.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -6.5e+89)
   (/ x y)
   (if (<= x -5.9e+50)
     1.0
     (if (<= x -2.7e+17)
       (/ x y)
       (if (<= x 2.3e+15) (/ x (+ x 1.0)) (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -6.5e+89) {
		tmp = x / y;
	} else if (x <= -5.9e+50) {
		tmp = 1.0;
	} else if (x <= -2.7e+17) {
		tmp = x / y;
	} else if (x <= 2.3e+15) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-6.5d+89)) then
        tmp = x / y
    else if (x <= (-5.9d+50)) then
        tmp = 1.0d0
    else if (x <= (-2.7d+17)) then
        tmp = x / y
    else if (x <= 2.3d+15) then
        tmp = x / (x + 1.0d0)
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -6.5e+89) {
		tmp = x / y;
	} else if (x <= -5.9e+50) {
		tmp = 1.0;
	} else if (x <= -2.7e+17) {
		tmp = x / y;
	} else if (x <= 2.3e+15) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -6.5e+89:
		tmp = x / y
	elif x <= -5.9e+50:
		tmp = 1.0
	elif x <= -2.7e+17:
		tmp = x / y
	elif x <= 2.3e+15:
		tmp = x / (x + 1.0)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -6.5e+89)
		tmp = Float64(x / y);
	elseif (x <= -5.9e+50)
		tmp = 1.0;
	elseif (x <= -2.7e+17)
		tmp = Float64(x / y);
	elseif (x <= 2.3e+15)
		tmp = Float64(x / Float64(x + 1.0));
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -6.5e+89)
		tmp = x / y;
	elseif (x <= -5.9e+50)
		tmp = 1.0;
	elseif (x <= -2.7e+17)
		tmp = x / y;
	elseif (x <= 2.3e+15)
		tmp = x / (x + 1.0);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -6.5e+89], N[(x / y), $MachinePrecision], If[LessEqual[x, -5.9e+50], 1.0, If[LessEqual[x, -2.7e+17], N[(x / y), $MachinePrecision], If[LessEqual[x, 2.3e+15], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.4999999999999996e89 or -5.8999999999999998e50 < x < -2.7e17 or 2.3e15 < x

   1. Initial program 72.6%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 77.7%

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

   if -6.4999999999999996e89 < x < -5.8999999999999998e50

   1. Initial program 89.7%

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

      1. distribute-lft-in 89.7%

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

      2. add-cube-cbrt 89.1%

         \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{x}{y} + x \cdot 1}{x + 1} \]

      3. associate-*l* 89.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right)} + x \cdot 1}{x + 1} \]

      4. *-rgt-identity 89.1%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + \color{blue}{x}}{x + 1} \]

      5. fma-def 89.1%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]

      6. cbrt-unprod 89.3%

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\sqrt[3]{x \cdot x}}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}{x + 1} \]

   3. Applied egg-rr 89.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x \cdot x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]
   4. Step-by-step derivation

      1. fma-udef 89.3%

         \[\leadsto \frac{\color{blue}{\sqrt[3]{x \cdot x} \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + x}}{x + 1} \]

      2. *-commutative 89.3%

         \[\leadsto \frac{\sqrt[3]{x \cdot x} \cdot \color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x}\right)} + x}{x + 1} \]

      3. associate-*r* 89.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot x} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{x}} + x}{x + 1} \]

      4. *-commutative 89.3%

         \[\leadsto \frac{\color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}\right)} \cdot \sqrt[3]{x} + x}{x + 1} \]

      5. fma-udef 89.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   5. Simplified 89.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   6. Taylor expanded in x around inf 72.5%

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

   if -2.7e17 < x < 2.3e15

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 80.8%

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

4. Final simplification 79.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.5 \cdot 10^{+89}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -5.9 \cdot 10^{+50}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -2.7 \cdot 10^{+17}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 4: 86.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -29000 \lor \neg \left(x \leq 16.5\right):\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -29000.0) (not (<= x 16.5)))
   (+ (+ 1.0 (/ x y)) (/ -1.0 y))
   (/ x (+ x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -29000.0) || !(x <= 16.5)) {
		tmp = (1.0 + (x / y)) + (-1.0 / y);
	} 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 <= (-29000.0d0)) .or. (.not. (x <= 16.5d0))) then
        tmp = (1.0d0 + (x / y)) + ((-1.0d0) / y)
    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 <= -29000.0) || !(x <= 16.5)) {
		tmp = (1.0 + (x / y)) + (-1.0 / y);
	} else {
		tmp = x / (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -29000.0) or not (x <= 16.5):
		tmp = (1.0 + (x / y)) + (-1.0 / y)
	else:
		tmp = x / (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -29000.0) || !(x <= 16.5))
		tmp = Float64(Float64(1.0 + Float64(x / y)) + Float64(-1.0 / y));
	else
		tmp = Float64(x / Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -29000.0) || ~((x <= 16.5)))
		tmp = (1.0 + (x / y)) + (-1.0 / y);
	else
		tmp = x / (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -29000.0], N[Not[LessEqual[x, 16.5]], $MachinePrecision]], N[(N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision] + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -29000 or 16.5 < x

   1. Initial program 74.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.2%

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

   if -29000 < x < 16.5

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around inf 81.9%

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

4. Final simplification 91.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -29000 \lor \neg \left(x \leq 16.5\right):\\ \;\;\;\;\left(1 + \frac{x}{y}\right) + \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{x + 1}\\ \end{array} \]

Alternative 5: 73.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.85e+84)
   (/ x y)
   (if (<= x -7.4e+51)
     1.0
     (if (<= x -1.0) (/ x y) (if (<= x 0.19) x (/ x y))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+84) {
		tmp = x / y;
	} else if (x <= -7.4e+51) {
		tmp = 1.0;
	} else if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 0.19) {
		tmp = x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.85d+84)) then
        tmp = x / y
    else if (x <= (-7.4d+51)) then
        tmp = 1.0d0
    else if (x <= (-1.0d0)) then
        tmp = x / y
    else if (x <= 0.19d0) then
        tmp = x
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.85e+84) {
		tmp = x / y;
	} else if (x <= -7.4e+51) {
		tmp = 1.0;
	} else if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 0.19) {
		tmp = x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.85e+84:
		tmp = x / y
	elif x <= -7.4e+51:
		tmp = 1.0
	elif x <= -1.0:
		tmp = x / y
	elif x <= 0.19:
		tmp = x
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.85e+84)
		tmp = Float64(x / y);
	elseif (x <= -7.4e+51)
		tmp = 1.0;
	elseif (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= 0.19)
		tmp = x;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.85e+84)
		tmp = x / y;
	elseif (x <= -7.4e+51)
		tmp = 1.0;
	elseif (x <= -1.0)
		tmp = x / y;
	elseif (x <= 0.19)
		tmp = x;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.85e+84], N[(x / y), $MachinePrecision], If[LessEqual[x, -7.4e+51], 1.0, If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 0.19], x, N[(x / y), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -1.85e84 or -7.4000000000000005e51 < x < -1 or 0.19 < x

   1. Initial program 73.5%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 75.8%

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

   if -1.85e84 < x < -7.4000000000000005e51

   1. Initial program 89.7%

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

      1. distribute-lft-in 89.7%

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

      2. add-cube-cbrt 89.1%

         \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{x}{y} + x \cdot 1}{x + 1} \]

      3. associate-*l* 89.1%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right)} + x \cdot 1}{x + 1} \]

      4. *-rgt-identity 89.1%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + \color{blue}{x}}{x + 1} \]

      5. fma-def 89.1%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]

      6. cbrt-unprod 89.3%

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\sqrt[3]{x \cdot x}}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}{x + 1} \]

   3. Applied egg-rr 89.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x \cdot x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]
   4. Step-by-step derivation

      1. fma-udef 89.3%

         \[\leadsto \frac{\color{blue}{\sqrt[3]{x \cdot x} \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + x}}{x + 1} \]

      2. *-commutative 89.3%

         \[\leadsto \frac{\sqrt[3]{x \cdot x} \cdot \color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x}\right)} + x}{x + 1} \]

      3. associate-*r* 89.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot x} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{x}} + x}{x + 1} \]

      4. *-commutative 89.3%

         \[\leadsto \frac{\color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}\right)} \cdot \sqrt[3]{x} + x}{x + 1} \]

      5. fma-udef 89.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   5. Simplified 89.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   6. Taylor expanded in x around inf 72.5%

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

   if -1 < x < 0.19

   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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 81.1%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.85 \cdot 10^{+84}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{+51}:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 0.19:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \]

Alternative 6: 75.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-34} \lor \neg \left(y \leq 7.8 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.16e-34) (not (<= y 7.8e-45)))
   (/ x (+ x 1.0))
   (/ x (+ y (/ y x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.16e-34) || !(y <= 7.8e-45)) {
		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 <= (-1.16d-34)) .or. (.not. (y <= 7.8d-45))) 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 <= -1.16e-34) || !(y <= 7.8e-45)) {
		tmp = x / (x + 1.0);
	} else {
		tmp = x / (y + (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.16e-34) or not (y <= 7.8e-45):
		tmp = x / (x + 1.0)
	else:
		tmp = x / (y + (y / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.16e-34) || !(y <= 7.8e-45))
		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 <= -1.16e-34) || ~((y <= 7.8e-45)))
		tmp = x / (x + 1.0);
	else
		tmp = x / (y + (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.16e-34], N[Not[LessEqual[y, 7.8e-45]], $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 < -1.1600000000000001e-34 or 7.7999999999999999e-45 < y

   1. Initial program 87.4%

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

      1. associate-/l* 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around inf 75.8%

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

   if -1.1600000000000001e-34 < y < 7.7999999999999999e-45

   1. Initial program 84.0%

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

      1. associate-/l* 99.9%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in y around 0 88.7%

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

   5. Taylor expanded in x around 0 88.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.16 \cdot 10^{-34} \lor \neg \left(y \leq 7.8 \cdot 10^{-45}\right):\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \end{array} \]

Alternative 7: 50.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -57000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -57000.0) 1.0 (if (<= x 1.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -57000.0) {
		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 <= (-57000.0d0)) 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 <= -57000.0) {
		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 <= -57000.0:
		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 <= -57000.0)
		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 <= -57000.0)
		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, -57000.0], 1.0, If[LessEqual[x, 1.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if x < -57000 or 1 < x

   1. Initial program 74.3%

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

      1. distribute-lft-in 74.3%

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

      2. add-cube-cbrt 73.9%

         \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{x}{y} + x \cdot 1}{x + 1} \]

      3. associate-*l* 74.0%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right)} + x \cdot 1}{x + 1} \]

      4. *-rgt-identity 74.0%

         \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + \color{blue}{x}}{x + 1} \]

      5. fma-def 74.0%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]

      6. cbrt-unprod 64.3%

         \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\sqrt[3]{x \cdot x}}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}{x + 1} \]

   3. Applied egg-rr 64.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x \cdot x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]
   4. Step-by-step derivation

      1. fma-udef 64.3%

         \[\leadsto \frac{\color{blue}{\sqrt[3]{x \cdot x} \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + x}}{x + 1} \]

      2. *-commutative 64.3%

         \[\leadsto \frac{\sqrt[3]{x \cdot x} \cdot \color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x}\right)} + x}{x + 1} \]

      3. associate-*r* 64.3%

         \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot x} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{x}} + x}{x + 1} \]

      4. *-commutative 64.3%

         \[\leadsto \frac{\color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}\right)} \cdot \sqrt[3]{x} + x}{x + 1} \]

      5. fma-udef 64.3%

         \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   5. Simplified 64.3%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

   6. Taylor expanded in x around inf 27.2%

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

   if -57000 < 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%

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

   3. Simplified 99.9%

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

   4. Taylor expanded in x around 0 80.4%

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

4. Final simplification 51.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -57000:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 1:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 8: 14.6% 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 86.1%

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

   1. distribute-lft-in 86.1%

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

   2. add-cube-cbrt 85.8%

      \[\leadsto \frac{\color{blue}{\left(\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{x}\right)} \cdot \frac{x}{y} + x \cdot 1}{x + 1} \]

   3. associate-*l* 85.8%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right)} + x \cdot 1}{x + 1} \]

   4. *-rgt-identity 85.8%

      \[\leadsto \frac{\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + \color{blue}{x}}{x + 1} \]

   5. fma-def 85.8%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x} \cdot \sqrt[3]{x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]

   6. cbrt-unprod 79.4%

      \[\leadsto \frac{\mathsf{fma}\left(\color{blue}{\sqrt[3]{x \cdot x}}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}{x + 1} \]

3. Applied egg-rr 79.4%

   \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x \cdot x}, \sqrt[3]{x} \cdot \frac{x}{y}, x\right)}}{x + 1} \]
4. Step-by-step derivation

   1. fma-udef 79.4%

      \[\leadsto \frac{\color{blue}{\sqrt[3]{x \cdot x} \cdot \left(\sqrt[3]{x} \cdot \frac{x}{y}\right) + x}}{x + 1} \]

   2. *-commutative 79.4%

      \[\leadsto \frac{\sqrt[3]{x \cdot x} \cdot \color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x}\right)} + x}{x + 1} \]

   3. associate-*r* 79.4%

      \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{x \cdot x} \cdot \frac{x}{y}\right) \cdot \sqrt[3]{x}} + x}{x + 1} \]

   4. *-commutative 79.4%

      \[\leadsto \frac{\color{blue}{\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}\right)} \cdot \sqrt[3]{x} + x}{x + 1} \]

   5. fma-udef 79.4%

      \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

5. Simplified 79.4%

   \[\leadsto \frac{\color{blue}{\mathsf{fma}\left(\frac{x}{y} \cdot \sqrt[3]{x \cdot x}, \sqrt[3]{x}, x\right)}}{x + 1} \]

6. Taylor expanded in x around inf 16.2%

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

7. Final simplification 16.2%

   \[\leadsto 1 \]

Developer target: 99.9% accurate, 0.8× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023271 
(FPCore (x y)
  :name "Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1"
  :precision binary64

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

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