Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 72.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 5.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.75:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4e+53)
   1.0
   (if (<= y -7.4e+15)
     (/ x y)
     (if (<= y 5.8e-44)
       x
       (if (<= y 0.75) (* y (- 1.0 y)) (if (<= y 6.4e+83) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4e+53) {
		tmp = 1.0;
	} else if (y <= -7.4e+15) {
		tmp = x / y;
	} else if (y <= 5.8e-44) {
		tmp = x;
	} else if (y <= 0.75) {
		tmp = y * (1.0 - y);
	} else if (y <= 6.4e+83) {
		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 <= (-4d+53)) then
        tmp = 1.0d0
    else if (y <= (-7.4d+15)) then
        tmp = x / y
    else if (y <= 5.8d-44) then
        tmp = x
    else if (y <= 0.75d0) then
        tmp = y * (1.0d0 - y)
    else if (y <= 6.4d+83) 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 <= -4e+53) {
		tmp = 1.0;
	} else if (y <= -7.4e+15) {
		tmp = x / y;
	} else if (y <= 5.8e-44) {
		tmp = x;
	} else if (y <= 0.75) {
		tmp = y * (1.0 - y);
	} else if (y <= 6.4e+83) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4e+53:
		tmp = 1.0
	elif y <= -7.4e+15:
		tmp = x / y
	elif y <= 5.8e-44:
		tmp = x
	elif y <= 0.75:
		tmp = y * (1.0 - y)
	elif y <= 6.4e+83:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4e+53)
		tmp = 1.0;
	elseif (y <= -7.4e+15)
		tmp = Float64(x / y);
	elseif (y <= 5.8e-44)
		tmp = x;
	elseif (y <= 0.75)
		tmp = Float64(y * Float64(1.0 - y));
	elseif (y <= 6.4e+83)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4e+53)
		tmp = 1.0;
	elseif (y <= -7.4e+15)
		tmp = x / y;
	elseif (y <= 5.8e-44)
		tmp = x;
	elseif (y <= 0.75)
		tmp = y * (1.0 - y);
	elseif (y <= 6.4e+83)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4e+53], 1.0, If[LessEqual[y, -7.4e+15], N[(x / y), $MachinePrecision], If[LessEqual[y, 5.8e-44], x, If[LessEqual[y, 0.75], N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 6.4e+83], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -4e53 or 6.3999999999999998e83 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

   if -4e53 < y < -7.4e15 or 0.75 < y < 6.3999999999999998e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.3%

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

      1. +-commutative 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf 77.2%

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

   if -7.4e15 < y < 5.8000000000000003e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.4%

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

   if 5.8000000000000003e-44 < y < 0.75

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. +-commutative 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in y around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. sub-neg 86.0%

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

   8. Simplified 86.0%

      \[\leadsto \color{blue}{y \cdot \left(1 - y\right)} \]
3. Recombined 4 regimes into one program.
4. Add Preprocessing

Alternative 3: 72.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{+15}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{elif}\;y \leq 1.28 \cdot 10^{-43}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.46:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e+53)
   1.0
   (if (<= y -7.4e+15)
     (/ x y)
     (if (<= y 1.28e-43)
       x
       (if (<= y 0.46) y (if (<= y 6.4e+83) (/ x y) 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+53) {
		tmp = 1.0;
	} else if (y <= -7.4e+15) {
		tmp = x / y;
	} else if (y <= 1.28e-43) {
		tmp = x;
	} else if (y <= 0.46) {
		tmp = y;
	} else if (y <= 6.4e+83) {
		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 <= (-3.5d+53)) then
        tmp = 1.0d0
    else if (y <= (-7.4d+15)) then
        tmp = x / y
    else if (y <= 1.28d-43) then
        tmp = x
    else if (y <= 0.46d0) then
        tmp = y
    else if (y <= 6.4d+83) 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 <= -3.5e+53) {
		tmp = 1.0;
	} else if (y <= -7.4e+15) {
		tmp = x / y;
	} else if (y <= 1.28e-43) {
		tmp = x;
	} else if (y <= 0.46) {
		tmp = y;
	} else if (y <= 6.4e+83) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e+53:
		tmp = 1.0
	elif y <= -7.4e+15:
		tmp = x / y
	elif y <= 1.28e-43:
		tmp = x
	elif y <= 0.46:
		tmp = y
	elif y <= 6.4e+83:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e+53)
		tmp = 1.0;
	elseif (y <= -7.4e+15)
		tmp = Float64(x / y);
	elseif (y <= 1.28e-43)
		tmp = x;
	elseif (y <= 0.46)
		tmp = y;
	elseif (y <= 6.4e+83)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.5e+53)
		tmp = 1.0;
	elseif (y <= -7.4e+15)
		tmp = x / y;
	elseif (y <= 1.28e-43)
		tmp = x;
	elseif (y <= 0.46)
		tmp = y;
	elseif (y <= 6.4e+83)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e+53], 1.0, If[LessEqual[y, -7.4e+15], N[(x / y), $MachinePrecision], If[LessEqual[y, 1.28e-43], x, If[LessEqual[y, 0.46], y, If[LessEqual[y, 6.4e+83], N[(x / y), $MachinePrecision], 1.0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -3.50000000000000019e53 or 6.3999999999999998e83 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

   if -3.50000000000000019e53 < y < -7.4e15 or 0.46000000000000002 < y < 6.3999999999999998e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 79.3%

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

      1. +-commutative 79.3%

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

   5. Simplified 79.3%

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

   6. Taylor expanded in y around inf 77.2%

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

   if -7.4e15 < y < 1.27999999999999998e-43

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 72.4%

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

   if 1.27999999999999998e-43 < y < 0.46000000000000002

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. +-commutative 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in y around 0 82.4%

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

Alternative 4: 87.3% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -7600:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-44}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq 0.95:\\ \;\;\;\;y \cdot \left(1 - y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ (+ x -1.0) y))))
   (if (<= y -7600.0)
     t_0
     (if (<= y 1.95e-44)
       (/ x (+ y 1.0))
       (if (<= y 0.95) (* y (- 1.0 y)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + ((x + -1.0) / y);
	double tmp;
	if (y <= -7600.0) {
		tmp = t_0;
	} else if (y <= 1.95e-44) {
		tmp = x / (y + 1.0);
	} else if (y <= 0.95) {
		tmp = y * (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 + (-1.0d0)) / y)
    if (y <= (-7600.0d0)) then
        tmp = t_0
    else if (y <= 1.95d-44) then
        tmp = x / (y + 1.0d0)
    else if (y <= 0.95d0) then
        tmp = y * (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 + -1.0) / y);
	double tmp;
	if (y <= -7600.0) {
		tmp = t_0;
	} else if (y <= 1.95e-44) {
		tmp = x / (y + 1.0);
	} else if (y <= 0.95) {
		tmp = y * (1.0 - y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + ((x + -1.0) / y)
	tmp = 0
	if y <= -7600.0:
		tmp = t_0
	elif y <= 1.95e-44:
		tmp = x / (y + 1.0)
	elif y <= 0.95:
		tmp = y * (1.0 - y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(Float64(x + -1.0) / y))
	tmp = 0.0
	if (y <= -7600.0)
		tmp = t_0;
	elseif (y <= 1.95e-44)
		tmp = Float64(x / Float64(y + 1.0));
	elseif (y <= 0.95)
		tmp = Float64(y * Float64(1.0 - y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + ((x + -1.0) / y);
	tmp = 0.0;
	if (y <= -7600.0)
		tmp = t_0;
	elseif (y <= 1.95e-44)
		tmp = x / (y + 1.0);
	elseif (y <= 0.95)
		tmp = y * (1.0 - y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7600.0], t$95$0, If[LessEqual[y, 1.95e-44], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.95], N[(y * N[(1.0 - y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7600 or 0.94999999999999996 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. div-sub 99.6%

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

      3. sub-neg 99.6%

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

      4. metadata-eval 99.6%

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

   5. Simplified 99.6%

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

   if -7600 < y < 1.9500000000000001e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 74.5%

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

      1. +-commutative 74.5%

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

   5. Simplified 74.5%

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

   if 1.9500000000000001e-44 < y < 0.94999999999999996

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. +-commutative 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in y around 0 86.0%

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

      1. neg-mul-1 86.0%

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

      2. sub-neg 86.0%

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

   8. Simplified 86.0%

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

Alternative 5: 74.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-46}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 1.25e-46) x (if (<= y 1.0) y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.25e-46) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = 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 <= 1.25d-46) then
        tmp = x
    else if (y <= 1.0d0) then
        tmp = 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 <= 1.25e-46) {
		tmp = x;
	} else if (y <= 1.0) {
		tmp = y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1.25e-46:
		tmp = x
	elif y <= 1.0:
		tmp = y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = 1.0;
	elseif (y <= 1.25e-46)
		tmp = x;
	elseif (y <= 1.0)
		tmp = 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 <= 1.25e-46)
		tmp = x;
	elseif (y <= 1.0)
		tmp = y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], 1.0, If[LessEqual[y, 1.25e-46], x, If[LessEqual[y, 1.0], y, 1.0]]]

Derivation

1. Split input into 3 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 75.3%

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

   if -1 < y < 1.24999999999999998e-46

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 74.1%

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

   if 1.24999999999999998e-46 < y < 1

   1. Initial program 99.8%

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

   3. Taylor expanded in x around 0 85.8%

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

      1. +-commutative 85.8%

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

   5. Simplified 85.8%

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

   6. Taylor expanded in y around 0 82.4%

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

Alternative 6: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.5 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+83}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.5e+53) 1.0 (if (<= y 6.4e+83) (/ x (+ y 1.0)) (/ y (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+53) {
		tmp = 1.0;
	} else if (y <= 6.4e+83) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (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 <= (-3.5d+53)) then
        tmp = 1.0d0
    else if (y <= 6.4d+83) then
        tmp = x / (y + 1.0d0)
    else
        tmp = y / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -3.5e+53) {
		tmp = 1.0;
	} else if (y <= 6.4e+83) {
		tmp = x / (y + 1.0);
	} else {
		tmp = y / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.5e+53:
		tmp = 1.0
	elif y <= 6.4e+83:
		tmp = x / (y + 1.0)
	else:
		tmp = y / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.5e+53)
		tmp = 1.0;
	elseif (y <= 6.4e+83)
		tmp = Float64(x / Float64(y + 1.0));
	else
		tmp = Float64(y / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.5e+53)
		tmp = 1.0;
	elseif (y <= 6.4e+83)
		tmp = x / (y + 1.0);
	else
		tmp = y / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.5e+53], 1.0, If[LessEqual[y, 6.4e+83], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.50000000000000019e53

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.7%

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

   if -3.50000000000000019e53 < y < 6.3999999999999998e83

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.0%

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

      1. +-commutative 71.0%

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

   5. Simplified 71.0%

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

   if 6.3999999999999998e83 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 88.2%

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

      1. +-commutative 88.2%

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

   5. Simplified 88.2%

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

Alternative 7: 73.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.8 \cdot 10^{+53}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+85}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.8e+53) 1.0 (if (<= y 1.65e+85) (/ x (+ y 1.0)) 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.8e+53) {
		tmp = 1.0;
	} else if (y <= 1.65e+85) {
		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 <= (-3.8d+53)) then
        tmp = 1.0d0
    else if (y <= 1.65d+85) 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 <= -3.8e+53) {
		tmp = 1.0;
	} else if (y <= 1.65e+85) {
		tmp = x / (y + 1.0);
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.8e+53:
		tmp = 1.0
	elif y <= 1.65e+85:
		tmp = x / (y + 1.0)
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.8e+53)
		tmp = 1.0;
	elseif (y <= 1.65e+85)
		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 <= -3.8e+53)
		tmp = 1.0;
	elseif (y <= 1.65e+85)
		tmp = x / (y + 1.0);
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.8e+53], 1.0, If[LessEqual[y, 1.65e+85], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -3.79999999999999997e53 or 1.65e85 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 89.1%

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

   if -3.79999999999999997e53 < y < 1.65e85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 71.0%

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

      1. +-commutative 71.0%

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

   5. Simplified 71.0%

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

Alternative 8: 72.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-39}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 1.35e-39) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 1.35e-39) {
		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 <= 1.35d-39) 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 <= 1.35e-39) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 1.35e-39:
		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 <= 1.35e-39)
		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 <= 1.35e-39)
		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, 1.35e-39], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.35e-39 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.9%

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

   if -1 < y < 1.35e-39

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.2%

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

Alternative 9: 38.9% 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 40.6%

   \[\leadsto \color{blue}{1} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024170 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))