Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.4s

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. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \frac{x + y}{y + 1} \]
4. Add Preprocessing

Alternative 2: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;x \leq -8.6 \cdot 10^{+27}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+161} \lor \neg \left(x \leq 3.1 \cdot 10^{+182}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= x -8.6e+27)
     t_0
     (if (<= x 2.6e+23)
       (/ y (+ y 1.0))
       (if (or (<= x 3.9e+161) (not (<= x 3.1e+182))) t_0 1.0)))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (x <= -8.6e+27) {
		tmp = t_0;
	} else if (x <= 2.6e+23) {
		tmp = y / (y + 1.0);
	} else if ((x <= 3.9e+161) || !(x <= 3.1e+182)) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (y + 1.0d0)
    if (x <= (-8.6d+27)) then
        tmp = t_0
    else if (x <= 2.6d+23) then
        tmp = y / (y + 1.0d0)
    else if ((x <= 3.9d+161) .or. (.not. (x <= 3.1d+182))) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (x <= -8.6e+27) {
		tmp = t_0;
	} else if (x <= 2.6e+23) {
		tmp = y / (y + 1.0);
	} else if ((x <= 3.9e+161) || !(x <= 3.1e+182)) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if x <= -8.6e+27:
		tmp = t_0
	elif x <= 2.6e+23:
		tmp = y / (y + 1.0)
	elif (x <= 3.9e+161) or not (x <= 3.1e+182):
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (x <= -8.6e+27)
		tmp = t_0;
	elseif (x <= 2.6e+23)
		tmp = Float64(y / Float64(y + 1.0));
	elseif ((x <= 3.9e+161) || !(x <= 3.1e+182))
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (x <= -8.6e+27)
		tmp = t_0;
	elseif (x <= 2.6e+23)
		tmp = y / (y + 1.0);
	elseif ((x <= 3.9e+161) || ~((x <= 3.1e+182)))
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -8.6e+27], t$95$0, If[LessEqual[x, 2.6e+23], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 3.9e+161], N[Not[LessEqual[x, 3.1e+182]], $MachinePrecision]], t$95$0, 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if x < -8.60000000000000017e27 or 2.59999999999999992e23 < x < 3.9000000000000002e161 or 3.09999999999999996e182 < x

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 83.6%

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

      1. +-commutative 83.6%

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

   5. Simplified 83.6%

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

   if -8.60000000000000017e27 < x < 2.59999999999999992e23

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 79.2%

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

      1. +-commutative 79.2%

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

   5. Simplified 79.2%

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

   if 3.9000000000000002e161 < x < 3.09999999999999996e182

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 100.0%

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

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -8.6 \cdot 10^{+27}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+23}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 3.9 \cdot 10^{+161} \lor \neg \left(x \leq 3.1 \cdot 10^{+182}\right):\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 87.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -19000 \lor \neg \left(y \leq 1260000000000\right):\\ \;\;\;\;\frac{x + -1}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -19000.0) (not (<= y 1260000000000.0)))
   (+ (/ (+ x -1.0) y) 1.0)
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -19000.0) || !(y <= 1260000000000.0)) {
		tmp = ((x + -1.0) / y) + 1.0;
	} 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 <= (-19000.0d0)) .or. (.not. (y <= 1260000000000.0d0))) then
        tmp = ((x + (-1.0d0)) / y) + 1.0d0
    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 <= -19000.0) || !(y <= 1260000000000.0)) {
		tmp = ((x + -1.0) / y) + 1.0;
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -19000.0) or not (y <= 1260000000000.0):
		tmp = ((x + -1.0) / y) + 1.0
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -19000.0) || !(y <= 1260000000000.0))
		tmp = Float64(Float64(Float64(x + -1.0) / y) + 1.0);
	else
		tmp = Float64(x / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -19000.0) || ~((y <= 1260000000000.0)))
		tmp = ((x + -1.0) / y) + 1.0;
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -19000.0], N[Not[LessEqual[y, 1260000000000.0]], $MachinePrecision]], N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -19000 or 1.26e12 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

   5. Simplified 99.8%

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

   if -19000 < y < 1.26e12

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19000 \lor \neg \left(y \leq 1260000000000\right):\\ \;\;\;\;\frac{x + -1}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -135000 \lor \neg \left(y \leq 1260000000000\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -135000.0) (not (<= y 1260000000000.0)))
   (+ (/ x y) 1.0)
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -135000.0) || !(y <= 1260000000000.0)) {
		tmp = (x / y) + 1.0;
	} 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 <= (-135000.0d0)) .or. (.not. (y <= 1260000000000.0d0))) then
        tmp = (x / y) + 1.0d0
    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 <= -135000.0) || !(y <= 1260000000000.0)) {
		tmp = (x / y) + 1.0;
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -135000.0) or not (y <= 1260000000000.0):
		tmp = (x / y) + 1.0
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -135000.0) || !(y <= 1260000000000.0))
		tmp = Float64(Float64(x / y) + 1.0);
	else
		tmp = Float64(x / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -135000.0) || ~((y <= 1260000000000.0)))
		tmp = (x / y) + 1.0;
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -135000.0], N[Not[LessEqual[y, 1260000000000.0]], $MachinePrecision]], N[(N[(x / y), $MachinePrecision] + 1.0), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -135000 or 1.26e12 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 84.9%

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

   4. Taylor expanded in y around -inf 99.8%

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

      1. mul-1-neg 99.8%

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

      2. unsub-neg 99.8%

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

      3. sub-neg 99.8%

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

      4. metadata-eval 99.8%

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

      5. distribute-rgt-in 99.8%

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

      6. neg-mul-1 99.8%

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

      7. unsub-neg 99.8%

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

      8. lft-mult-inverse 99.8%

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

   6. Simplified 99.8%

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

   7. Taylor expanded in x around inf 99.4%

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

      1. neg-mul-1 99.4%

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

      2. distribute-neg-frac 99.4%

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

   9. Simplified 99.4%

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

   if -135000 < y < 1.26e12

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.4%

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

      1. +-commutative 75.4%

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

   5. Simplified 75.4%

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

4. Final simplification 86.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -135000 \lor \neg \left(y \leq 1260000000000\right):\\ \;\;\;\;\frac{x}{y} + 1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 16200000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3e+44) 1.0 (if (<= y 16200000000000.0) (/ x (+ y 1.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3e+44) {
		tmp = 1.0;
	} else if (y <= 16200000000000.0) {
		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 <= (-3d+44)) then
        tmp = 1.0d0
    else if (y <= 16200000000000.0d0) 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 <= -3e+44) {
		tmp = 1.0;
	} else if (y <= 16200000000000.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3e+44:
		tmp = 1.0
	elif y <= 16200000000000.0:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3e+44)
		tmp = 1.0;
	elseif (y <= 16200000000000.0)
		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 <= -3e+44)
		tmp = 1.0;
	elseif (y <= 16200000000000.0)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3e+44], 1.0, If[LessEqual[y, 16200000000000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -2.99999999999999987e44 or 1.62e13 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 79.8%

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

   if -2.99999999999999987e44 < y < 1.62e13

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 75.1%

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

      1. +-commutative 75.1%

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

   5. Simplified 75.1%

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

4. Final simplification 77.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3 \cdot 10^{+44}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 16200000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1260000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 1260000000000.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1260000000000.0) {
		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 <= 1260000000000.0d0) 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 <= 1260000000000.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1260000000000.0:
		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 <= 1260000000000.0)
		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 <= 1260000000000.0)
		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, 1260000000000.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.26e12 < y

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 77.4%

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

   if -1 < y < 1.26e12

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 72.0%

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

4. Final simplification 74.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1260000000000:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 39.5% 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. Add Preprocessing

3. Taylor expanded in y around inf 38.5%

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

4. Final simplification 38.5%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024080 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))