Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 9

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: 73.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.5e+44)
   1.0
   (if (<= y -1.04e+37)
     (/ x y)
     (if (<= y -5e-8)
       1.0
       (if (<= y -1.95e-35) y (if (<= y 1.12e+72) (/ x (+ y 1.0)) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+44) {
		tmp = 1.0;
	} else if (y <= -1.04e+37) {
		tmp = x / y;
	} else if (y <= -5e-8) {
		tmp = 1.0;
	} else if (y <= -1.95e-35) {
		tmp = y;
	} else if (y <= 1.12e+72) {
		tmp = x / (y + 1.0);
	} 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 <= (-5.5d+44)) then
        tmp = 1.0d0
    else if (y <= (-1.04d+37)) then
        tmp = x / y
    else if (y <= (-5d-8)) then
        tmp = 1.0d0
    else if (y <= (-1.95d-35)) then
        tmp = y
    else if (y <= 1.12d+72) then
        tmp = x / (y + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+44) {
		tmp = 1.0;
	} else if (y <= -1.04e+37) {
		tmp = x / y;
	} else if (y <= -5e-8) {
		tmp = 1.0;
	} else if (y <= -1.95e-35) {
		tmp = y;
	} else if (y <= 1.12e+72) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.5e+44:
		tmp = 1.0
	elif y <= -1.04e+37:
		tmp = x / y
	elif y <= -5e-8:
		tmp = 1.0
	elif y <= -1.95e-35:
		tmp = y
	elif y <= 1.12e+72:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.5e+44)
		tmp = 1.0;
	elseif (y <= -1.04e+37)
		tmp = Float64(x / y);
	elseif (y <= -5e-8)
		tmp = 1.0;
	elseif (y <= -1.95e-35)
		tmp = y;
	elseif (y <= 1.12e+72)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.5e+44)
		tmp = 1.0;
	elseif (y <= -1.04e+37)
		tmp = x / y;
	elseif (y <= -5e-8)
		tmp = 1.0;
	elseif (y <= -1.95e-35)
		tmp = y;
	elseif (y <= 1.12e+72)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.5e+44], 1.0, If[LessEqual[y, -1.04e+37], N[(x / y), $MachinePrecision], If[LessEqual[y, -5e-8], 1.0, If[LessEqual[y, -1.95e-35], y, If[LessEqual[y, 1.12e+72], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.5000000000000001e44 or -1.0400000000000001e37 < y < -4.9999999999999998e-8 or 1.12000000000000001e72 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.5%

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

   if -5.5000000000000001e44 < y < -1.0400000000000001e37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -4.9999999999999998e-8 < y < -1.9499999999999999e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 95.2%

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

   3. Taylor expanded in x around 0 95.2%

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

   if -1.9499999999999999e-35 < y < 1.12000000000000001e72

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{x}{y + 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.04 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -5 \cdot 10^{-8}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.95 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.12 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.78:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.5e+44)
   1.0
   (if (<= y -6.4e+37)
     (/ x y)
     (if (<= y -1.0) 1.0 (if (<= y 0.78) (- x (* x y)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+44) {
		tmp = 1.0;
	} else if (y <= -6.4e+37) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.78) {
		tmp = x - (x * y);
	} 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 <= (-5.5d+44)) then
        tmp = 1.0d0
    else if (y <= (-6.4d+37)) then
        tmp = x / y
    else if (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 0.78d0) then
        tmp = x - (x * y)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+44) {
		tmp = 1.0;
	} else if (y <= -6.4e+37) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.78) {
		tmp = x - (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.5e+44:
		tmp = 1.0
	elif y <= -6.4e+37:
		tmp = x / y
	elif y <= -1.0:
		tmp = 1.0
	elif y <= 0.78:
		tmp = x - (x * y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.5e+44)
		tmp = 1.0;
	elseif (y <= -6.4e+37)
		tmp = Float64(x / y);
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 0.78)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.5e+44)
		tmp = 1.0;
	elseif (y <= -6.4e+37)
		tmp = x / y;
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 0.78)
		tmp = x - (x * y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.5e+44], 1.0, If[LessEqual[y, -6.4e+37], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 0.78], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5000000000000001e44 or -6.40000000000000027e37 < y < -1 or 0.78000000000000003 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 76.1%

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

   if -5.5000000000000001e44 < y < -6.40000000000000027e37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1 < y < 0.78000000000000003

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

   3. Taylor expanded in x around inf 78.5%

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

      1. neg-mul-1 78.5%

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

      2. distribute-lft-in 78.5%

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

      3. *-rgt-identity 78.5%

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

      4. distribute-rgt-neg-in 78.5%

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

      5. unsub-neg 78.5%

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

   5. Simplified 78.5%

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

4. Final simplification 77.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.4 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.78:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 4: 74.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.2e+44)
   1.0
   (if (<= y -7.6e+37)
     (/ x y)
     (if (<= y -1.6e-35)
       (/ y (+ y 1.0))
       (if (<= y 1.9e+72) (/ x (+ y 1.0)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.2e+44) {
		tmp = 1.0;
	} else if (y <= -7.6e+37) {
		tmp = x / y;
	} else if (y <= -1.6e-35) {
		tmp = y / (y + 1.0);
	} else if (y <= 1.9e+72) {
		tmp = x / (y + 1.0);
	} 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 <= (-6.2d+44)) then
        tmp = 1.0d0
    else if (y <= (-7.6d+37)) then
        tmp = x / y
    else if (y <= (-1.6d-35)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 1.9d+72) then
        tmp = x / (y + 1.0d0)
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6.2e+44) {
		tmp = 1.0;
	} else if (y <= -7.6e+37) {
		tmp = x / y;
	} else if (y <= -1.6e-35) {
		tmp = y / (y + 1.0);
	} else if (y <= 1.9e+72) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.2e+44:
		tmp = 1.0
	elif y <= -7.6e+37:
		tmp = x / y
	elif y <= -1.6e-35:
		tmp = y / (y + 1.0)
	elif y <= 1.9e+72:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.2e+44)
		tmp = 1.0;
	elseif (y <= -7.6e+37)
		tmp = Float64(x / y);
	elseif (y <= -1.6e-35)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 1.9e+72)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.2e+44)
		tmp = 1.0;
	elseif (y <= -7.6e+37)
		tmp = x / y;
	elseif (y <= -1.6e-35)
		tmp = y / (y + 1.0);
	elseif (y <= 1.9e+72)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.2e+44], 1.0, If[LessEqual[y, -7.6e+37], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.6e-35], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.9e+72], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -6.19999999999999991e44 or 1.90000000000000003e72 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.5%

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

   if -6.19999999999999991e44 < y < -7.59999999999999979e37

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -7.59999999999999979e37 < y < -1.5999999999999999e-35

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 76.5%

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

      1. +-commutative 76.5%

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

   4. Simplified 76.5%

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

   if -1.5999999999999999e-35 < y < 1.90000000000000003e72

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

      \[\leadsto \color{blue}{\frac{x}{y + 1}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 80.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6.2 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.6 \cdot 10^{+37}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+72}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.86\right):\\ \;\;\;\;\frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.86))) (/ (+ x y) y) (+ x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.86)) {
		tmp = (x + y) / y;
	} else {
		tmp = x + (y * (1.0 - 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 <= 0.86d0))) then
        tmp = (x + y) / y
    else
        tmp = x + (y * (1.0d0 - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.86)) {
		tmp = (x + y) / y;
	} else {
		tmp = x + (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.86):
		tmp = (x + y) / y
	else:
		tmp = x + (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.86))
		tmp = Float64(Float64(x + y) / y);
	else
		tmp = Float64(x + Float64(y * Float64(1.0 - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.86)))
		tmp = (x + y) / y;
	else
		tmp = x + (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.86]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.859999999999999987 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 96.5%

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

      1. *-commutative 96.5%

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

      2. div-inv 96.7%

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

      3. +-commutative 96.7%

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

   6. Applied egg-rr 96.7%

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

   if -1 < y < 0.859999999999999987

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 99.6%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.86\right):\\ \;\;\;\;\frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]

Alternative 6: 73.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.8e+44)
   1.0
   (if (<= y -1.7e+38)
     (/ x y)
     (if (<= y -1.0) 1.0 (if (<= y 13000.0) x 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.8e+44) {
		tmp = 1.0;
	} else if (y <= -1.7e+38) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13000.0) {
		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 (y <= (-5.8d+44)) then
        tmp = 1.0d0
    else if (y <= (-1.7d+38)) then
        tmp = x / y
    else if (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 13000.0d0) 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 (y <= -5.8e+44) {
		tmp = 1.0;
	} else if (y <= -1.7e+38) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.8e+44:
		tmp = 1.0
	elif y <= -1.7e+38:
		tmp = x / y
	elif y <= -1.0:
		tmp = 1.0
	elif y <= 13000.0:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.8e+44)
		tmp = 1.0;
	elseif (y <= -1.7e+38)
		tmp = Float64(x / y);
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 13000.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.8e+44)
		tmp = 1.0;
	elseif (y <= -1.7e+38)
		tmp = x / y;
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 13000.0)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.8e+44], 1.0, If[LessEqual[y, -1.7e+38], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 13000.0], x, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.8000000000000004e44 or -1.69999999999999998e38 < y < -1 or 13000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 77.9%

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

   if -5.8000000000000004e44 < y < -1.69999999999999998e38

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. +-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

   if -1 < y < 13000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 77.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{+38}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 7: 86.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2900000 \lor \neg \left(y \leq 6600000\right):\\ \;\;\;\;\frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2900000.0) (not (<= y 6600000.0)))
   (/ (+ x y) y)
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2900000.0) || !(y <= 6600000.0)) {
		tmp = (x + y) / 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 <= (-2900000.0d0)) .or. (.not. (y <= 6600000.0d0))) then
        tmp = (x + y) / 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 <= -2900000.0) || !(y <= 6600000.0)) {
		tmp = (x + y) / y;
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2900000.0) or not (y <= 6600000.0):
		tmp = (x + y) / y
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2900000.0) || !(y <= 6600000.0))
		tmp = Float64(Float64(x + y) / 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 <= -2900000.0) || ~((y <= 6600000.0)))
		tmp = (x + y) / y;
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2900000.0], N[Not[LessEqual[y, 6600000.0]], $MachinePrecision]], N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e6 or 6.6e6 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Step-by-step derivation

      1. clear-num 99.9%

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

      2. associate-/r/ 99.7%

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

   3. Applied egg-rr 99.7%

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

   4. Taylor expanded in y around inf 98.9%

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

      1. *-commutative 98.9%

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

      2. div-inv 99.2%

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

      3. +-commutative 99.2%

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

   6. Applied egg-rr 99.2%

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

   if -2.9e6 < y < 6.6e6

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 78.5%

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

      1. +-commutative 78.5%

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

   4. Simplified 78.5%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2900000 \lor \neg \left(y \leq 6600000\right):\\ \;\;\;\;\frac{x + y}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 8: 73.8% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 13000.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13000.0) {
		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 (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 13000.0d0) 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 (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 13000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 13000.0:
		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 <= 13000.0)
		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 <= 13000.0)
		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, 13000.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 13000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 74.9%

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

   if -1 < y < 13000

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 76.0%

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

4. Final simplification 75.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 13000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 39.3% 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 38.5%

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

3. Final simplification 38.5%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023290 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))