Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.8s

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: 87.8% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9500000 \lor \neg \left(y \leq 14500\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9500000.0) (not (<= y 14500.0)))
   (+ 1.0 (/ (+ x -1.0) y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9500000.0) || !(y <= 14500.0)) {
		tmp = 1.0 + ((x + -1.0) / 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 <= (-9500000.0d0)) .or. (.not. (y <= 14500.0d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) / 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 <= -9500000.0) || !(y <= 14500.0)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9500000.0) or not (y <= 14500.0):
		tmp = 1.0 + ((x + -1.0) / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9500000.0) || !(y <= 14500.0))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / 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 <= -9500000.0) || ~((y <= 14500.0)))
		tmp = 1.0 + ((x + -1.0) / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9500000.0], N[Not[LessEqual[y, 14500.0]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -9.5e6 or 14500 < 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 -9.5e6 < y < 14500

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 87.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9500000 \lor \neg \left(y \leq 14500\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.4% accurate, 0.4× speedup

Math

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

FPCore

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

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 * (1.0 - x));
	}
	return tmp;
}

Fortran

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

Java

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

   3. Taylor expanded in y around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. div-sub 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 99.2%

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

4. Final simplification 99.3%

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

Alternative 4: 87.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.062\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.062))) (+ 1.0 (/ x y)) (* x (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.062)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x * (1.0 - 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 <= (-1.0d0)) .or. (.not. (y <= 0.062d0))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x * (1.0d0 - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.062)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.062):
		tmp = 1.0 + (x / y)
	else:
		tmp = x * (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.062))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(x * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.062)))
		tmp = 1.0 + (x / y);
	else
		tmp = x * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.062]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.062 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. div-sub 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   5. Simplified 99.4%

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

   6. Taylor expanded in x around inf 98.5%

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

   if -1 < y < 0.062

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. *-rgt-identity 75.9%

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

      4. distribute-lft-out-- 75.9%

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

   8. Simplified 75.9%

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

4. Final simplification 87.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.062\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 87.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -15600000 \lor \neg \left(y \leq 3600000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -15600000.0) (not (<= y 3600000.0)))
   (+ 1.0 (/ x y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -15600000.0) || !(y <= 3600000.0)) {
		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 <= (-15600000.0d0)) .or. (.not. (y <= 3600000.0d0))) 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 <= -15600000.0) || !(y <= 3600000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -15600000.0) or not (y <= 3600000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -15600000.0) || !(y <= 3600000.0))
		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 <= -15600000.0) || ~((y <= 3600000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -15600000.0], N[Not[LessEqual[y, 3600000.0]], $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 < -1.56e7 or 3.6e6 < 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%

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

   6. Taylor expanded in x around inf 98.9%

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

   if -1.56e7 < y < 3.6e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 76.0%

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

      1. +-commutative 76.0%

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

   5. Simplified 76.0%

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

4. Final simplification 87.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -15600000 \lor \neg \left(y \leq 3600000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.36:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 0.36) (* x (- 1.0 y)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.36) {
		tmp = x * (1.0 - 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 <= 0.36d0) then
        tmp = x * (1.0d0 - 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 <= 0.36) {
		tmp = x * (1.0 - y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.36:
		tmp = x * (1.0 - y)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 0.36)
		tmp = Float64(x * Float64(1.0 - 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 <= 0.36)
		tmp = x * (1.0 - y);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 0.36], N[(x * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.35999999999999999 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.9%

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

   if -1 < y < 0.35999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.9%

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

      1. +-commutative 75.9%

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

   5. Simplified 75.9%

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

   6. Taylor expanded in y around 0 75.9%

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

      1. mul-1-neg 75.9%

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

      2. unsub-neg 75.9%

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

      3. *-rgt-identity 75.9%

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

      4. distribute-lft-out-- 75.9%

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

   8. Simplified 75.9%

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

4. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.36:\\ \;\;\;\;x \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 2.4) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 2.4) {
		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 <= 2.4d0) 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 <= 2.4) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 2.4:
		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 <= 2.4)
		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 <= 2.4)
		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, 2.4], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.39999999999999991 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 75.9%

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

   if -1 < y < 2.39999999999999991

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.4:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 38.8% 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 40.1%

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

4. Final simplification 40.1%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))