Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 8

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: 74.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;x \leq -2.3 \cdot 10^{+45}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= x -2.3e+45)
     t_0
     (if (<= x 3e-35)
       (/ y (+ y 1.0))
       (if (<= x 1.16e+24) x (if (<= x 3.6e+34) 1.0 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (x <= -2.3e+45) {
		tmp = t_0;
	} else if (x <= 3e-35) {
		tmp = y / (y + 1.0);
	} else if (x <= 1.16e+24) {
		tmp = x;
	} else if (x <= 3.6e+34) {
		tmp = 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 = x / (y + 1.0d0)
    if (x <= (-2.3d+45)) then
        tmp = t_0
    else if (x <= 3d-35) then
        tmp = y / (y + 1.0d0)
    else if (x <= 1.16d+24) then
        tmp = x
    else if (x <= 3.6d+34) then
        tmp = 1.0d0
    else
        tmp = t_0
    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 <= -2.3e+45) {
		tmp = t_0;
	} else if (x <= 3e-35) {
		tmp = y / (y + 1.0);
	} else if (x <= 1.16e+24) {
		tmp = x;
	} else if (x <= 3.6e+34) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if x <= -2.3e+45:
		tmp = t_0
	elif x <= 3e-35:
		tmp = y / (y + 1.0)
	elif x <= 1.16e+24:
		tmp = x
	elif x <= 3.6e+34:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (x <= -2.3e+45)
		tmp = t_0;
	elseif (x <= 3e-35)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (x <= 1.16e+24)
		tmp = x;
	elseif (x <= 3.6e+34)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (x <= -2.3e+45)
		tmp = t_0;
	elseif (x <= 3e-35)
		tmp = y / (y + 1.0);
	elseif (x <= 1.16e+24)
		tmp = x;
	elseif (x <= 3.6e+34)
		tmp = 1.0;
	else
		tmp = t_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, -2.3e+45], t$95$0, If[LessEqual[x, 3e-35], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.16e+24], x, If[LessEqual[x, 3.6e+34], 1.0, t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -2.30000000000000012e45 or 3.6e34 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.2%

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

      1. +-commutative 81.2%

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

   5. Simplified 81.2%

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

   if -2.30000000000000012e45 < x < 2.99999999999999989e-35

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 82.3%

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

      1. +-commutative 82.3%

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

   5. Simplified 82.3%

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

   if 2.99999999999999989e-35 < x < 1.16000000000000005e24

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.7%

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

   if 1.16000000000000005e24 < x < 3.6e34

   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 4 regimes into one program.

4. Final simplification 81.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.3 \cdot 10^{+45}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;x \leq 3 \cdot 10^{-35}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 1.16 \cdot 10^{+24}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+34}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 3.7) x (if (<= y 5.7e+69) 1.0 (if (<= y 6.5e+96) (/ x y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.7) {
		tmp = x;
	} else if (y <= 5.7e+69) {
		tmp = 1.0;
	} else if (y <= 6.5e+96) {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 3.7d0) then
        tmp = x
    else if (y <= 5.7d+69) then
        tmp = 1.0d0
    else if (y <= 6.5d+96) then
        tmp = 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 <= -1.0) {
		tmp = 1.0;
	} else if (y <= 3.7) {
		tmp = x;
	} else if (y <= 5.7e+69) {
		tmp = 1.0;
	} else if (y <= 6.5e+96) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 3.7:
		tmp = x
	elif y <= 5.7e+69:
		tmp = 1.0
	elif y <= 6.5e+96:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 3.7)
		tmp = x;
	elseif (y <= 5.7e+69)
		tmp = 1.0;
	elseif (y <= 6.5e+96)
		tmp = Float64(x / y);
	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 <= 3.7)
		tmp = x;
	elseif (y <= 5.7e+69)
		tmp = 1.0;
	elseif (y <= 6.5e+96)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 3.7], x, If[LessEqual[y, 5.7e+69], 1.0, If[LessEqual[y, 6.5e+96], N[(x / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.7000000000000002 < y < 5.7e69 or 6.5e96 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -1 < y < 3.7000000000000002

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.9%

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

   if 5.7e69 < y < 6.5e96

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 86.2%

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

4. Final simplification 77.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.7:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5.7 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.068:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y 0.068)
     (- x (* x y))
     (if (<= y 1.35e+69) 1.0 (if (<= y 2.7e+98) (/ x y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.068) {
		tmp = x - (x * y);
	} else if (y <= 1.35e+69) {
		tmp = 1.0;
	} else if (y <= 2.7e+98) {
		tmp = 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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 0.068d0) then
        tmp = x - (x * y)
    else if (y <= 1.35d+69) then
        tmp = 1.0d0
    else if (y <= 2.7d+98) then
        tmp = 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 <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.068) {
		tmp = x - (x * y);
	} else if (y <= 1.35e+69) {
		tmp = 1.0;
	} else if (y <= 2.7e+98) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.068:
		tmp = x - (x * y)
	elif y <= 1.35e+69:
		tmp = 1.0
	elif y <= 2.7e+98:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 0.068)
		tmp = Float64(x - Float64(x * y));
	elseif (y <= 1.35e+69)
		tmp = 1.0;
	elseif (y <= 2.7e+98)
		tmp = Float64(x / y);
	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 <= 0.068)
		tmp = x - (x * y);
	elseif (y <= 1.35e+69)
		tmp = 1.0;
	elseif (y <= 2.7e+98)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 0.068], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.35e+69], 1.0, If[LessEqual[y, 2.7e+98], N[(x / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.068000000000000005 < y < 1.3499999999999999e69 or 2.7e98 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 79.6%

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

   if -1 < y < 0.068000000000000005

   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%

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

   6. Taylor expanded in y around 0 74.8%

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

      1. mul-1-neg 74.8%

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

      2. unsub-neg 74.8%

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

      3. *-commutative 74.8%

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

   8. Simplified 74.8%

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

   if 1.3499999999999999e69 < y < 2.7e98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 86.2%

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

4. Final simplification 77.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.068:\\ \;\;\;\;x - x \cdot y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+98}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.04e+18)
   1.0
   (if (<= y 3.8e+23)
     (/ x (+ y 1.0))
     (if (<= y 2.95e+69) 1.0 (if (<= y 5e+96) (/ x y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.04e+18) {
		tmp = 1.0;
	} else if (y <= 3.8e+23) {
		tmp = x / (y + 1.0);
	} else if (y <= 2.95e+69) {
		tmp = 1.0;
	} else if (y <= 5e+96) {
		tmp = 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 <= (-1.04d+18)) then
        tmp = 1.0d0
    else if (y <= 3.8d+23) then
        tmp = x / (y + 1.0d0)
    else if (y <= 2.95d+69) then
        tmp = 1.0d0
    else if (y <= 5d+96) then
        tmp = 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 <= -1.04e+18) {
		tmp = 1.0;
	} else if (y <= 3.8e+23) {
		tmp = x / (y + 1.0);
	} else if (y <= 2.95e+69) {
		tmp = 1.0;
	} else if (y <= 5e+96) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.04e+18:
		tmp = 1.0
	elif y <= 3.8e+23:
		tmp = x / (y + 1.0)
	elif y <= 2.95e+69:
		tmp = 1.0
	elif y <= 5e+96:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.04e+18)
		tmp = 1.0;
	elseif (y <= 3.8e+23)
		tmp = Float64(x / Float64(y + 1.0));
	elseif (y <= 2.95e+69)
		tmp = 1.0;
	elseif (y <= 5e+96)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.04e+18)
		tmp = 1.0;
	elseif (y <= 3.8e+23)
		tmp = x / (y + 1.0);
	elseif (y <= 2.95e+69)
		tmp = 1.0;
	elseif (y <= 5e+96)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.04e+18], 1.0, If[LessEqual[y, 3.8e+23], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.95e+69], 1.0, If[LessEqual[y, 5e+96], N[(x / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.04e18 or 3.79999999999999975e23 < y < 2.95000000000000002e69 or 5.0000000000000004e96 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 83.7%

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

   if -1.04e18 < y < 3.79999999999999975e23

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.9%

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

      1. +-commutative 74.9%

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

   5. Simplified 74.9%

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

   if 2.95000000000000002e69 < y < 5.0000000000000004e96

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 86.2%

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

4. Final simplification 79.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.04 \cdot 10^{+18}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 3.8 \cdot 10^{+23}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 2.95 \cdot 10^{+69}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+96}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -0.05:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.00024:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y 1.0))))
   (if (<= y -0.05)
     t_0
     (if (<= y 0.00024)
       (+ x (* y (- 1.0 x)))
       (if (<= y 2.6e+69) t_0 (if (<= y 3.2e+105) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -0.05) {
		tmp = t_0;
	} else if (y <= 0.00024) {
		tmp = x + (y * (1.0 - x));
	} else if (y <= 2.6e+69) {
		tmp = t_0;
	} else if (y <= 3.2e+105) {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = y / (y + 1.0d0)
    if (y <= (-0.05d0)) then
        tmp = t_0
    else if (y <= 0.00024d0) then
        tmp = x + (y * (1.0d0 - x))
    else if (y <= 2.6d+69) then
        tmp = t_0
    else if (y <= 3.2d+105) then
        tmp = x / y
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -0.05) {
		tmp = t_0;
	} else if (y <= 0.00024) {
		tmp = x + (y * (1.0 - x));
	} else if (y <= 2.6e+69) {
		tmp = t_0;
	} else if (y <= 3.2e+105) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + 1.0)
	tmp = 0
	if y <= -0.05:
		tmp = t_0
	elif y <= 0.00024:
		tmp = x + (y * (1.0 - x))
	elif y <= 2.6e+69:
		tmp = t_0
	elif y <= 3.2e+105:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -0.05)
		tmp = t_0;
	elseif (y <= 0.00024)
		tmp = Float64(x + Float64(y * Float64(1.0 - x)));
	elseif (y <= 2.6e+69)
		tmp = t_0;
	elseif (y <= 3.2e+105)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + 1.0);
	tmp = 0.0;
	if (y <= -0.05)
		tmp = t_0;
	elseif (y <= 0.00024)
		tmp = x + (y * (1.0 - x));
	elseif (y <= 2.6e+69)
		tmp = t_0;
	elseif (y <= 3.2e+105)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -0.05], t$95$0, If[LessEqual[y, 0.00024], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.6e+69], t$95$0, If[LessEqual[y, 3.2e+105], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -0.050000000000000003 or 2.40000000000000006e-4 < y < 2.6000000000000002e69

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.5%

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

      1. +-commutative 74.5%

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

   5. Simplified 74.5%

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

   if -0.050000000000000003 < y < 2.40000000000000006e-4

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.8%

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

   if 2.6000000000000002e69 < y < 3.2e105

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 86.2%

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

      1. +-commutative 86.2%

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

   5. Simplified 86.2%

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

   6. Taylor expanded in y around inf 86.2%

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

   if 3.2e105 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 92.8%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.05:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 0.00024:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \mathbf{elif}\;y \leq 2.6 \cdot 10^{+69}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+105}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 2.5) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 2.5) {
		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 <= 2.5d0) 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 <= 2.5) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 2.5:
		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 <= 2.5)
		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 <= 2.5)
		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, 2.5], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 76.3%

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

   if -1 < y < 2.5

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.9%

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

4. Final simplification 75.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.5:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.4% 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 41.6%

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

4. Final simplification 41.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024046 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))