Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.4s

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. *-commutative 100.0%

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

   3. +-commutative 100.0%

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

   4. distribute-rgt-in 100.0%

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

   5. associate-+l+ 100.0%

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

   6. +-commutative 100.0%

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

   7. *-lft-identity 100.0%

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

   8. neg-mul-1 100.0%

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

   9. *-commutative 100.0%

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

   10. distribute-lft-out 100.0%

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

   11. fma-def 100.0%

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

   12. +-commutative 100.0%

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

   13. *-lft-identity 100.0%

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

   14. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(x, -1 + y, y\right) \]

Alternative 2: 75.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -480000000000 \lor \neg \left(x \leq 280000000000\right) \land x \leq 2.8 \cdot 10^{+218}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -480000000000.0)
         (and (not (<= x 280000000000.0)) (<= x 2.8e+218)))
   (* x y)
   (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -480000000000.0) || (!(x <= 280000000000.0) && (x <= 2.8e+218))) {
		tmp = x * y;
	} 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 <= (-480000000000.0d0)) .or. (.not. (x <= 280000000000.0d0)) .and. (x <= 2.8d+218)) then
        tmp = x * y
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -480000000000.0) || (!(x <= 280000000000.0) && (x <= 2.8e+218))) {
		tmp = x * y;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -480000000000.0) or (not (x <= 280000000000.0) and (x <= 2.8e+218)):
		tmp = x * y
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -480000000000.0) || (!(x <= 280000000000.0) && (x <= 2.8e+218)))
		tmp = Float64(x * y);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -480000000000.0) || (~((x <= 280000000000.0)) && (x <= 2.8e+218)))
		tmp = x * y;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -480000000000.0], And[N[Not[LessEqual[x, 280000000000.0]], $MachinePrecision], LessEqual[x, 2.8e+218]]], N[(x * y), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.8e11 or 2.8e11 < x < 2.7999999999999998e218

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.7%

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

      1. *-commutative 99.7%

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

   4. Simplified 99.7%

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

   5. Taylor expanded in y around inf 61.9%

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

   if -4.8e11 < x < 2.8e11 or 2.7999999999999998e218 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 93.1%

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

4. Final simplification 80.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -480000000000 \lor \neg \left(x \leq 280000000000\right) \land x \leq 2.8 \cdot 10^{+218}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 3: 98.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.2 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 4.2e-11))) (- (* x y) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 4.2e-11)) {
		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 <= (-1.0d0)) .or. (.not. (x <= 4.2d-11))) 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 <= -1.0) || !(x <= 4.2e-11)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 4.2e-11):
		tmp = (x * y) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 4.2e-11))
		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 <= -1.0) || ~((x <= 4.2e-11)))
		tmp = (x * y) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 4.2e-11]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 4.1999999999999997e-11 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 99.3%

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

      1. *-commutative 99.3%

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

   4. Simplified 99.3%

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

   if -1 < x < 4.1999999999999997e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 4.2 \cdot 10^{-11}\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]

Alternative 4: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9.0) (not (<= y 1.0))) (* x y) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9.0) || !(y <= 1.0)) {
		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 ((y <= (-9.0d0)) .or. (.not. (y <= 1.0d0))) 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 ((y <= -9.0) || !(y <= 1.0)) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -9.0) or not (y <= 1.0):
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -9.0) || !(y <= 1.0))
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -9.0) || ~((y <= 1.0)))
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -9.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x * y), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -9 or 1 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 53.5%

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

      1. *-commutative 53.5%

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

   4. Simplified 53.5%

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

   5. Taylor expanded in y around inf 52.8%

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

   if -9 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 68.7%

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

      1. *-commutative 68.7%

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

   4. Simplified 68.7%

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

   5. Taylor expanded in y around 0 67.3%

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

      1. mul-1-neg 67.3%

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

   7. Simplified 67.3%

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

4. Final simplification 59.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \lor \neg \left(y \leq 1\right):\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

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: 38.3% 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 60.7%

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

   1. *-commutative 60.7%

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

4. Simplified 60.7%

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

5. Taylor expanded in y around 0 33.0%

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

   1. mul-1-neg 33.0%

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

7. Simplified 33.0%

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

8. Final simplification 33.0%

   \[\leadsto -x \]

Reproduce

herbie shell --seed 2023301 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))