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. Add Preprocessing
3. Add Preprocessing

Alternative 2: 85.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -2000000:\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 2.75 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 280000:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\frac{x + y}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y 1.0))))
   (if (<= y -2000000.0)
     (+ 1.0 (/ x y))
     (if (<= y -5.8e-98)
       t_0
       (if (<= y 2.75e-19) x (if (<= y 280000.0) t_0 (/ (+ x y) y)))))))

C

double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -2000000.0) {
		tmp = 1.0 + (x / y);
	} else if (y <= -5.8e-98) {
		tmp = t_0;
	} else if (y <= 2.75e-19) {
		tmp = x;
	} else if (y <= 280000.0) {
		tmp = t_0;
	} else {
		tmp = (x + y) / y;
	}
	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 = y / (y + 1.0d0)
    if (y <= (-2000000.0d0)) then
        tmp = 1.0d0 + (x / y)
    else if (y <= (-5.8d-98)) then
        tmp = t_0
    else if (y <= 2.75d-19) then
        tmp = x
    else if (y <= 280000.0d0) then
        tmp = t_0
    else
        tmp = (x + y) / y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -2000000.0) {
		tmp = 1.0 + (x / y);
	} else if (y <= -5.8e-98) {
		tmp = t_0;
	} else if (y <= 2.75e-19) {
		tmp = x;
	} else if (y <= 280000.0) {
		tmp = t_0;
	} else {
		tmp = (x + y) / y;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + 1.0)
	tmp = 0
	if y <= -2000000.0:
		tmp = 1.0 + (x / y)
	elif y <= -5.8e-98:
		tmp = t_0
	elif y <= 2.75e-19:
		tmp = x
	elif y <= 280000.0:
		tmp = t_0
	else:
		tmp = (x + y) / y
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -2000000.0)
		tmp = Float64(1.0 + Float64(x / y));
	elseif (y <= -5.8e-98)
		tmp = t_0;
	elseif (y <= 2.75e-19)
		tmp = x;
	elseif (y <= 280000.0)
		tmp = t_0;
	else
		tmp = Float64(Float64(x + y) / y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + 1.0);
	tmp = 0.0;
	if (y <= -2000000.0)
		tmp = 1.0 + (x / y);
	elseif (y <= -5.8e-98)
		tmp = t_0;
	elseif (y <= 2.75e-19)
		tmp = x;
	elseif (y <= 280000.0)
		tmp = t_0;
	else
		tmp = (x + y) / y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -2000000.0], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -5.8e-98], t$95$0, If[LessEqual[y, 2.75e-19], x, If[LessEqual[y, 280000.0], t$95$0, N[(N[(x + y), $MachinePrecision] / y), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -2e6

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.9%

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

      1. associate--l+ 98.9%

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

      2. div-sub 98.9%

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

      3. sub-neg 98.9%

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

      4. metadata-eval 98.9%

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

   5. Simplified 98.9%

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

   6. Taylor expanded in x around inf 98.9%

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

   if -2e6 < y < -5.8e-98 or 2.7499999999999998e-19 < y < 2.8e5

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.9%

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

      1. +-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -5.8e-98 < y < 2.7499999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

   if 2.8e5 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 98.6%

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

      1. associate--l+ 98.6%

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

      2. div-sub 98.6%

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

      3. sub-neg 98.6%

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

      4. metadata-eval 98.6%

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

   5. Simplified 98.6%

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

   6. Taylor expanded in x around inf 98.6%

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

   7. Taylor expanded in y around 0 98.6%

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

Alternative 3: 85.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ t_1 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -12200000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-22}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 63000:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))) (t_1 (/ y (+ y 1.0))))
   (if (<= y -12200000.0)
     t_0
     (if (<= y -5.8e-98)
       t_1
       (if (<= y 1.2e-22) x (if (<= y 63000.0) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double t_1 = y / (y + 1.0);
	double tmp;
	if (y <= -12200000.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = t_1;
	} else if (y <= 1.2e-22) {
		tmp = x;
	} else if (y <= 63000.0) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 1.0d0 + (x / y)
    t_1 = y / (y + 1.0d0)
    if (y <= (-12200000.0d0)) then
        tmp = t_0
    else if (y <= (-5.8d-98)) then
        tmp = t_1
    else if (y <= 1.2d-22) then
        tmp = x
    else if (y <= 63000.0d0) then
        tmp = t_1
    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 t_1 = y / (y + 1.0);
	double tmp;
	if (y <= -12200000.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = t_1;
	} else if (y <= 1.2e-22) {
		tmp = x;
	} else if (y <= 63000.0) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	t_1 = y / (y + 1.0)
	tmp = 0
	if y <= -12200000.0:
		tmp = t_0
	elif y <= -5.8e-98:
		tmp = t_1
	elif y <= 1.2e-22:
		tmp = x
	elif y <= 63000.0:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	t_1 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -12200000.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = t_1;
	elseif (y <= 1.2e-22)
		tmp = x;
	elseif (y <= 63000.0)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 1.0 + (x / y);
	t_1 = y / (y + 1.0);
	tmp = 0.0;
	if (y <= -12200000.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = t_1;
	elseif (y <= 1.2e-22)
		tmp = x;
	elseif (y <= 63000.0)
		tmp = t_1;
	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]}, Block[{t$95$1 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -12200000.0], t$95$0, If[LessEqual[y, -5.8e-98], t$95$1, If[LessEqual[y, 1.2e-22], x, If[LessEqual[y, 63000.0], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.22e7 or 63000 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 98.7%

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

      1. associate--l+ 98.7%

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

      2. div-sub 98.7%

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

      3. sub-neg 98.7%

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

      4. metadata-eval 98.7%

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

   5. Simplified 98.7%

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

   6. Taylor expanded in x around inf 98.7%

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

   if -1.22e7 < y < -5.8e-98 or 1.20000000000000001e-22 < y < 63000

   1. Initial program 99.9%

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

   3. Taylor expanded in x around 0 74.9%

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

      1. +-commutative 74.9%

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

   5. Simplified 74.9%

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

   if -5.8e-98 < y < 1.20000000000000001e-22

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

Alternative 4: 70.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0005:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.35 \cdot 10^{-17}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{+151}:\\ \;\;\;\;\frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0005)
   1.0
   (if (<= y -5.8e-98)
     y
     (if (<= y 1.35e-17) x (if (<= y 2.7e+151) (/ x y) 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0005) {
		tmp = 1.0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 1.35e-17) {
		tmp = x;
	} else if (y <= 2.7e+151) {
		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 <= (-0.0005d0)) then
        tmp = 1.0d0
    else if (y <= (-5.8d-98)) then
        tmp = y
    else if (y <= 1.35d-17) then
        tmp = x
    else if (y <= 2.7d+151) 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 <= -0.0005) {
		tmp = 1.0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 1.35e-17) {
		tmp = x;
	} else if (y <= 2.7e+151) {
		tmp = x / y;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0005:
		tmp = 1.0
	elif y <= -5.8e-98:
		tmp = y
	elif y <= 1.35e-17:
		tmp = x
	elif y <= 2.7e+151:
		tmp = x / y
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0005)
		tmp = 1.0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 1.35e-17)
		tmp = x;
	elseif (y <= 2.7e+151)
		tmp = Float64(x / y);
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0005)
		tmp = 1.0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 1.35e-17)
		tmp = x;
	elseif (y <= 2.7e+151)
		tmp = x / y;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0005], 1.0, If[LessEqual[y, -5.8e-98], y, If[LessEqual[y, 1.35e-17], x, If[LessEqual[y, 2.7e+151], N[(x / y), $MachinePrecision], 1.0]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.0000000000000001e-4 or 2.7000000000000001e151 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 70.1%

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

   if -5.0000000000000001e-4 < y < -5.8e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 69.3%

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

      1. +-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0 69.3%

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

   if -5.8e-98 < y < 1.3500000000000001e-17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 79.8%

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

   if 1.3500000000000001e-17 < y < 2.7000000000000001e151

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 52.4%

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

      1. +-commutative 52.4%

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

   5. Simplified 52.4%

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

   6. Taylor expanded in y around inf 49.9%

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

Alternative 5: 85.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 11000000000:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -5.8e-98) y (if (<= y 11000000000.0) (/ x (+ y 1.0)) t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 11000000000.0) {
		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 <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-5.8d-98)) then
        tmp = y
    else if (y <= 11000000000.0d0) 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 <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 11000000000.0) {
		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 <= -1.0:
		tmp = t_0
	elif y <= -5.8e-98:
		tmp = y
	elif y <= 11000000000.0:
		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 <= -1.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 11000000000.0)
		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 <= -1.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 11000000000.0)
		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, -1.0], t$95$0, If[LessEqual[y, -5.8e-98], y, If[LessEqual[y, 11000000000.0], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.1e10 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.3%

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

      1. associate--l+ 99.3%

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

      2. div-sub 99.3%

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

      3. sub-neg 99.3%

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

      4. metadata-eval 99.3%

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

   5. Simplified 99.3%

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

   6. Taylor expanded in x around inf 99.0%

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

   if -1 < y < -5.8e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 65.7%

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

      1. +-commutative 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around 0 65.7%

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

   if -5.8e-98 < y < 1.1e10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 77.2%

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

      1. +-commutative 77.2%

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

   5. Simplified 77.2%

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

Alternative 6: 84.9% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 1 + \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ 1.0 (/ x y))))
   (if (<= y -1.0) t_0 (if (<= y -5.8e-98) y (if (<= y 6.2e-19) x t_0)))))

C

double code(double x, double y) {
	double t_0 = 1.0 + (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 6.2e-19) {
		tmp = x;
	} 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 <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-5.8d-98)) then
        tmp = y
    else if (y <= 6.2d-19) then
        tmp = x
    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 <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 6.2e-19) {
		tmp = x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 1.0 + (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -5.8e-98:
		tmp = y
	elif y <= 6.2e-19:
		tmp = x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(1.0 + Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 6.2e-19)
		tmp = x;
	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 <= -1.0)
		tmp = t_0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 6.2e-19)
		tmp = x;
	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, -1.0], t$95$0, If[LessEqual[y, -5.8e-98], y, If[LessEqual[y, 6.2e-19], x, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 6.1999999999999998e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 93.8%

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

      1. associate--l+ 93.8%

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

      2. div-sub 93.8%

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

      3. sub-neg 93.8%

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

      4. metadata-eval 93.8%

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

   5. Simplified 93.8%

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

   6. Taylor expanded in x around inf 93.8%

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

   if -1 < y < -5.8e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 65.7%

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

      1. +-commutative 65.7%

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

   5. Simplified 65.7%

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

   6. Taylor expanded in y around 0 65.7%

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

   if -5.8e-98 < y < 6.1999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

Alternative 7: 72.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.0005:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -5.8 \cdot 10^{-98}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -0.0005) 1.0 (if (<= y -5.8e-98) y (if (<= y 6.2e-19) x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -0.0005) {
		tmp = 1.0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 6.2e-19) {
		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 <= (-0.0005d0)) then
        tmp = 1.0d0
    else if (y <= (-5.8d-98)) then
        tmp = y
    else if (y <= 6.2d-19) 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 <= -0.0005) {
		tmp = 1.0;
	} else if (y <= -5.8e-98) {
		tmp = y;
	} else if (y <= 6.2e-19) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -0.0005:
		tmp = 1.0
	elif y <= -5.8e-98:
		tmp = y
	elif y <= 6.2e-19:
		tmp = x
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -0.0005)
		tmp = 1.0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 6.2e-19)
		tmp = x;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -0.0005)
		tmp = 1.0;
	elseif (y <= -5.8e-98)
		tmp = y;
	elseif (y <= 6.2e-19)
		tmp = x;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -0.0005], 1.0, If[LessEqual[y, -5.8e-98], y, If[LessEqual[y, 6.2e-19], x, 1.0]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000001e-4 or 6.1999999999999998e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.4%

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

   if -5.0000000000000001e-4 < y < -5.8e-98

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 69.3%

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

      1. +-commutative 69.3%

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

   5. Simplified 69.3%

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

   6. Taylor expanded in y around 0 69.3%

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

   if -5.8e-98 < y < 6.1999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 80.4%

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

Alternative 8: 73.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-19}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) 1.0 (if (<= y 6.2e-19) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 6.2e-19) {
		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-19) 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-19) {
		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-19:
		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-19)
		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-19)
		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-19], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 6.1999999999999998e-19 < y

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 60.9%

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

   if -1 < y < 6.1999999999999998e-19

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 73.8%

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

Alternative 9: 38.8% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 100.0%

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

3. Taylor expanded in y around inf 29.2%

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

Reproduce

herbie shell --seed 2024152 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))