Data.Colour.SRGB:invTransferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.1s

Alternatives: 6

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

3. Final simplification 100.0%

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

Alternative 2: 71.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ \mathbf{if}\;y \leq -95:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-33}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+112}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))))
   (if (<= y -95.0)
     1.0
     (if (<= y -7.4e-33)
       t_0
       (if (<= y -1.15e-125) (* x (/ y x)) (if (<= y 1.65e+112) t_0 1.0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -95.0) {
		tmp = 1.0;
	} else if (y <= -7.4e-33) {
		tmp = t_0;
	} else if (y <= -1.15e-125) {
		tmp = x * (y / x);
	} else if (y <= 1.65e+112) {
		tmp = t_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) :: t_0
    real(8) :: tmp
    t_0 = x / (y + 1.0d0)
    if (y <= (-95.0d0)) then
        tmp = 1.0d0
    else if (y <= (-7.4d-33)) then
        tmp = t_0
    else if (y <= (-1.15d-125)) then
        tmp = x * (y / x)
    else if (y <= 1.65d+112) then
        tmp = t_0
    else
        tmp = 1.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double tmp;
	if (y <= -95.0) {
		tmp = 1.0;
	} else if (y <= -7.4e-33) {
		tmp = t_0;
	} else if (y <= -1.15e-125) {
		tmp = x * (y / x);
	} else if (y <= 1.65e+112) {
		tmp = t_0;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	tmp = 0
	if y <= -95.0:
		tmp = 1.0
	elif y <= -7.4e-33:
		tmp = t_0
	elif y <= -1.15e-125:
		tmp = x * (y / x)
	elif y <= 1.65e+112:
		tmp = t_0
	else:
		tmp = 1.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -95.0)
		tmp = 1.0;
	elseif (y <= -7.4e-33)
		tmp = t_0;
	elseif (y <= -1.15e-125)
		tmp = Float64(x * Float64(y / x));
	elseif (y <= 1.65e+112)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	tmp = 0.0;
	if (y <= -95.0)
		tmp = 1.0;
	elseif (y <= -7.4e-33)
		tmp = t_0;
	elseif (y <= -1.15e-125)
		tmp = x * (y / x);
	elseif (y <= 1.65e+112)
		tmp = t_0;
	else
		tmp = 1.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -95.0], 1.0, If[LessEqual[y, -7.4e-33], t$95$0, If[LessEqual[y, -1.15e-125], N[(x * N[(y / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.65e+112], t$95$0, 1.0]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -95 or 1.64999999999999995e112 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 72.8%

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

   if -95 < y < -7.40000000000000028e-33 or -1.15e-125 < y < 1.64999999999999995e112

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 81.4%

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

      1. +-commutative 81.4%

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

   5. Simplified 81.4%

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

   if -7.40000000000000028e-33 < y < -1.15e-125

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in x around 0 64.5%

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

      1. associate-/r* 64.5%

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

      2. +-commutative 64.5%

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

   6. Simplified 64.5%

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

   7. Taylor expanded in y around 0 64.5%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -95:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq -7.4 \cdot 10^{-33}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;y \leq -1.15 \cdot 10^{-125}:\\ \;\;\;\;x \cdot \frac{y}{x}\\ \mathbf{elif}\;y \leq 1.65 \cdot 10^{+112}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x}{y + 1}\\ t_1 := \frac{y}{y + 1}\\ \mathbf{if}\;x \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-107}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ x (+ y 1.0))) (t_1 (/ y (+ y 1.0))))
   (if (<= x -4.6e-9)
     t_0
     (if (<= x 6e-107)
       t_1
       (if (<= x 7.8e-44) x (if (<= x 6.2e+63) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = x / (y + 1.0);
	double t_1 = y / (y + 1.0);
	double tmp;
	if (x <= -4.6e-9) {
		tmp = t_0;
	} else if (x <= 6e-107) {
		tmp = t_1;
	} else if (x <= 7.8e-44) {
		tmp = x;
	} else if (x <= 6.2e+63) {
		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 = x / (y + 1.0d0)
    t_1 = y / (y + 1.0d0)
    if (x <= (-4.6d-9)) then
        tmp = t_0
    else if (x <= 6d-107) then
        tmp = t_1
    else if (x <= 7.8d-44) then
        tmp = x
    else if (x <= 6.2d+63) 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 = x / (y + 1.0);
	double t_1 = y / (y + 1.0);
	double tmp;
	if (x <= -4.6e-9) {
		tmp = t_0;
	} else if (x <= 6e-107) {
		tmp = t_1;
	} else if (x <= 7.8e-44) {
		tmp = x;
	} else if (x <= 6.2e+63) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x / (y + 1.0)
	t_1 = y / (y + 1.0)
	tmp = 0
	if x <= -4.6e-9:
		tmp = t_0
	elif x <= 6e-107:
		tmp = t_1
	elif x <= 7.8e-44:
		tmp = x
	elif x <= 6.2e+63:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x / Float64(y + 1.0))
	t_1 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (x <= -4.6e-9)
		tmp = t_0;
	elseif (x <= 6e-107)
		tmp = t_1;
	elseif (x <= 7.8e-44)
		tmp = x;
	elseif (x <= 6.2e+63)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x / (y + 1.0);
	t_1 = y / (y + 1.0);
	tmp = 0.0;
	if (x <= -4.6e-9)
		tmp = t_0;
	elseif (x <= 6e-107)
		tmp = t_1;
	elseif (x <= 7.8e-44)
		tmp = x;
	elseif (x <= 6.2e+63)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -4.6e-9], t$95$0, If[LessEqual[x, 6e-107], t$95$1, If[LessEqual[x, 7.8e-44], x, If[LessEqual[x, 6.2e+63], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -4.5999999999999998e-9 or 6.2000000000000001e63 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 82.6%

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

      1. +-commutative 82.6%

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

   5. Simplified 82.6%

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

   if -4.5999999999999998e-9 < x < 5.9999999999999994e-107 or 7.8000000000000004e-44 < x < 6.2000000000000001e63

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 79.1%

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

      1. +-commutative 79.1%

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

   5. Simplified 79.1%

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

   if 5.9999999999999994e-107 < x < 7.8000000000000004e-44

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 77.7%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-9}:\\ \;\;\;\;\frac{x}{y + 1}\\ \mathbf{elif}\;x \leq 6 \cdot 10^{-107}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{elif}\;x \leq 7.8 \cdot 10^{-44}:\\ \;\;\;\;x\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{+63}:\\ \;\;\;\;\frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 87.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -66 \lor \neg \left(y \leq 155000\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -66.0) (not (<= y 155000.0)))
   (+ 1.0 (/ (+ x -1.0) y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -66.0) || !(y <= 155000.0)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-66.0d0)) .or. (.not. (y <= 155000.0d0))) then
        tmp = 1.0d0 + ((x + (-1.0d0)) / y)
    else
        tmp = x / (y + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -66.0) || !(y <= 155000.0)) {
		tmp = 1.0 + ((x + -1.0) / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -66.0) or not (y <= 155000.0):
		tmp = 1.0 + ((x + -1.0) / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -66.0) || !(y <= 155000.0))
		tmp = Float64(1.0 + Float64(Float64(x + -1.0) / y));
	else
		tmp = Float64(x / Float64(y + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -66.0) || ~((y <= 155000.0)))
		tmp = 1.0 + ((x + -1.0) / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -66.0], N[Not[LessEqual[y, 155000.0]], $MachinePrecision]], N[(1.0 + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -66 or 155000 < y

   1. Initial program 100.0%

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

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

   if -66 < y < 155000

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 75.6%

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

      1. +-commutative 75.6%

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

   5. Simplified 75.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66 \lor \neg \left(y \leq 155000\right):\\ \;\;\;\;1 + \frac{x + -1}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.18:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 0.18) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.18) {
		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 <= 0.18d0) 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 <= 0.18) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.18:
		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 <= 0.18)
		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 <= 0.18)
		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, 0.18], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.17999999999999999 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 65.9%

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

   if -1 < y < 0.17999999999999999

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 75.2%

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

4. Final simplification 70.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.18:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 38.5% 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 34.7%

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

4. Final simplification 34.7%

   \[\leadsto 1 \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))