Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.5s

Alternatives: 7

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 - \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -600000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- 1.0 (/ (- 1.0 x) y))))
   (if (<= y -600000.0)
     t_0
     (if (<= y -1.5e-34)
       (/ y (+ y 1.0))
       (if (<= y 28000.0) (/ x (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 - ((1.0 - x) / y);
	double tmp;
	if (y <= -600000.0) {
		tmp = t_0;
	} else if (y <= -1.5e-34) {
		tmp = y / (y + 1.0);
	} else if (y <= 28000.0) {
		tmp = x / (y + 1.0);
	} 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) :: tmp
    t_0 = 1.0d0 - ((1.0d0 - x) / y)
    if (y <= (-600000.0d0)) then
        tmp = t_0
    else if (y <= (-1.5d-34)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 28000.0d0) then
        tmp = x / (y + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 - ((1.0 - x) / y);
	double tmp;
	if (y <= -600000.0) {
		tmp = t_0;
	} else if (y <= -1.5e-34) {
		tmp = y / (y + 1.0);
	} else if (y <= 28000.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 - ((1.0 - x) / y)
	tmp = 0
	if y <= -600000.0:
		tmp = t_0
	elif y <= -1.5e-34:
		tmp = y / (y + 1.0)
	elif y <= 28000.0:
		tmp = x / (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 - Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -600000.0)
		tmp = t_0;
	elseif (y <= -1.5e-34)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 28000.0)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 - ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -600000.0)
		tmp = t_0;
	elseif (y <= -1.5e-34)
		tmp = y / (y + 1.0);
	elseif (y <= 28000.0)
		tmp = x / (y + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -600000.0], t$95$0, If[LessEqual[y, -1.5e-34], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 28000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6e5 or 28000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. mul-1-neg 99.4%

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

      4. sub-neg 99.4%

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

   4. Simplified 99.4%

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

   if -6e5 < y < -1.5e-34

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 86.1%

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

   4. Simplified 86.1%

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

   if -1.5e-34 < y < 28000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.9%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 74.9%

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

   4. Simplified 74.9%

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

4. Final simplification 89.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -600000:\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq -1.5 \cdot 10^{-34}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 28000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \end{array} \]

Alternative 3: 86.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -740000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 6200:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -740000.0)
     t_0
     (if (<= y -2.1e-33)
       (/ y (+ y 1.0))
       (if (<= y 6200.0) (/ x (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -740000.0) {
		tmp = t_0;
	} else if (y <= -2.1e-33) {
		tmp = y / (y + 1.0);
	} else if (y <= 6200.0) {
		tmp = x / (y + 1.0);
	} 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) :: tmp
    t_0 = 1.0d0 + (x / y)
    if (y <= (-740000.0d0)) then
        tmp = t_0
    else if (y <= (-2.1d-33)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 6200.0d0) then
        tmp = x / (y + 1.0d0)
    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 tmp;
	if (y <= -740000.0) {
		tmp = t_0;
	} else if (y <= -2.1e-33) {
		tmp = y / (y + 1.0);
	} else if (y <= 6200.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -740000.0:
		tmp = t_0
	elif y <= -2.1e-33:
		tmp = y / (y + 1.0)
	elif y <= 6200.0:
		tmp = x / (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -740000.0)
		tmp = t_0;
	elseif (y <= -2.1e-33)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 6200.0)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if (y <= -740000.0)
		tmp = t_0;
	elseif (y <= -2.1e-33)
		tmp = y / (y + 1.0);
	elseif (y <= 6200.0)
		tmp = x / (y + 1.0);
	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]}, If[LessEqual[y, -740000.0], t$95$0, If[LessEqual[y, -2.1e-33], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6200.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.4e5 or 6200 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. mul-1-neg 99.4%

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

      4. sub-neg 99.4%

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

   4. Simplified 99.4%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. neg-mul-1 98.7%

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

      2. distribute-neg-frac 98.7%

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

   7. Simplified 98.7%

      \[\leadsto 1 - \color{blue}{\frac{-x}{y}} \]
   8. Step-by-step derivation

      1. sub-neg 98.7%

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

      2. distribute-frac-neg 98.7%

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

      3. remove-double-neg 98.7%

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

      4. +-commutative 98.7%

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

   9. Applied egg-rr 98.7%

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

   if -7.4e5 < y < -2.1e-33

   1. Initial program 99.8%

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

   2. Taylor expanded in x around 0 86.1%

      \[\leadsto \color{blue}{\frac{y}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 86.1%

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

   4. Simplified 86.1%

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

   if -2.1e-33 < y < 6200

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 74.9%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 74.9%

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

   4. Simplified 74.9%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -740000:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-33}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 6200:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 4: 85.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.1 \cdot 10^{-13}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.1e-13))) (+ 1.0 (/ x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.1e-13)) {
		tmp = 1.0 + (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 ((y <= (-1.0d0)) .or. (.not. (y <= 2.1d-13))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.1e-13)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 2.1e-13):
		tmp = 1.0 + (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2.1e-13))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2.1e-13)))
		tmp = 1.0 + (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2.1e-13]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.09999999999999989e-13 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 98.0%

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

      1. mul-1-neg 98.0%

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

      2. unsub-neg 98.0%

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

      3. mul-1-neg 98.0%

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

      4. sub-neg 98.0%

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

   4. Simplified 98.0%

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

   5. Taylor expanded in x around inf 97.2%

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

      1. neg-mul-1 97.2%

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

      2. distribute-neg-frac 97.2%

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

   7. Simplified 97.2%

      \[\leadsto 1 - \color{blue}{\frac{-x}{y}} \]
   8. Step-by-step derivation

      1. sub-neg 97.2%

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

      2. distribute-frac-neg 97.2%

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

      3. remove-double-neg 97.2%

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

      4. +-commutative 97.2%

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

   9. Applied egg-rr 97.2%

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

   if -1 < y < 2.09999999999999989e-13

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 71.6%

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

4. Final simplification 86.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.1 \cdot 10^{-13}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 5: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7800 \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7800.0) (not (<= y 14000.0))) (+ 1.0 (/ x y)) (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7800.0) || !(y <= 14000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 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 ((y <= (-7800.0d0)) .or. (.not. (y <= 14000.0d0))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7800.0) || !(y <= 14000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7800.0) or not (y <= 14000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7800.0) || !(y <= 14000.0))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(x / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7800.0) || ~((y <= 14000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7800.0], N[Not[LessEqual[y, 14000.0]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -7800 or 14000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around inf 98.3%

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

      1. neg-mul-1 98.3%

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

      2. distribute-neg-frac 98.3%

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

   7. Simplified 98.3%

      \[\leadsto 1 - \color{blue}{\frac{-x}{y}} \]
   8. Step-by-step derivation

      1. sub-neg 98.3%

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

      2. distribute-frac-neg 98.3%

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

      3. remove-double-neg 98.3%

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

      4. +-commutative 98.3%

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

   9. Applied egg-rr 98.3%

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

   if -7800 < y < 14000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 71.9%

      \[\leadsto \color{blue}{\frac{x}{1 + y}} \]
   3. Step-by-step derivation

      1. +-commutative 71.9%

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

   4. Simplified 71.9%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7800 \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 6: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 8.5) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 8.5) {
		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 (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 8.5d0) 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 (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 8.5) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 8.5:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 8.5)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 8.5)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 8.5], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8.5 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.4%

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

   if -1 < y < 8.5

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 70.5%

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

4. Final simplification 72.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 39.0% accurate, 7.0× 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 100.0%

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

2. Taylor expanded in y around inf 43.7%

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

3. Final simplification 43.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023283 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))