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. Final simplification 100.0%

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

Alternative 2: 87.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -34 \lor \neg \left(y \leq 17000\right):\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -34.0) (not (<= y 17000.0)))
   (- 1.0 (/ (- 1.0 x) y))
   (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -34.0) || !(y <= 17000.0)) {
		tmp = 1.0 - ((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 <= (-34.0d0)) .or. (.not. (y <= 17000.0d0))) then
        tmp = 1.0d0 - ((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 <= -34.0) || !(y <= 17000.0)) {
		tmp = 1.0 - ((1.0 - x) / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -34.0) or not (y <= 17000.0):
		tmp = 1.0 - ((1.0 - x) / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -34.0) || !(y <= 17000.0))
		tmp = Float64(1.0 - Float64(Float64(1.0 - 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 <= -34.0) || ~((y <= 17000.0)))
		tmp = 1.0 - ((1.0 - x) / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -34.0], N[Not[LessEqual[y, 17000.0]], $MachinePrecision]], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -34 or 17000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   4. Simplified 99.2%

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

   if -34 < y < 17000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 73.7%

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

      1. +-commutative 73.7%

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

   4. Simplified 73.7%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -34 \lor \neg \left(y \leq 17000\right):\\ \;\;\;\;1 - \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 3: 86.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.018\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.018))) (+ 1.0 (/ x y)) x))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.018)) {
		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 <= 0.018d0))) 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 <= 0.018)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.018):
		tmp = 1.0 + (x / y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.018))
		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 <= 0.018)))
		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, 0.018]], $MachinePrecision]], N[(1.0 + N[(x / y), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.0179999999999999986 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. neg-mul-1 97.8%

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

      2. distribute-neg-frac 97.8%

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

   7. Simplified 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-frac-neg 97.8%

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

      3. remove-double-neg 97.8%

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

      4. +-commutative 97.8%

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

   9. Applied egg-rr 97.8%

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

   if -1 < y < 0.0179999999999999986

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.0%

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

4. Final simplification 84.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.018\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 4: 86.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 29000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -90.0) (not (<= y 29000.0))) (+ 1.0 (/ x y)) (/ x (+ y 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -90.0) || !(y <= 29000.0)) {
		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 <= (-90.0d0)) .or. (.not. (y <= 29000.0d0))) 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 <= -90.0) || !(y <= 29000.0)) {
		tmp = 1.0 + (x / y);
	} else {
		tmp = x / (y + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -90.0) or not (y <= 29000.0):
		tmp = 1.0 + (x / y)
	else:
		tmp = x / (y + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -90.0) || !(y <= 29000.0))
		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 <= -90.0) || ~((y <= 29000.0)))
		tmp = 1.0 + (x / y);
	else
		tmp = x / (y + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -90.0], N[Not[LessEqual[y, 29000.0]], $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 < -90 or 29000 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around -inf 99.2%

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

      1. mul-1-neg 99.2%

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

      2. unsub-neg 99.2%

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

      3. mul-1-neg 99.2%

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

      4. sub-neg 99.2%

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

   4. Simplified 99.2%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. neg-mul-1 97.8%

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

      2. distribute-neg-frac 97.8%

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

   7. Simplified 97.8%

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

      1. sub-neg 97.8%

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

      2. distribute-frac-neg 97.8%

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

      3. remove-double-neg 97.8%

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

      4. +-commutative 97.8%

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

   9. Applied egg-rr 97.8%

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

   if -90 < y < 29000

   1. Initial program 99.9%

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

   2. Taylor expanded in x around inf 73.7%

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

      1. +-commutative 73.7%

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

   4. Simplified 73.7%

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

4. Final simplification 85.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -90 \lor \neg \left(y \leq 29000\right):\\ \;\;\;\;1 + \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y + 1}\\ \end{array} \]

Alternative 5: 74.0% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.155:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) 1.0 (if (<= y 0.155) x 1.0)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = 1.0;
	} else if (y <= 0.155) {
		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 <= 0.155d0) 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 <= 0.155) {
		tmp = x;
	} else {
		tmp = 1.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = 1.0
	elif y <= 0.155:
		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 <= 0.155)
		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 <= 0.155)
		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, 0.155], x, 1.0]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.154999999999999999 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 80.2%

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

   if -1 < y < 0.154999999999999999

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 71.0%

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

4. Final simplification 75.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 0.155:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array} \]

Alternative 6: 37.9% 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. Taylor expanded in y around inf 40.7%

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

3. Final simplification 40.7%

   \[\leadsto 1 \]

Reproduce

herbie shell --seed 2023238 
(FPCore (x y)
  :name "Data.Colour.SRGB:invTransferFunction from colour-2.3.3"
  :precision binary64
  (/ (+ x y) (+ y 1.0)))