Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.8s

Alternatives: 10

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: 71.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y -1.05e-135) y (if (<= y 2.7e-13) (- x (* x y)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.05e-135) {
		tmp = y;
	} else if (y <= 2.7e-13) {
		tmp = x - (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 <= (-1.05d-135)) then
        tmp = y
    else if (y <= 2.7d-13) then
        tmp = x - (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 <= -1.05e-135) {
		tmp = y;
	} else if (y <= 2.7e-13) {
		tmp = x - (x * y);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -1.05e-135:
		tmp = y
	elif y <= 2.7e-13:
		tmp = x - (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 <= -1.05e-135)
		tmp = y;
	elseif (y <= 2.7e-13)
		tmp = Float64(x - 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 <= -1.05e-135)
		tmp = y;
	elseif (y <= 2.7e-13)
		tmp = x - (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, -1.05e-135], y, If[LessEqual[y, 2.7e-13], N[(x - N[(x * y), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.70000000000000011e-13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -1 < y < -1.05e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in y around 0 71.1%

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

   if -1.05e-135 < y < 2.70000000000000011e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.0%

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

      1. +-commutative 82.0%

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

   5. Simplified 82.0%

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

   6. Taylor expanded in y around 0 82.0%

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

      1. mul-1-neg 82.0%

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

      2. unsub-neg 82.0%

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

   8. Simplified 82.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x - x \cdot y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 71.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   1.0
   (if (<= y -1.05e-135) y (if (<= y 3.1e+32) (/ x (+ y 1.0)) 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.05e-135) {
		tmp = y;
	} else if (y <= 3.1e+32) {
		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 <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= (-1.05d-135)) then
        tmp = y
    else if (y <= 3.1d+32) 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 <= -1.0) {
		tmp = 1.0;
	} else if (y <= -1.05e-135) {
		tmp = y;
	} else if (y <= 3.1e+32) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -1.05e-135:
		tmp = y
	elif y <= 3.1e+32:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= -1.05e-135)
		tmp = y;
	elseif (y <= 3.1e+32)
		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 <= -1.0)
		tmp = 1.0;
	elseif (y <= -1.05e-135)
		tmp = y;
	elseif (y <= 3.1e+32)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, -1.05e-135], y, If[LessEqual[y, 3.1e+32], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 3.09999999999999993e32 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.2%

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

   if -1 < y < -1.05e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in y around 0 71.1%

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

   if -1.05e-135 < y < 3.09999999999999993e32

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.1 \cdot 10^{+32}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -7500:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 2050000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -7500.0)
     t_0
     (if (<= y -1.05e-135)
       (/ y (+ y 1.0))
       (if (<= y 2050000000.0) (/ x (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -7500.0) {
		tmp = t_0;
	} else if (y <= -1.05e-135) {
		tmp = y / (y + 1.0);
	} else if (y <= 2050000000.0) {
		tmp = x / (y + 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 = 1.0d0 + (x / y)
    if (y <= (-7500.0d0)) then
        tmp = t_0
    else if (y <= (-1.05d-135)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 2050000000.0d0) then
        tmp = x / (y + 1.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -7500.0) {
		tmp = t_0;
	} else if (y <= -1.05e-135) {
		tmp = y / (y + 1.0);
	} else if (y <= 2050000000.0) {
		tmp = x / (y + 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -7500.0:
		tmp = t_0
	elif y <= -1.05e-135:
		tmp = y / (y + 1.0)
	elif y <= 2050000000.0:
		tmp = x / (y + 1.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -7500.0)
		tmp = t_0;
	elseif (y <= -1.05e-135)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 2050000000.0)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	tmp = 0.0;
	if (y <= -7500.0)
		tmp = t_0;
	elseif (y <= -1.05e-135)
		tmp = y / (y + 1.0);
	elseif (y <= 2050000000.0)
		tmp = x / (y + 1.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7500.0], t$95$0, If[LessEqual[y, -1.05e-135], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2050000000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7500 or 2.05e9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. +-commutative 99.2%

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

      4. associate--r- 99.2%

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

      5. div-sub 99.2%

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

   5. Simplified 99.2%

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

   6. Taylor expanded in x around inf 98.8%

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

      1. neg-mul-1 98.8%

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

      2. distribute-neg-frac 98.8%

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

   8. Simplified 98.8%

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

   if -7500 < y < -1.05e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   if -1.05e-135 < y < 2.05e9

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 80.1%

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

      1. +-commutative 80.1%

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

   5. Simplified 80.1%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7500:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 2050000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.76\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.76))) (+ 1.0 (/ x y)) (* (+ x y) (- 1.0 y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.76)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = (x + y) * (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 <= 0.76d0))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = (x + y) * (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 <= 0.76)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = (x + y) * (1.0 - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.76):
		tmp = 1.0 + (x / y)
	else:
		tmp = (x + y) * (1.0 - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.76))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = Float64(Float64(x + y) * Float64(1.0 - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.76)))
		tmp = 1.0 + (x / y);
	else
		tmp = (x + y) * (1.0 - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.76]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(1.0 - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.76000000000000001 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.0%

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

      1. +-commutative 99.0%

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

      2. associate--l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--r- 99.0%

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

      5. div-sub 99.0%

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

   5. Simplified 99.0%

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

   6. Taylor expanded in x around inf 98.6%

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

      1. neg-mul-1 98.6%

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

      2. distribute-neg-frac 98.6%

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

   8. Simplified 98.6%

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

   if -1 < y < 0.76000000000000001

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ 100.0%

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

      2. associate-/r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. neg-mul-1 99.5%

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

      3. +-commutative 99.5%

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

      4. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

   10. Taylor expanded in y around 0 99.6%

       \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot \left(x - 1\right)\right) + -1 \cdot {y}^{2}\right)} \]

   12. Simplified 99.5%

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

4. Final simplification 99.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.76\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\left(x + y\right) \cdot \left(1 - y\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Python

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

Julia

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

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = 1.0 - ((1.0 - x) / y);
	else
		tmp = (x + y) * (1.0 - y);
	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[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(N[(x + y), $MachinePrecision] * N[(1.0 - y), $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 99.0%

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

      1. +-commutative 99.0%

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

      2. associate--l+ 99.0%

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

      3. +-commutative 99.0%

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

      4. associate--r- 99.0%

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

      5. div-sub 99.0%

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

   5. Simplified 99.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[\frac{x + y}{y + 1} \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. flip-+ 100.0%

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

      2. associate-/r/ 100.0%

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

      3. metadata-eval 100.0%

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

      4. fma-neg 100.0%

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

      5. metadata-eval 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

   4. Applied egg-rr 100.0%

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

      1. +-commutative 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in y around 0 99.5%

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

      1. neg-mul-1 99.5%

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

      2. neg-mul-1 99.5%

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

      3. +-commutative 99.5%

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

      4. unsub-neg 99.5%

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

   9. Simplified 99.5%

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

   10. Taylor expanded in y around 0 99.6%

       \[\leadsto \color{blue}{x + \left(-1 \cdot \left(y \cdot \left(x - 1\right)\right) + -1 \cdot {y}^{2}\right)} \]

   12. Simplified 99.5%

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

4. Final simplification 99.3%

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

Alternative 7: 72.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.05e-135)
   (/ y (+ y 1.0))
   (if (<= y 8.5e+31) (/ x (+ y 1.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.05e-135) {
		tmp = y / (y + 1.0);
	} else if (y <= 8.5e+31) {
		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 <= (-1.05d-135)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 8.5d+31) 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 <= -1.05e-135) {
		tmp = y / (y + 1.0);
	} else if (y <= 8.5e+31) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.05e-135:
		tmp = y / (y + 1.0)
	elif y <= 8.5e+31:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.05e-135)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 8.5e+31)
		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 <= -1.05e-135)
		tmp = y / (y + 1.0);
	elseif (y <= 8.5e+31)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.05e-135], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+31], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 3 regimes

2. if y < -1.05e-135

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 76.1%

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

      1. +-commutative 76.1%

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

   5. Simplified 76.1%

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

   if -1.05e-135 < y < 8.49999999999999947e31

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.4%

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

      1. +-commutative 79.4%

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

   5. Simplified 79.4%

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

   if 8.49999999999999947e31 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 78.6%

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

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-135}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+31}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 71.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-136}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y -6.2e-136) y (if (<= y 2.7e-13) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= -6.2e-136) {
		tmp = y;
	} else if (y <= 2.7e-13) {
		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 <= (-6.2d-136)) then
        tmp = y
    else if (y <= 2.7d-13) 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 <= -6.2e-136) {
		tmp = y;
	} else if (y <= 2.7e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= -6.2e-136:
		tmp = y
	elif y <= 2.7e-13:
		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 <= -6.2e-136)
		tmp = y;
	elseif (y <= 2.7e-13)
		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 <= -6.2e-136)
		tmp = y;
	elseif (y <= 2.7e-13)
		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, -6.2e-136], y, If[LessEqual[y, 2.7e-13], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.70000000000000011e-13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -1 < y < -6.2e-136

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 73.0%

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

      1. +-commutative 73.0%

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

   5. Simplified 73.0%

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

   6. Taylor expanded in y around 0 71.1%

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

   if -6.2e-136 < y < 2.70000000000000011e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.0%

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

4. Final simplification 76.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.2 \cdot 10^{-136}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.5% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 2.7e-13) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 2.7e-13) {
		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 <= 2.7d-13) 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 <= 2.7e-13) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 2.7e-13:
		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 <= 2.7e-13)
		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 <= 2.7e-13)
		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, 2.7e-13], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.70000000000000011e-13 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 73.1%

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

   if -1 < y < 2.70000000000000011e-13

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.3%

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

4. Final simplification 73.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-13}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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. Add Preprocessing

3. Taylor expanded in y around inf 38.6%

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

4. Final simplification 38.6%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024011 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))