Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 88.0% → 99.9%

Time: 7.1s

Alternatives: 13

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: 88.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x \cdot \left(1 + \frac{x}{y}\right)}{x + 1}\\ \mathbf{if}\;t_0 \leq -5 \cdot 10^{+121}:\\ \;\;\;\;\frac{\frac{x}{y}}{1 + \frac{1}{x}}\\ \mathbf{elif}\;t_0 \leq 500000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* x (+ 1.0 (/ x y))) (+ x 1.0))))
   (if (<= t_0 -5e+121)
     (/ (/ x y) (+ 1.0 (/ 1.0 x)))
     (if (<= t_0 500000000000.0) t_0 (/ x (+ y (/ y x)))))))

C

double code(double x, double y) {
	double t_0 = (x * (1.0 + (x / y))) / (x + 1.0);
	double tmp;
	if (t_0 <= -5e+121) {
		tmp = (x / y) / (1.0 + (1.0 / x));
	} else if (t_0 <= 500000000000.0) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = (x * (1.0d0 + (x / y))) / (x + 1.0d0)
    if (t_0 <= (-5d+121)) then
        tmp = (x / y) / (1.0d0 + (1.0d0 / x))
    else if (t_0 <= 500000000000.0d0) then
        tmp = t_0
    else
        tmp = x / (y + (y / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x * (1.0 + (x / y))) / (x + 1.0);
	double tmp;
	if (t_0 <= -5e+121) {
		tmp = (x / y) / (1.0 + (1.0 / x));
	} else if (t_0 <= 500000000000.0) {
		tmp = t_0;
	} else {
		tmp = x / (y + (y / x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x * (1.0 + (x / y))) / (x + 1.0)
	tmp = 0
	if t_0 <= -5e+121:
		tmp = (x / y) / (1.0 + (1.0 / x))
	elif t_0 <= 500000000000.0:
		tmp = t_0
	else:
		tmp = x / (y + (y / x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x * Float64(1.0 + Float64(x / y))) / Float64(x + 1.0))
	tmp = 0.0
	if (t_0 <= -5e+121)
		tmp = Float64(Float64(x / y) / Float64(1.0 + Float64(1.0 / x)));
	elseif (t_0 <= 500000000000.0)
		tmp = t_0;
	else
		tmp = Float64(x / Float64(y + Float64(y / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x * (1.0 + (x / y))) / (x + 1.0);
	tmp = 0.0;
	if (t_0 <= -5e+121)
		tmp = (x / y) / (1.0 + (1.0 / x));
	elseif (t_0 <= 500000000000.0)
		tmp = t_0;
	else
		tmp = x / (y + (y / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x * N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, -5e+121], N[(N[(x / y), $MachinePrecision] / N[(1.0 + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 500000000000.0], t$95$0, N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 2: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 3: 75.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -4.7 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -3 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-61}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 730000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))))
   (if (<= x -4.7e+14)
     (/ x y)
     (if (<= x -3e-22)
       t_0
       (if (<= x -3.4e-61)
         (* x (/ x y))
         (if (<= x 730000000.0) t_0 (/ x y)))))))

C

double code(double x, double y) {
	double t_0 = x / (x + 1.0);
	double tmp;
	if (x <= -4.7e+14) {
		tmp = x / y;
	} else if (x <= -3e-22) {
		tmp = t_0;
	} else if (x <= -3.4e-61) {
		tmp = x * (x / y);
	} else if (x <= 730000000.0) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    if (x <= (-4.7d+14)) then
        tmp = x / y
    else if (x <= (-3d-22)) then
        tmp = t_0
    else if (x <= (-3.4d-61)) then
        tmp = x * (x / y)
    else if (x <= 730000000.0d0) then
        tmp = t_0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + 1.0);
	double tmp;
	if (x <= -4.7e+14) {
		tmp = x / y;
	} else if (x <= -3e-22) {
		tmp = t_0;
	} else if (x <= -3.4e-61) {
		tmp = x * (x / y);
	} else if (x <= 730000000.0) {
		tmp = t_0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + 1.0)
	tmp = 0
	if x <= -4.7e+14:
		tmp = x / y
	elif x <= -3e-22:
		tmp = t_0
	elif x <= -3.4e-61:
		tmp = x * (x / y)
	elif x <= 730000000.0:
		tmp = t_0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -4.7e+14)
		tmp = Float64(x / y);
	elseif (x <= -3e-22)
		tmp = t_0;
	elseif (x <= -3.4e-61)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 730000000.0)
		tmp = t_0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -4.7e+14)
		tmp = x / y;
	elseif (x <= -3e-22)
		tmp = t_0;
	elseif (x <= -3.4e-61)
		tmp = x * (x / y);
	elseif (x <= 730000000.0)
		tmp = t_0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.7e+14], N[(x / y), $MachinePrecision], If[LessEqual[x, -3e-22], t$95$0, If[LessEqual[x, -3.4e-61], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 730000000.0], t$95$0, N[(x / y), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 4: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -1600000000000:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -2.4 \cdot 10^{-24}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq -7.4 \cdot 10^{-62}:\\ \;\;\;\;x \cdot \left(x \cdot \frac{1}{y}\right)\\ \mathbf{elif}\;x \leq 6000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))))
   (if (<= x -1600000000000.0)
     (/ x y)
     (if (<= x -2.4e-24)
       t_0
       (if (<= x -7.4e-62)
         (* x (* x (/ 1.0 y)))
         (if (<= x 6000.0) t_0 (/ x y)))))))

C

double code(double x, double y) {
	double t_0 = x / (x + 1.0);
	double tmp;
	if (x <= -1600000000000.0) {
		tmp = x / y;
	} else if (x <= -2.4e-24) {
		tmp = t_0;
	} else if (x <= -7.4e-62) {
		tmp = x * (x * (1.0 / y));
	} else if (x <= 6000.0) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (x + 1.0d0)
    if (x <= (-1600000000000.0d0)) then
        tmp = x / y
    else if (x <= (-2.4d-24)) then
        tmp = t_0
    else if (x <= (-7.4d-62)) then
        tmp = x * (x * (1.0d0 / y))
    else if (x <= 6000.0d0) then
        tmp = t_0
    else
        tmp = x / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (x + 1.0);
	double tmp;
	if (x <= -1600000000000.0) {
		tmp = x / y;
	} else if (x <= -2.4e-24) {
		tmp = t_0;
	} else if (x <= -7.4e-62) {
		tmp = x * (x * (1.0 / y));
	} else if (x <= 6000.0) {
		tmp = t_0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + 1.0)
	tmp = 0
	if x <= -1600000000000.0:
		tmp = x / y
	elif x <= -2.4e-24:
		tmp = t_0
	elif x <= -7.4e-62:
		tmp = x * (x * (1.0 / y))
	elif x <= 6000.0:
		tmp = t_0
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -1600000000000.0)
		tmp = Float64(x / y);
	elseif (x <= -2.4e-24)
		tmp = t_0;
	elseif (x <= -7.4e-62)
		tmp = Float64(x * Float64(x * Float64(1.0 / y)));
	elseif (x <= 6000.0)
		tmp = t_0;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -1600000000000.0)
		tmp = x / y;
	elseif (x <= -2.4e-24)
		tmp = t_0;
	elseif (x <= -7.4e-62)
		tmp = x * (x * (1.0 / y));
	elseif (x <= 6000.0)
		tmp = t_0;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1600000000000.0], N[(x / y), $MachinePrecision], If[LessEqual[x, -2.4e-24], t$95$0, If[LessEqual[x, -7.4e-62], N[(x * N[(x * N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6000.0], t$95$0, N[(x / y), $MachinePrecision]]]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 5: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -2.5 \cdot 10^{-10}:\\ \;\;\;\;\frac{x}{x + 1}\\ \mathbf{elif}\;x \leq 44:\\ \;\;\;\;x + x \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -3.4e+15)
   (/ x y)
   (if (<= x -2.5e-10)
     (/ x (+ x 1.0))
     (if (<= x 44.0) (+ x (* x (/ x y))) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -3.4e+15) {
		tmp = x / y;
	} else if (x <= -2.5e-10) {
		tmp = x / (x + 1.0);
	} else if (x <= 44.0) {
		tmp = x + (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 <= (-3.4d+15)) then
        tmp = x / y
    else if (x <= (-2.5d-10)) then
        tmp = x / (x + 1.0d0)
    else if (x <= 44.0d0) then
        tmp = x + (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 <= -3.4e+15) {
		tmp = x / y;
	} else if (x <= -2.5e-10) {
		tmp = x / (x + 1.0);
	} else if (x <= 44.0) {
		tmp = x + (x * (x / y));
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -3.4e+15:
		tmp = x / y
	elif x <= -2.5e-10:
		tmp = x / (x + 1.0)
	elif x <= 44.0:
		tmp = x + (x * (x / y))
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -3.4e+15)
		tmp = Float64(x / y);
	elseif (x <= -2.5e-10)
		tmp = Float64(x / Float64(x + 1.0));
	elseif (x <= 44.0)
		tmp = Float64(x + 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 <= -3.4e+15)
		tmp = x / y;
	elseif (x <= -2.5e-10)
		tmp = x / (x + 1.0);
	elseif (x <= 44.0)
		tmp = x + (x * (x / y));
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -3.4e+15], N[(x / y), $MachinePrecision], If[LessEqual[x, -2.5e-10], N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 44.0], N[(x + N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 6: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.2 \lor \neg \left(x \leq 3.9 \cdot 10^{+15}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y + \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5.2) (not (<= x 3.9e+15)))
   (+ 1.0 (/ x y))
   (+ x (/ x (+ y (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5.2) || !(x <= 3.9e+15)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x + (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 ((x <= (-5.2d0)) .or. (.not. (x <= 3.9d+15))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x + (x / (y + (y / x)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5.2) || !(x <= 3.9e+15)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x + (x / (y + (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5.2) or not (x <= 3.9e+15):
		tmp = 1.0 + (x / y)
	else:
		tmp = x + (x / (y + (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5.2) || !(x <= 3.9e+15))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(x + Float64(x / Float64(y + Float64(y / x))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5.2) || ~((x <= 3.9e+15)))
		tmp = 1.0 + (x / y);
	else
		tmp = x + (x / (y + (y / x)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5.2], N[Not[LessEqual[x, 3.9e+15]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x + N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 7: 86.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.05 \cdot 10^{-7} \lor \neg \left(x \leq 1.5 \cdot 10^{-9}\right):\\ \;\;\;\;\frac{x}{y + \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + x \cdot \frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.05e-7) (not (<= x 1.5e-9)))
   (/ x (+ y (/ y x)))
   (+ x (* x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.05e-7) || !(x <= 1.5e-9)) {
		tmp = x / (y + (y / x));
	} else {
		tmp = x + (x * (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 <= (-2.05d-7)) .or. (.not. (x <= 1.5d-9))) then
        tmp = x / (y + (y / x))
    else
        tmp = x + (x * (x / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -2.05e-7) || !(x <= 1.5e-9)) {
		tmp = x / (y + (y / x));
	} else {
		tmp = x + (x * (x / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.05e-7) or not (x <= 1.5e-9):
		tmp = x / (y + (y / x))
	else:
		tmp = x + (x * (x / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.05e-7) || !(x <= 1.5e-9))
		tmp = Float64(x / Float64(y + Float64(y / x)));
	else
		tmp = Float64(x + Float64(x * Float64(x / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.05e-7) || ~((x <= 1.5e-9)))
		tmp = x / (y + (y / x));
	else
		tmp = x + (x * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.05e-7], N[Not[LessEqual[x, 1.5e-9]], $MachinePrecision]], N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 8: 97.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Python

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

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(x + Float64(x * Float64(x / 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);
	else
		tmp = x + (x * (x / y));
	end
	tmp_2 = tmp;
end

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 9: 99.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 10: 74.2% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.5:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq -6.8 \cdot 10^{-60}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 0.031:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -5.5)
   (/ x y)
   (if (<= x -6.8e-60) (* x (/ x y)) (if (<= x 0.031) x (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -5.5) {
		tmp = x / y;
	} else if (x <= -6.8e-60) {
		tmp = x * (x / y);
	} else if (x <= 0.031) {
		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 <= (-5.5d0)) then
        tmp = x / y
    else if (x <= (-6.8d-60)) then
        tmp = x * (x / y)
    else if (x <= 0.031d0) 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 <= -5.5) {
		tmp = x / y;
	} else if (x <= -6.8e-60) {
		tmp = x * (x / y);
	} else if (x <= 0.031) {
		tmp = x;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -5.5:
		tmp = x / y
	elif x <= -6.8e-60:
		tmp = x * (x / y)
	elif x <= 0.031:
		tmp = x
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -5.5)
		tmp = Float64(x / y);
	elseif (x <= -6.8e-60)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 0.031)
		tmp = x;
	else
		tmp = Float64(x / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -5.5)
		tmp = x / y;
	elseif (x <= -6.8e-60)
		tmp = x * (x / y);
	elseif (x <= 0.031)
		tmp = x;
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -5.5], N[(x / y), $MachinePrecision], If[LessEqual[x, -6.8e-60], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 0.031], x, N[(x / y), $MachinePrecision]]]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 11: 74.3% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 3.75\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 3.75))) (/ x y) x))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 3.75)) {
		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 <= 3.75d0))) 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 <= 3.75)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 3.75):
		tmp = x / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 3.75))
		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 <= 3.75)))
		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, 3.75]], $MachinePrecision]], N[(x / y), $MachinePrecision], x]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 12: 49.4% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;x \leq 9.2 \cdot 10^{+17}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) 1.0 (if (<= x 9.2e+17) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 9.2e+17) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= (-1.0d0)) then
        tmp = 1.0d0
    else if (x <= 9.2d+17) then
        tmp = x
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = 1.0;
	} else if (x <= 9.2e+17) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = 1.0
	elif x <= 9.2e+17:
		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 <= 9.2e+17)
		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 <= 9.2e+17)
		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, 9.2e+17], x, 1.0]]

Derivation

&prev;&pcontext;&pcontext2;&ctx;
1. Add Preprocessing

Alternative 13: 14.1% 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

&prev;&pcontext;&pcontext2;&ctx;
1. 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 2023364 
(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)))