Codec.Picture.Types:toneMapping from JuicyPixels-3.2.6.1

Percentage Accurate: 87.9% → 99.7%

Time: 6.6s

Alternatives: 11

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: 87.9% 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: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;x \leq -4.5 \cdot 10^{+51}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2500000000000:\\ \;\;\;\;\frac{x \cdot t_0}{x + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{-1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= x -4.5e+51)
     t_0
     (if (<= x 2500000000000.0) (/ (* x t_0) (+ x 1.0)) (+ t_0 (/ -1.0 y))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (x <= -4.5e+51) {
		tmp = t_0;
	} else if (x <= 2500000000000.0) {
		tmp = (x * t_0) / (x + 1.0);
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    if (x <= (-4.5d+51)) then
        tmp = t_0
    else if (x <= 2500000000000.0d0) then
        tmp = (x * t_0) / (x + 1.0d0)
    else
        tmp = t_0 + ((-1.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (x <= -4.5e+51) {
		tmp = t_0;
	} else if (x <= 2500000000000.0) {
		tmp = (x * t_0) / (x + 1.0);
	} else {
		tmp = t_0 + (-1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if x <= -4.5e+51:
		tmp = t_0
	elif x <= 2500000000000.0:
		tmp = (x * t_0) / (x + 1.0)
	else:
		tmp = t_0 + (-1.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (x <= -4.5e+51)
		tmp = t_0;
	elseif (x <= 2500000000000.0)
		tmp = Float64(Float64(x * t_0) / Float64(x + 1.0));
	else
		tmp = Float64(t_0 + Float64(-1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if (x <= -4.5e+51)
		tmp = t_0;
	elseif (x <= 2500000000000.0)
		tmp = (x * t_0) / (x + 1.0);
	else
		tmp = t_0 + (-1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.5e+51], t$95$0, If[LessEqual[x, 2500000000000.0], N[(N[(x * t$95$0), $MachinePrecision] / N[(x + 1.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.0 / y), $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: 74.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -3.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-13}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+65}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ x 1.0))))
   (if (<= x -3.6e+27)
     (/ x y)
     (if (<= x 1.7e-27)
       t_0
       (if (<= x 1.75e-13) (* x (/ x y)) (if (<= x 2.8e+65) t_0 (/ x y)))))))

C

double code(double x, double y) {
	double t_0 = x / (x + 1.0);
	double tmp;
	if (x <= -3.6e+27) {
		tmp = x / y;
	} else if (x <= 1.7e-27) {
		tmp = t_0;
	} else if (x <= 1.75e-13) {
		tmp = x * (x / y);
	} else if (x <= 2.8e+65) {
		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 <= (-3.6d+27)) then
        tmp = x / y
    else if (x <= 1.7d-27) then
        tmp = t_0
    else if (x <= 1.75d-13) then
        tmp = x * (x / y)
    else if (x <= 2.8d+65) 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 <= -3.6e+27) {
		tmp = x / y;
	} else if (x <= 1.7e-27) {
		tmp = t_0;
	} else if (x <= 1.75e-13) {
		tmp = x * (x / y);
	} else if (x <= 2.8e+65) {
		tmp = t_0;
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (x + 1.0)
	tmp = 0
	if x <= -3.6e+27:
		tmp = x / y
	elif x <= 1.7e-27:
		tmp = t_0
	elif x <= 1.75e-13:
		tmp = x * (x / y)
	elif x <= 2.8e+65:
		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 <= -3.6e+27)
		tmp = Float64(x / y);
	elseif (x <= 1.7e-27)
		tmp = t_0;
	elseif (x <= 1.75e-13)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 2.8e+65)
		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 <= -3.6e+27)
		tmp = x / y;
	elseif (x <= 1.7e-27)
		tmp = t_0;
	elseif (x <= 1.75e-13)
		tmp = x * (x / y);
	elseif (x <= 2.8e+65)
		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, -3.6e+27], N[(x / y), $MachinePrecision], If[LessEqual[x, 1.7e-27], t$95$0, If[LessEqual[x, 1.75e-13], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.8e+65], t$95$0, N[(x / y), $MachinePrecision]]]]]]

Derivation

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

Alternative 4: 85.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{x}{x + 1}\\ \mathbf{if}\;x \leq -2.5 \cdot 10^{+27}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{-30}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{-9}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{elif}\;x \leq 26500000:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (/ x (+ x 1.0))))
   (if (<= x -2.5e+27)
     t_0
     (if (<= x 4.8e-30)
       t_1
       (if (<= x 5.7e-9) (* x (/ x y)) (if (<= x 26500000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.5e+27) {
		tmp = t_0;
	} else if (x <= 4.8e-30) {
		tmp = t_1;
	} else if (x <= 5.7e-9) {
		tmp = x * (x / y);
	} else if (x <= 26500000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = x / (x + 1.0d0)
    if (x <= (-2.5d+27)) then
        tmp = t_0
    else if (x <= 4.8d-30) then
        tmp = t_1
    else if (x <= 5.7d-9) then
        tmp = x * (x / y)
    else if (x <= 26500000.0d0) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = x / (x + 1.0);
	double tmp;
	if (x <= -2.5e+27) {
		tmp = t_0;
	} else if (x <= 4.8e-30) {
		tmp = t_1;
	} else if (x <= 5.7e-9) {
		tmp = x * (x / y);
	} else if (x <= 26500000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = x / (x + 1.0)
	tmp = 0
	if x <= -2.5e+27:
		tmp = t_0
	elif x <= 4.8e-30:
		tmp = t_1
	elif x <= 5.7e-9:
		tmp = x * (x / y)
	elif x <= 26500000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(x / Float64(x + 1.0))
	tmp = 0.0
	if (x <= -2.5e+27)
		tmp = t_0;
	elseif (x <= 4.8e-30)
		tmp = t_1;
	elseif (x <= 5.7e-9)
		tmp = Float64(x * Float64(x / y));
	elseif (x <= 26500000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = x / (x + 1.0);
	tmp = 0.0;
	if (x <= -2.5e+27)
		tmp = t_0;
	elseif (x <= 4.8e-30)
		tmp = t_1;
	elseif (x <= 5.7e-9)
		tmp = x * (x / y);
	elseif (x <= 26500000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x / N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -2.5e+27], t$95$0, If[LessEqual[x, 4.8e-30], t$95$1, If[LessEqual[x, 5.7e-9], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 26500000.0], t$95$1, t$95$0]]]]]]

Derivation

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

Alternative 5: 98.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -15 \lor \neg \left(x \leq 2600000000000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{x}{y + \frac{y}{x}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -15.0) (not (<= x 2600000000000.0)))
   (+ 1.0 (/ x y))
   (+ x (/ x (+ y (/ y x))))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -15.0) || !(x <= 2600000000000.0)) {
		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 <= (-15.0d0)) .or. (.not. (x <= 2600000000000.0d0))) 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 <= -15.0) || !(x <= 2600000000000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x + (x / (y + (y / x)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -15.0) or not (x <= 2600000000000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x + (x / (y + (y / x)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -15.0) || !(x <= 2600000000000.0))
		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 <= -15.0) || ~((x <= 2600000000000.0)))
		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, -15.0], N[Not[LessEqual[x, 2600000000000.0]], $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 6: 98.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;x \leq -15:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 8500:\\ \;\;\;\;x + \frac{x}{y + \frac{y}{x}}\\ \mathbf{else}:\\ \;\;\;\;t_0 + \frac{-1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= x -15.0)
     t_0
     (if (<= x 8500.0) (+ x (/ x (+ y (/ y x)))) (+ t_0 (/ -1.0 y))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (x <= -15.0) {
		tmp = t_0;
	} else if (x <= 8500.0) {
		tmp = x + (x / (y + (y / x)));
	} else {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    if (x <= (-15.0d0)) then
        tmp = t_0
    else if (x <= 8500.0d0) then
        tmp = x + (x / (y + (y / x)))
    else
        tmp = t_0 + ((-1.0d0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (x <= -15.0) {
		tmp = t_0;
	} else if (x <= 8500.0) {
		tmp = x + (x / (y + (y / x)));
	} else {
		tmp = t_0 + (-1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if x <= -15.0:
		tmp = t_0
	elif x <= 8500.0:
		tmp = x + (x / (y + (y / x)))
	else:
		tmp = t_0 + (-1.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (x <= -15.0)
		tmp = t_0;
	elseif (x <= 8500.0)
		tmp = Float64(x + Float64(x / Float64(y + Float64(y / x))));
	else
		tmp = Float64(t_0 + Float64(-1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if (x <= -15.0)
		tmp = t_0;
	elseif (x <= 8500.0)
		tmp = x + (x / (y + (y / x)));
	else
		tmp = t_0 + (-1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -15.0], t$95$0, If[LessEqual[x, 8500.0], N[(x + N[(x / N[(y + N[(y / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

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

Alternative 7: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{-27}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-8}:\\ \;\;\;\;x \cdot \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0)
   (/ x y)
   (if (<= x 4.2e-27) x (if (<= x 2.45e-8) (* x (/ x y)) (/ x y)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = x / y;
	} else if (x <= 4.2e-27) {
		tmp = x;
	} else if (x <= 2.45e-8) {
		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 <= (-1.0d0)) then
        tmp = x / y
    else if (x <= 4.2d-27) then
        tmp = x
    else if (x <= 2.45d-8) 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 <= -1.0) {
		tmp = x / y;
	} else if (x <= 4.2e-27) {
		tmp = x;
	} else if (x <= 2.45e-8) {
		tmp = x * (x / y);
	} else {
		tmp = x / y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = x / y
	elif x <= 4.2e-27:
		tmp = x
	elif x <= 2.45e-8:
		tmp = x * (x / y)
	else:
		tmp = x / y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(x / y);
	elseif (x <= 4.2e-27)
		tmp = x;
	elseif (x <= 2.45e-8)
		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 <= -1.0)
		tmp = x / y;
	elseif (x <= 4.2e-27)
		tmp = x;
	elseif (x <= 2.45e-8)
		tmp = x * (x / y);
	else
		tmp = x / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(x / y), $MachinePrecision], If[LessEqual[x, 4.2e-27], x, If[LessEqual[x, 2.45e-8], N[(x * N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / y), $MachinePrecision]]]]

Derivation

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

Alternative 8: 97.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (or (<= x -1.0) (not (<= x 1.0))) t_0 (* x t_0))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if ((x <= -1.0) || !(x <= 1.0)) {
		tmp = t_0;
	} else {
		tmp = x * t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    if ((x <= (-1.0d0)) .or. (.not. (x <= 1.0d0))) then
        tmp = t_0
    else
        tmp = x * t_0
    end if
    code = tmp
end function

Java

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

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if (x <= -1.0) or not (x <= 1.0):
		tmp = t_0
	else:
		tmp = x * t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.0))
		tmp = t_0;
	else
		tmp = Float64(x * t_0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.0)))
		tmp = t_0;
	else
		tmp = x * t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], t$95$0, N[(x * t$95$0), $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: 73.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 0.98\right):\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 0.98))) (/ x y) x))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 0.98)) {
		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 <= 0.98d0))) 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 <= 0.98)) {
		tmp = x / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 0.98):
		tmp = x / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 0.98))
		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 <= 0.98)))
		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, 0.98]], $MachinePrecision]], N[(x / y), $MachinePrecision], x]

Derivation

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

Alternative 11: 38.4% accurate, 11.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

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 2024008 
(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)))