Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 7.0s

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: 85.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.23:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.2e+78)
   1.0
   (if (<= y -0.23) (/ x (+ y 1.0)) (if (<= y 8e+22) (+ x y) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.2e+78) {
		tmp = 1.0;
	} else if (y <= -0.23) {
		tmp = x / (y + 1.0);
	} else if (y <= 8e+22) {
		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 <= (-1.2d+78)) then
        tmp = 1.0d0
    else if (y <= (-0.23d0)) then
        tmp = x / (y + 1.0d0)
    else if (y <= 8d+22) 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 <= -1.2e+78) {
		tmp = 1.0;
	} else if (y <= -0.23) {
		tmp = x / (y + 1.0);
	} else if (y <= 8e+22) {
		tmp = x + y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.2e+78:
		tmp = 1.0
	elif y <= -0.23:
		tmp = x / (y + 1.0)
	elif y <= 8e+22:
		tmp = x + y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.2e+78)
		tmp = 1.0;
	elseif (y <= -0.23)
		tmp = Float64(x / Float64(y + 1.0));
	elseif (y <= 8e+22)
		tmp = Float64(x + y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.2e+78)
		tmp = 1.0;
	elseif (y <= -0.23)
		tmp = x / (y + 1.0);
	elseif (y <= 8e+22)
		tmp = x + y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.2e+78], 1.0, If[LessEqual[y, -0.23], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e+22], N[(x + y), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1999999999999999e78 or 8e22 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 81.1%

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

   if -1.1999999999999999e78 < y < -0.23000000000000001

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.2%

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

      1. +-commutative 62.2%

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

   5. Simplified 62.2%

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

   if -0.23000000000000001 < y < 8e22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

   4. Taylor expanded in x around 0 98.0%

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

      1. neg-mul-1 98.0%

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

      2. sub-neg 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in y around 0 97.1%

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

      1. +-commutative 97.1%

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

   9. Simplified 97.1%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.2 \cdot 10^{+78}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -0.23:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.00041 \lor \neg \left(y \leq 9.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.00041) (not (<= y 9.2e-8)))
   (/ y (+ y 1.0))
   (+ x (* y (- 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.00041) || !(y <= 9.2e-8)) {
		tmp = y / (y + 1.0);
	} 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 <= (-0.00041d0)) .or. (.not. (y <= 9.2d-8))) then
        tmp = y / (y + 1.0d0)
    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 <= -0.00041) || !(y <= 9.2e-8)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + (y * (1.0 - x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.00041) or not (y <= 9.2e-8):
		tmp = y / (y + 1.0)
	else:
		tmp = x + (y * (1.0 - x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.00041) || !(y <= 9.2e-8))
		tmp = Float64(y / Float64(y + 1.0));
	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 <= -0.00041) || ~((y <= 9.2e-8)))
		tmp = y / (y + 1.0);
	else
		tmp = x + (y * (1.0 - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.00041], N[Not[LessEqual[y, 9.2e-8]], $MachinePrecision]], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.0999999999999999e-4 or 9.2000000000000003e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -4.0999999999999999e-4 < y < 9.2000000000000003e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.4%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.00041 \lor \neg \left(y \leq 9.2 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(1 - x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.0% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y -5.8e-29) y (if (<= y 9.2e-8) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -5.8e-29) {
		tmp = y;
	} else if (y <= 9.2e-8) {
		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 <= (-5.8d-29)) then
        tmp = y
    else if (y <= 9.2d-8) 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 <= -5.8e-29) {
		tmp = y;
	} else if (y <= 9.2e-8) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -5.8e-29:
		tmp = y
	elif y <= 9.2e-8:
		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 <= -5.8e-29)
		tmp = y;
	elseif (y <= 9.2e-8)
		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 <= -5.8e-29)
		tmp = y;
	elseif (y <= 9.2e-8)
		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, -5.8e-29], y, If[LessEqual[y, 9.2e-8], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 9.2000000000000003e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

   if -1 < y < -5.80000000000000048e-29

   1. Initial program 99.9%

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

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

   6. Taylor expanded in y around 0 71.7%

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

   if -5.80000000000000048e-29 < y < 9.2000000000000003e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 76.5%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-29}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-5} \lor \neg \left(y \leq 6.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7e-5) (not (<= y 6.8e-8))) (/ y (+ y 1.0)) (+ x y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7e-5) || !(y <= 6.8e-8)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-7d-5)) .or. (.not. (y <= 6.8d-8))) then
        tmp = y / (y + 1.0d0)
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7e-5) || !(y <= 6.8e-8)) {
		tmp = y / (y + 1.0);
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7e-5) or not (y <= 6.8e-8):
		tmp = y / (y + 1.0)
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7e-5) || !(y <= 6.8e-8))
		tmp = Float64(y / Float64(y + 1.0));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7e-5) || ~((y <= 6.8e-8)))
		tmp = y / (y + 1.0);
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7e-5], N[Not[LessEqual[y, 6.8e-8]], $MachinePrecision]], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.9999999999999994e-5 or 6.8e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 74.6%

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

      1. +-commutative 74.6%

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

   5. Simplified 74.6%

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

   if -6.9999999999999994e-5 < y < 6.8e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 100.0%

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

   4. Taylor expanded in x around 0 99.2%

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

      1. neg-mul-1 99.2%

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

      2. sub-neg 99.2%

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

   6. Simplified 99.2%

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

   7. Taylor expanded in y around 0 98.6%

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

      1. +-commutative 98.6%

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

   9. Simplified 98.6%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7 \cdot 10^{-5} \lor \neg \left(y \leq 6.8 \cdot 10^{-8}\right):\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 8e+22) (+ x y) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 8e+22) {
		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 <= 8d+22) 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 <= 8e+22) {
		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 <= 8e+22:
		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 <= 8e+22)
		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 <= 8e+22)
		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, 8e+22], N[(x + y), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8e22 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 74.3%

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

   if -1 < y < 8e22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 98.7%

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

   4. Taylor expanded in x around 0 98.0%

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

      1. neg-mul-1 98.0%

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

      2. sub-neg 98.0%

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

   6. Simplified 98.0%

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

   7. Taylor expanded in y around 0 97.1%

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

      1. +-commutative 97.1%

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

   9. Simplified 97.1%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+22}:\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 9.2e-8) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 9.2e-8) {
		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 <= 9.2d-8) 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 <= 9.2e-8) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 9.2e-8:
		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 <= 9.2e-8)
		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 <= 9.2e-8)
		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, 9.2e-8], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 9.2000000000000003e-8 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.2%

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

   if -1 < y < 9.2000000000000003e-8

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 71.9%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-8}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 39.2% 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 35.6%

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

4. Final simplification 35.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))