Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 11

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: 72.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{-1}{y}\\ \mathbf{if}\;y \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ -1.0 y))))
   (if (<= y -4.8e+100)
     1.0
     (if (<= y -4.2e+40)
       (/ x y)
       (if (<= y -1.0) t_0 (if (<= y -3.5e-54) y (if (<= y 2.0) x t_0)))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-1.0 / y);
	double tmp;
	if (y <= -4.8e+100) {
		tmp = 1.0;
	} else if (y <= -4.2e+40) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -3.5e-54) {
		tmp = y;
	} else if (y <= 2.0) {
		tmp = x;
	} 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) / y)
    if (y <= (-4.8d+100)) then
        tmp = 1.0d0
    else if (y <= (-4.2d+40)) then
        tmp = x / y
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-3.5d-54)) then
        tmp = y
    else if (y <= 2.0d0) then
        tmp = x
    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 / y);
	double tmp;
	if (y <= -4.8e+100) {
		tmp = 1.0;
	} else if (y <= -4.2e+40) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -3.5e-54) {
		tmp = y;
	} else if (y <= 2.0) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-1.0 / y)
	tmp = 0
	if y <= -4.8e+100:
		tmp = 1.0
	elif y <= -4.2e+40:
		tmp = x / y
	elif y <= -1.0:
		tmp = t_0
	elif y <= -3.5e-54:
		tmp = y
	elif y <= 2.0:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -4.8e+100)
		tmp = 1.0;
	elseif (y <= -4.2e+40)
		tmp = Float64(x / y);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -3.5e-54)
		tmp = y;
	elseif (y <= 2.0)
		tmp = x;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-1.0 / y);
	tmp = 0.0;
	if (y <= -4.8e+100)
		tmp = 1.0;
	elseif (y <= -4.2e+40)
		tmp = x / y;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -3.5e-54)
		tmp = y;
	elseif (y <= 2.0)
		tmp = x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.8e+100], 1.0, If[LessEqual[y, -4.2e+40], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -3.5e-54], y, If[LessEqual[y, 2.0], x, t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.80000000000000023e100

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

   if -4.80000000000000023e100 < y < -4.2000000000000002e40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. +-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around inf 78.7%

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

   if -4.2000000000000002e40 < y < -1 or 2 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

      1. +-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 73.4%

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

   if -1 < y < -3.49999999999999982e-54

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in y around 0 55.5%

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

   if -3.49999999999999982e-54 < y < 2

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 78.7%

      \[\leadsto \color{blue}{x} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -4.2 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1 + \frac{-1}{y}\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{y}\\ \end{array} \]

Alternative 3: 72.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{-1}{y}\\ \mathbf{if}\;y \leq -4.2 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ -1.0 y))))
   (if (<= y -4.2e+100)
     1.0
     (if (<= y -2.4e+40)
       (/ x y)
       (if (<= y -1.0)
         t_0
         (if (<= y -5.2e-54) y (if (<= y 1.0) (- x (* x y)) t_0)))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (-1.0 / y);
	double tmp;
	if (y <= -4.2e+100) {
		tmp = 1.0;
	} else if (y <= -2.4e+40) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.2e-54) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = x - (x * y);
	} 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) / y)
    if (y <= (-4.2d+100)) then
        tmp = 1.0d0
    else if (y <= (-2.4d+40)) then
        tmp = x / y
    else if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-5.2d-54)) then
        tmp = y
    else if (y <= 1.0d0) then
        tmp = x - (x * y)
    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 / y);
	double tmp;
	if (y <= -4.2e+100) {
		tmp = 1.0;
	} else if (y <= -2.4e+40) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.2e-54) {
		tmp = y;
	} else if (y <= 1.0) {
		tmp = x - (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (-1.0 / y)
	tmp = 0
	if y <= -4.2e+100:
		tmp = 1.0
	elif y <= -2.4e+40:
		tmp = x / y
	elif y <= -1.0:
		tmp = t_0
	elif y <= -5.2e-54:
		tmp = y
	elif y <= 1.0:
		tmp = x - (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -4.2e+100)
		tmp = 1.0;
	elseif (y <= -2.4e+40)
		tmp = Float64(x / y);
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.2e-54)
		tmp = y;
	elseif (y <= 1.0)
		tmp = Float64(x - Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (-1.0 / y);
	tmp = 0.0;
	if (y <= -4.2e+100)
		tmp = 1.0;
	elseif (y <= -2.4e+40)
		tmp = x / y;
	elseif (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.2e-54)
		tmp = y;
	elseif (y <= 1.0)
		tmp = x - (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -4.2e+100], 1.0, If[LessEqual[y, -2.4e+40], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -5.2e-54], y, If[LessEqual[y, 1.0], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -4.1999999999999997e100

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 91.4%

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

   if -4.1999999999999997e100 < y < -2.4e40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. +-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around inf 78.7%

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

   if -2.4e40 < y < -1 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.4%

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

      1. +-commutative 74.4%

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

   4. Simplified 74.4%

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

   5. Taylor expanded in y around inf 73.4%

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

   if -1 < y < -5.20000000000000004e-54

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 59.3%

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

      1. +-commutative 59.3%

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

   4. Simplified 59.3%

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

   5. Taylor expanded in y around 0 55.5%

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

   if -5.20000000000000004e-54 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 80.4%

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

      1. +-commutative 80.4%

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

   4. Simplified 80.4%

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

   5. Taylor expanded in y around 0 79.3%

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

      1. mul-1-neg 79.3%

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

      2. distribute-rgt-neg-out 79.3%

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

      3. +-commutative 79.3%

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

      4. distribute-rgt-neg-out 79.3%

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

      5. unsub-neg 79.3%

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

      6. *-commutative 79.3%

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

   7. Simplified 79.3%

      \[\leadsto \color{blue}{x - x \cdot y} \]
3. Recombined 5 regimes into one program.

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.2 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.4 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1 + \frac{-1}{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{-1}{y}\\ \end{array} \]

Alternative 4: 73.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.68 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -66:\\ \;\;\;\;1 + \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.68e+100)
   1.0
   (if (<= y -2.1e+40)
     (/ x y)
     (if (<= y -66.0)
       (+ 1.0 (/ -1.0 y))
       (if (<= y 1.5e+23) (/ x (+ y 1.0)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.68e+100) {
		tmp = 1.0;
	} else if (y <= -2.1e+40) {
		tmp = x / y;
	} else if (y <= -66.0) {
		tmp = 1.0 + (-1.0 / y);
	} else if (y <= 1.5e+23) {
		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 <= (-1.68d+100)) then
        tmp = 1.0d0
    else if (y <= (-2.1d+40)) then
        tmp = x / y
    else if (y <= (-66.0d0)) then
        tmp = 1.0d0 + ((-1.0d0) / y)
    else if (y <= 1.5d+23) 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 <= -1.68e+100) {
		tmp = 1.0;
	} else if (y <= -2.1e+40) {
		tmp = x / y;
	} else if (y <= -66.0) {
		tmp = 1.0 + (-1.0 / y);
	} else if (y <= 1.5e+23) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.68e+100:
		tmp = 1.0
	elif y <= -2.1e+40:
		tmp = x / y
	elif y <= -66.0:
		tmp = 1.0 + (-1.0 / y)
	elif y <= 1.5e+23:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.68e+100)
		tmp = 1.0;
	elseif (y <= -2.1e+40)
		tmp = Float64(x / y);
	elseif (y <= -66.0)
		tmp = Float64(1.0 + Float64(-1.0 / y));
	elseif (y <= 1.5e+23)
		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 <= -1.68e+100)
		tmp = 1.0;
	elseif (y <= -2.1e+40)
		tmp = x / y;
	elseif (y <= -66.0)
		tmp = 1.0 + (-1.0 / y);
	elseif (y <= 1.5e+23)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.68e+100], 1.0, If[LessEqual[y, -2.1e+40], N[(x / y), $MachinePrecision], If[LessEqual[y, -66.0], N[(1.0 + N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+23], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.68000000000000008e100 or 1.5e23 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.9%

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

   if -1.68000000000000008e100 < y < -2.1000000000000001e40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. +-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around inf 78.7%

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

   if -2.1000000000000001e40 < y < -66

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 83.9%

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

      1. +-commutative 83.9%

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

   4. Simplified 83.9%

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

   5. Taylor expanded in y around inf 75.0%

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

   if -66 < y < 1.5e23

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 76.6%

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

      1. +-commutative 76.6%

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

   4. Simplified 76.6%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.68 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -66:\\ \;\;\;\;1 + \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 5: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+101}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+101)
   1.0
   (if (<= y -6.5e+40)
     (/ x y)
     (if (<= y -5.2e-54)
       (/ y (+ y 1.0))
       (if (<= y 2.6e+20) (/ x (+ y 1.0)) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+101) {
		tmp = 1.0;
	} else if (y <= -6.5e+40) {
		tmp = x / y;
	} else if (y <= -5.2e-54) {
		tmp = y / (y + 1.0);
	} else if (y <= 2.6e+20) {
		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 <= (-4.9d+101)) then
        tmp = 1.0d0
    else if (y <= (-6.5d+40)) then
        tmp = x / y
    else if (y <= (-5.2d-54)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 2.6d+20) 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 <= -4.9e+101) {
		tmp = 1.0;
	} else if (y <= -6.5e+40) {
		tmp = x / y;
	} else if (y <= -5.2e-54) {
		tmp = y / (y + 1.0);
	} else if (y <= 2.6e+20) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+101:
		tmp = 1.0
	elif y <= -6.5e+40:
		tmp = x / y
	elif y <= -5.2e-54:
		tmp = y / (y + 1.0)
	elif y <= 2.6e+20:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+101)
		tmp = 1.0;
	elseif (y <= -6.5e+40)
		tmp = Float64(x / y);
	elseif (y <= -5.2e-54)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 2.6e+20)
		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 <= -4.9e+101)
		tmp = 1.0;
	elseif (y <= -6.5e+40)
		tmp = x / y;
	elseif (y <= -5.2e-54)
		tmp = y / (y + 1.0);
	elseif (y <= 2.6e+20)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+101], 1.0, If[LessEqual[y, -6.5e+40], N[(x / y), $MachinePrecision], If[LessEqual[y, -5.2e-54], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+20], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4.89999999999999983e101 or 2.6e20 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 83.9%

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

   if -4.89999999999999983e101 < y < -6.5000000000000001e40

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 78.7%

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

      1. +-commutative 78.7%

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

   4. Simplified 78.7%

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

   5. Taylor expanded in y around inf 78.7%

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

   if -6.5000000000000001e40 < y < -5.20000000000000004e-54

   1. Initial program 99.9%

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

   2. Taylor expanded in x around 0 68.4%

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

      1. +-commutative 68.4%

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

   4. Simplified 68.4%

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

   if -5.20000000000000004e-54 < y < 2.6e20

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 79.8%

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

      1. +-commutative 79.8%

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

   4. Simplified 79.8%

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

4. Final simplification 80.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+101}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.5 \cdot 10^{+40}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -5.2 \cdot 10^{-54}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+20}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 98.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.82)))
   (+ 1.0 (/ x y))
   (- x (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.82)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x - (y * (x + -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)) .or. (.not. (y <= 0.82d0))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x - (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.82)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x - (y * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.82):
		tmp = 1.0 + (x / y)
	else:
		tmp = x - (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.82))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(x - Float64(y * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.82)))
		tmp = 1.0 + (x / y);
	else
		tmp = x - (y * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.82]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x - N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.819999999999999951 < 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 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   7. Simplified 98.2%

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

   if -1 < y < 0.819999999999999951

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.1%

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

4. Final simplification 98.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x - y \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 7: 98.5% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < 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%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 98.1%

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

4. Final simplification 98.7%

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

Alternative 8: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -66 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -66.0) (not (<= y 420000.0))) (+ 1.0 (/ x y)) (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -66.0) || !(y <= 420000.0)) {
		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 <= (-66.0d0)) .or. (.not. (y <= 420000.0d0))) 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 <= -66.0) || !(y <= 420000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -66.0) or not (y <= 420000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -66.0) || !(y <= 420000.0))
		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 <= -66.0) || ~((y <= 420000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -66.0], N[Not[LessEqual[y, 420000.0]], $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 < -66 or 4.2e5 < 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 98.2%

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

      1. neg-mul-1 98.2%

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

      2. distribute-neg-frac 98.2%

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

   7. Simplified 98.2%

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

   if -66 < y < 4.2e5

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 77.0%

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

      1. +-commutative 77.0%

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

   4. Simplified 77.0%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66 \lor \neg \left(y \leq 420000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 9: 72.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.7:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65e+100) 1.0 (if (<= y -3.8e+14) (/ x y) (if (<= y 1.7) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65e+100) {
		tmp = 1.0;
	} else if (y <= -3.8e+14) {
		tmp = x / y;
	} else if (y <= 1.7) {
		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 <= (-1.65d+100)) then
        tmp = 1.0d0
    else if (y <= (-3.8d+14)) then
        tmp = x / y
    else if (y <= 1.7d0) 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 <= -1.65e+100) {
		tmp = 1.0;
	} else if (y <= -3.8e+14) {
		tmp = x / y;
	} else if (y <= 1.7) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65e+100:
		tmp = 1.0
	elif y <= -3.8e+14:
		tmp = x / y
	elif y <= 1.7:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65e+100)
		tmp = 1.0;
	elseif (y <= -3.8e+14)
		tmp = Float64(x / y);
	elseif (y <= 1.7)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65e+100)
		tmp = 1.0;
	elseif (y <= -3.8e+14)
		tmp = x / y;
	elseif (y <= 1.7)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65e+100], 1.0, If[LessEqual[y, -3.8e+14], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.7], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6500000000000001e100 or 1.69999999999999996 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.6%

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

   if -1.6500000000000001e100 < y < -3.8e14

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 71.4%

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

      1. +-commutative 71.4%

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

   4. Simplified 71.4%

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

   5. Taylor expanded in y around inf 71.4%

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

   if -3.8e14 < y < 1.69999999999999996

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 72.9%

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

4. Final simplification 76.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+100}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{+14}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.7:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 10: 73.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 3.3) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.3) {
		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 <= 3.3d0) 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 <= 3.3) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 3.3:
		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 <= 3.3)
		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 <= 3.3)
		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, 3.3], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.2999999999999998 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 72.9%

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

   if -1 < y < 3.2999999999999998

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 74.9%

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

4. Final simplification 73.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.3:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 11: 39.1% 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 38.2%

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

3. Final simplification 38.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023200 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))