Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.9s

Alternatives: 9

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / (y + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / (y + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{x + y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (/ (+ x y) (+ y 1.0)))

C

double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (x + y) / (y + 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (x + y) / (y + 1.0);
}

Python

def code(x, y):
	return (x + y) / (y + 1.0)

Julia

function code(x, y)
	return Float64(Float64(x + y) / Float64(y + 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (x + y) / (y + 1.0);
end

Wolfram

code[x_, y_] := N[(N[(x + y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 100.0%

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

2. Final simplification 100.0%

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

Alternative 2: 70.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.7e+96)
   1.0
   (if (<= y -6.7e+19)
     (/ x y)
     (if (<= y -1.0)
       1.0
       (if (<= y 7800.0)
         x
         (if (<= y 5e+68) 1.0 (if (<= y 1.08e+130) (/ x y) 1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.7e+96) {
		tmp = 1.0;
	} else if (y <= -6.7e+19) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 7800.0) {
		tmp = x;
	} else if (y <= 5e+68) {
		tmp = 1.0;
	} else if (y <= 1.08e+130) {
		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 <= (-1.7d+96)) then
        tmp = 1.0d0
    else if (y <= (-6.7d+19)) then
        tmp = x / y
    else if (y <= (-1.0d0)) then
        tmp = 1.0d0
    else if (y <= 7800.0d0) then
        tmp = x
    else if (y <= 5d+68) then
        tmp = 1.0d0
    else if (y <= 1.08d+130) 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 <= -1.7e+96) {
		tmp = 1.0;
	} else if (y <= -6.7e+19) {
		tmp = x / y;
	} else if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 7800.0) {
		tmp = x;
	} else if (y <= 5e+68) {
		tmp = 1.0;
	} else if (y <= 1.08e+130) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.7e+96:
		tmp = 1.0
	elif y <= -6.7e+19:
		tmp = x / y
	elif y <= -1.0:
		tmp = 1.0
	elif y <= 7800.0:
		tmp = x
	elif y <= 5e+68:
		tmp = 1.0
	elif y <= 1.08e+130:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.7e+96)
		tmp = 1.0;
	elseif (y <= -6.7e+19)
		tmp = Float64(x / y);
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 7800.0)
		tmp = x;
	elseif (y <= 5e+68)
		tmp = 1.0;
	elseif (y <= 1.08e+130)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.7e+96)
		tmp = 1.0;
	elseif (y <= -6.7e+19)
		tmp = x / y;
	elseif (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 7800.0)
		tmp = x;
	elseif (y <= 5e+68)
		tmp = 1.0;
	elseif (y <= 1.08e+130)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.7e+96], 1.0, If[LessEqual[y, -6.7e+19], N[(x / y), $MachinePrecision], If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 7800.0], x, If[LessEqual[y, 5e+68], 1.0, If[LessEqual[y, 1.08e+130], N[(x / y), $MachinePrecision], 1.0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.7e96 or -6.7e19 < y < -1 or 7800 < y < 5.0000000000000004e68 or 1.08e130 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 78.2%

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

   if -1.7e96 < y < -6.7e19 or 5.0000000000000004e68 < y < 1.08e130

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r- 100.0%

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

      5. div-sub 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 69.7%

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

   if -1 < y < 7800

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.2%

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

4. Final simplification 77.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.7 \cdot 10^{+96}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -6.7 \cdot 10^{+19}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+68}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.08 \cdot 10^{+130}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 3: 85.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 75000:\\ \;\;\;\;x \cdot \frac{-1}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -2.15e+18)
     t_0
     (if (<= y -1.02e-55)
       (/ y (+ y 1.0))
       (if (<= y 75000.0) (* x (/ -1.0 (- -1.0 y))) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -2.15e+18) {
		tmp = t_0;
	} else if (y <= -1.02e-55) {
		tmp = y / (y + 1.0);
	} else if (y <= 75000.0) {
		tmp = x * (-1.0 / (-1.0 - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    if (y <= (-2.15d+18)) then
        tmp = t_0
    else if (y <= (-1.02d-55)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 75000.0d0) then
        tmp = x * ((-1.0d0) / ((-1.0d0) - y))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -2.15e+18) {
		tmp = t_0;
	} else if (y <= -1.02e-55) {
		tmp = y / (y + 1.0);
	} else if (y <= 75000.0) {
		tmp = x * (-1.0 / (-1.0 - y));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -2.15e+18:
		tmp = t_0
	elif y <= -1.02e-55:
		tmp = y / (y + 1.0)
	elif y <= 75000.0:
		tmp = x * (-1.0 / (-1.0 - y))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -2.15e+18)
		tmp = t_0;
	elseif (y <= -1.02e-55)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 75000.0)
		tmp = Float64(x * Float64(-1.0 / Float64(-1.0 - y)));
	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 <= -2.15e+18)
		tmp = t_0;
	elseif (y <= -1.02e-55)
		tmp = y / (y + 1.0);
	elseif (y <= 75000.0)
		tmp = x * (-1.0 / (-1.0 - y));
	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, -2.15e+18], t$95$0, If[LessEqual[y, -1.02e-55], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 75000.0], N[(x * N[(-1.0 / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.15e18 or 75000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. div-sub 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-neg-frac 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 99.5%

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

      1. +-commutative 99.5%

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

   10. Simplified 99.5%

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

   if -2.15e18 < y < -1.02e-55

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

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

   if -1.02e-55 < y < 75000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.7%

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

      1. +-commutative 84.7%

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

   4. Simplified 84.7%

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

      1. div-inv 84.7%

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

      2. *-commutative 84.7%

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

      3. frac-2neg 84.7%

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

      4. metadata-eval 84.7%

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

      5. distribute-neg-in 84.7%

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

      6. metadata-eval 84.7%

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

      7. +-commutative 84.7%

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

      8. sub-neg 84.7%

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

   6. Applied egg-rr 84.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 75000:\\ \;\;\;\;x \cdot \frac{-1}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 4: 86.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 8000:\\ \;\;\;\;x \cdot \frac{-1}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.15e+18)
   (+ 1.0 (/ x y))
   (if (<= y -9.5e-56)
     (/ y (+ y 1.0))
     (if (<= y 8000.0) (* x (/ -1.0 (- -1.0 y))) (+ 1.0 (/ (+ x -1.0) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+18) {
		tmp = 1.0 + (x / y);
	} else if (y <= -9.5e-56) {
		tmp = y / (y + 1.0);
	} else if (y <= 8000.0) {
		tmp = x * (-1.0 / (-1.0 - y));
	} else {
		tmp = 1.0 + ((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 <= (-2.15d+18)) then
        tmp = 1.0d0 + (x / y)
    else if (y <= (-9.5d-56)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 8000.0d0) then
        tmp = x * ((-1.0d0) / ((-1.0d0) - y))
    else
        tmp = 1.0d0 + ((x + (-1.0d0)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.15e+18) {
		tmp = 1.0 + (x / y);
	} else if (y <= -9.5e-56) {
		tmp = y / (y + 1.0);
	} else if (y <= 8000.0) {
		tmp = x * (-1.0 / (-1.0 - y));
	} else {
		tmp = 1.0 + ((x + -1.0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.15e+18:
		tmp = 1.0 + (x / y)
	elif y <= -9.5e-56:
		tmp = y / (y + 1.0)
	elif y <= 8000.0:
		tmp = x * (-1.0 / (-1.0 - y))
	else:
		tmp = 1.0 + ((x + -1.0) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.15e+18)
		tmp = Float64(1.0 + Float64(x / y));
	elseif (y <= -9.5e-56)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 8000.0)
		tmp = Float64(x * Float64(-1.0 / Float64(-1.0 - y)));
	else
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.15e+18)
		tmp = 1.0 + (x / y);
	elseif (y <= -9.5e-56)
		tmp = y / (y + 1.0);
	elseif (y <= 8000.0)
		tmp = x * (-1.0 / (-1.0 - y));
	else
		tmp = 1.0 + ((x + -1.0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.15e+18], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-56], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8000.0], N[(x * N[(-1.0 / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2.15e18

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. associate--r- 100.0%

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

      5. div-sub 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in x around inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. +-commutative 100.0%

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

   10. Simplified 100.0%

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

   if -2.15e18 < y < -9.4999999999999991e-56

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

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

   if -9.4999999999999991e-56 < y < 8e3

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.7%

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

      1. +-commutative 84.7%

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

   4. Simplified 84.7%

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

      1. div-inv 84.7%

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

      2. *-commutative 84.7%

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

      3. frac-2neg 84.7%

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

      4. metadata-eval 84.7%

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

      5. distribute-neg-in 84.7%

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

      6. metadata-eval 84.7%

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

      7. +-commutative 84.7%

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

      8. sub-neg 84.7%

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

   6. Applied egg-rr 84.7%

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

   if 8e3 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. +-commutative 99.5%

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

      4. associate--r- 99.5%

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

      5. div-sub 99.5%

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

   4. Simplified 99.5%

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

4. Final simplification 91.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-56}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 8000:\\ \;\;\;\;x \cdot \frac{-1}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \end{array} \]

Alternative 5: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -2.15e+18)
     t_0
     (if (<= y -1.02e-55)
       (/ y (+ y 1.0))
       (if (<= y 90000.0) (/ x (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -2.15e+18) {
		tmp = t_0;
	} else if (y <= -1.02e-55) {
		tmp = y / (y + 1.0);
	} else if (y <= 90000.0) {
		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 <= (-2.15d+18)) then
        tmp = t_0
    else if (y <= (-1.02d-55)) then
        tmp = y / (y + 1.0d0)
    else if (y <= 90000.0d0) 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 <= -2.15e+18) {
		tmp = t_0;
	} else if (y <= -1.02e-55) {
		tmp = y / (y + 1.0);
	} else if (y <= 90000.0) {
		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 <= -2.15e+18:
		tmp = t_0
	elif y <= -1.02e-55:
		tmp = y / (y + 1.0)
	elif y <= 90000.0:
		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 <= -2.15e+18)
		tmp = t_0;
	elseif (y <= -1.02e-55)
		tmp = Float64(y / Float64(y + 1.0));
	elseif (y <= 90000.0)
		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 <= -2.15e+18)
		tmp = t_0;
	elseif (y <= -1.02e-55)
		tmp = y / (y + 1.0);
	elseif (y <= 90000.0)
		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, -2.15e+18], t$95$0, If[LessEqual[y, -1.02e-55], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 90000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.15e18 or 9e4 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 99.7%

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

      1. +-commutative 99.7%

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

      2. associate--l+ 99.7%

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

      3. +-commutative 99.7%

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

      4. associate--r- 99.7%

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

      5. div-sub 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in x around inf 99.5%

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

      1. mul-1-neg 99.5%

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

      2. distribute-neg-frac 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in x around 0 99.5%

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

      1. +-commutative 99.5%

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

   10. Simplified 99.5%

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

   if -2.15e18 < y < -1.02e-55

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 79.9%

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

      1. +-commutative 79.9%

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

   4. Simplified 79.9%

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

   if -1.02e-55 < y < 9e4

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 84.7%

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

      1. +-commutative 84.7%

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

   4. Simplified 84.7%

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

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.15 \cdot 10^{+18}:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-55}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;y \leq 90000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{x}{y}\\ \end{array} \]

Alternative 6: 86.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 2.8e-9))) (+ 1.0 (/ x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.8e-9)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = 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 <= 2.8d-9))) then
        tmp = 1.0d0 + (x / y)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 2.8e-9)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 2.8e-9):
		tmp = 1.0 + (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 2.8e-9))
		tmp = Float64(1.0 + Float64(x / y));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 2.8e-9)))
		tmp = 1.0 + (x / y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 2.8e-9]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.79999999999999984e-9 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 96.4%

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

      1. +-commutative 96.4%

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

      2. associate--l+ 96.4%

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

      3. +-commutative 96.4%

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

      4. associate--r- 96.4%

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

      5. div-sub 96.4%

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

   4. Simplified 96.4%

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

   5. Taylor expanded in x around inf 95.8%

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

      1. mul-1-neg 95.8%

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

      2. distribute-neg-frac 95.8%

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

   7. Simplified 95.8%

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

   8. Taylor expanded in x around 0 95.8%

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

      1. +-commutative 95.8%

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

   10. Simplified 95.8%

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

   if -1 < y < 2.79999999999999984e-9

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 81.5%

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

4. Final simplification 88.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 2.8 \cdot 10^{-9}\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 7: 86.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -240 \lor \neg \left(y \leq 38000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -240.0) (not (<= y 38000.0))) (+ 1.0 (/ x y)) (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -240.0) || !(y <= 38000.0)) {
		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 <= (-240.0d0)) .or. (.not. (y <= 38000.0d0))) 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 <= -240.0) || !(y <= 38000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -240.0) or not (y <= 38000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -240.0) || !(y <= 38000.0))
		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 <= -240.0) || ~((y <= 38000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -240.0], N[Not[LessEqual[y, 38000.0]], $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 < -240 or 38000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 98.9%

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

      1. +-commutative 98.9%

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

      2. associate--l+ 98.9%

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

      3. +-commutative 98.9%

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

      4. associate--r- 98.9%

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

      5. div-sub 98.9%

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

   4. Simplified 98.9%

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

   5. Taylor expanded in x around inf 98.2%

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

      1. mul-1-neg 98.2%

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

      2. distribute-neg-frac 98.2%

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

   7. Simplified 98.2%

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

   8. Taylor expanded in x around 0 98.2%

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

      1. +-commutative 98.2%

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

   10. Simplified 98.2%

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

   if -240 < y < 38000

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 81.2%

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

      1. +-commutative 81.2%

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

   4. Simplified 81.2%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -240 \lor \neg \left(y \leq 38000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 8: 73.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 7800.0) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 7800.0) {
		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 <= 7800.0d0) 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 <= 7800.0) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 7800.0:
		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 <= 7800.0)
		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 <= 7800.0)
		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, 7800.0], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 7800 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 68.5%

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

   if -1 < y < 7800

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 79.2%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 7800:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 9: 39.3% accurate, 7.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0
end function

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in y around inf 36.2%

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

3. Final simplification 36.2%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))