Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 1.9s

Alternatives: 6

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x + 1\right) \cdot y - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* (+ x 1.0) y) x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return ((x + 1.0) * y) - x

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 100.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, y - x\right) \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (fma x y (- y x)))

C

double code(double x, double y) {
	return fma(x, y, (y - x));
}

Julia

function code(x, y)
	return fma(x, y, Float64(y - x))
end

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. *-commutative 100.0%

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

   3. distribute-lft1-in 100.0%

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

   4. associate--l+ 100.0%

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

   5. fma-def 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, y - x\right)} \]

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, y - x\right)} \]

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, y, y - x\right) \]

Alternative 2: 99.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -23 \lor \neg \left(x \leq 5.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -23.0) (not (<= x 5.5e-8))) (- (* x y) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -23.0) || !(x <= 5.5e-8)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-23.0d0)) .or. (.not. (x <= 5.5d-8))) then
        tmp = (x * y) - x
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -23.0) || !(x <= 5.5e-8)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -23.0) or not (x <= 5.5e-8):
		tmp = (x * y) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -23.0) || !(x <= 5.5e-8))
		tmp = Float64(Float64(x * y) - x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -23.0) || ~((x <= 5.5e-8)))
		tmp = (x * y) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -23.0], N[Not[LessEqual[x, 5.5e-8]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -23 or 5.5000000000000003e-8 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 97.1%

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

      1. *-commutative 97.1%

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

   4. Simplified 97.1%

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

   if -23 < x < 5.5000000000000003e-8

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 99.0%

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

4. Final simplification 98.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -23 \lor \neg \left(x \leq 5.5 \cdot 10^{-8}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 3: 62.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (* x y) (if (<= y 3.3e-6) (- x) (* x y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 3.3e-6) {
		tmp = -x;
	} else {
		tmp = x * 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 <= (-1.0d0)) then
        tmp = x * y
    else if (y <= 3.3d-6) then
        tmp = -x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x * y;
	} else if (y <= 3.3e-6) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x * y
	elif y <= 3.3e-6:
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x * y);
	elseif (y <= 3.3e-6)
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x * y;
	elseif (y <= 3.3e-6)
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.3e-6], (-x), N[(x * y), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3.30000000000000017e-6 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 43.6%

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

      1. *-commutative 43.6%

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

   4. Simplified 43.6%

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

   5. Taylor expanded in y around inf 42.2%

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

   if -1 < y < 3.30000000000000017e-6

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 72.5%

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

      1. *-commutative 72.5%

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

   4. Simplified 72.5%

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

   5. Taylor expanded in y around 0 71.3%

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

      1. neg-mul-1 71.3%

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

   7. Simplified 71.3%

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

4. Final simplification 56.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]

Alternative 4: 74.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+263}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 7.2e+127) (- y x) (if (<= x 2.3e+263) (* x y) (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7.2e+127) {
		tmp = y - x;
	} else if (x <= 2.3e+263) {
		tmp = 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 (x <= 7.2d+127) then
        tmp = y - x
    else if (x <= 2.3d+263) then
        tmp = x * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 7.2e+127) {
		tmp = y - x;
	} else if (x <= 2.3e+263) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7.2e+127:
		tmp = y - x
	elif x <= 2.3e+263:
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7.2e+127)
		tmp = Float64(y - x);
	elseif (x <= 2.3e+263)
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 7.2e+127)
		tmp = y - x;
	elseif (x <= 2.3e+263)
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7.2e+127], N[(y - x), $MachinePrecision], If[LessEqual[x, 2.3e+263], N[(x * y), $MachinePrecision], (-x)]]

Derivation

1. Split input into 3 regimes

2. if x < 7.19999999999999958e127

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around 0 82.7%

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

   if 7.19999999999999958e127 < x < 2.29999999999999997e263

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around inf 75.7%

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

   if 2.29999999999999997e263 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

   4. Simplified 100.0%

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

   5. Taylor expanded in y around 0 100.0%

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

      1. neg-mul-1 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 82.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{+127}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{+263}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 5: 100.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ y \cdot \left(x + 1\right) - x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- (* y (+ x 1.0)) x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return (y * (x + 1.0)) - x

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Final simplification 100.0%

   \[\leadsto y \cdot \left(x + 1\right) - x \]

Alternative 6: 39.7% accurate, 3.5× speedup

Math

\[\begin{array}{l} \\ -x \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- x))

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return -x

Julia

function code(x, y)
	return Float64(-x)
end

MATLAB

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

Wolfram

code[x_, y_] := (-x)

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]

2. Taylor expanded in x around inf 57.4%

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

   1. *-commutative 57.4%

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

4. Simplified 57.4%

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

5. Taylor expanded in y around 0 35.4%

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

   1. neg-mul-1 35.4%

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

7. Simplified 35.4%

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

8. Final simplification 35.4%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023293 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))