Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.0s

Alternatives: 7

Speedup: 1.0×

• could not determine a ground truth

  1. x = -5.639766565159213e-266
  2. y = 5.697857327413027e-266

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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. fma-neg 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.1% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+214}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 30000000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -2.6e+214)
   (- x)
   (if (<= x -7.5e+67)
     (* x y)
     (if (<= x -3.4e-16)
       (- x)
       (if (<= x 3.6e-94) y (if (<= x 30000000000.0) (- x) (* x y)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -2.6e+214) {
		tmp = -x;
	} else if (x <= -7.5e+67) {
		tmp = x * y;
	} else if (x <= -3.4e-16) {
		tmp = -x;
	} else if (x <= 3.6e-94) {
		tmp = y;
	} else if (x <= 30000000000.0) {
		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 (x <= (-2.6d+214)) then
        tmp = -x
    else if (x <= (-7.5d+67)) then
        tmp = x * y
    else if (x <= (-3.4d-16)) then
        tmp = -x
    else if (x <= 3.6d-94) then
        tmp = y
    else if (x <= 30000000000.0d0) 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 (x <= -2.6e+214) {
		tmp = -x;
	} else if (x <= -7.5e+67) {
		tmp = x * y;
	} else if (x <= -3.4e-16) {
		tmp = -x;
	} else if (x <= 3.6e-94) {
		tmp = y;
	} else if (x <= 30000000000.0) {
		tmp = -x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -2.6e+214:
		tmp = -x
	elif x <= -7.5e+67:
		tmp = x * y
	elif x <= -3.4e-16:
		tmp = -x
	elif x <= 3.6e-94:
		tmp = y
	elif x <= 30000000000.0:
		tmp = -x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -2.6e+214)
		tmp = Float64(-x);
	elseif (x <= -7.5e+67)
		tmp = Float64(x * y);
	elseif (x <= -3.4e-16)
		tmp = Float64(-x);
	elseif (x <= 3.6e-94)
		tmp = y;
	elseif (x <= 30000000000.0)
		tmp = Float64(-x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -2.6e+214)
		tmp = -x;
	elseif (x <= -7.5e+67)
		tmp = x * y;
	elseif (x <= -3.4e-16)
		tmp = -x;
	elseif (x <= 3.6e-94)
		tmp = y;
	elseif (x <= 30000000000.0)
		tmp = -x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -2.6e+214], (-x), If[LessEqual[x, -7.5e+67], N[(x * y), $MachinePrecision], If[LessEqual[x, -3.4e-16], (-x), If[LessEqual[x, 3.6e-94], y, If[LessEqual[x, 30000000000.0], (-x), N[(x * y), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -2.59999999999999993e214 or -7.5000000000000005e67 < x < -3.4e-16 or 3.6e-94 < x < 3e10

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 78.8%

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

      1. neg-mul-1 78.8%

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

   5. Simplified 78.8%

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

   if -2.59999999999999993e214 < x < -7.5000000000000005e67 or 3e10 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 100.0%

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

   4. Taylor expanded in y around inf 59.9%

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

   if -3.4e-16 < x < 3.6e-94

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.6%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.6 \cdot 10^{+214}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq -7.5 \cdot 10^{+67}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;x \leq -3.4 \cdot 10^{-16}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{-94}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 30000000000:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-16} \lor \neg \left(x \leq 1.6 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -5e-16) (not (<= x 1.6e-94))) (* x (+ y -1.0)) y))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -5e-16) || !(x <= 1.6e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-5d-16)) .or. (.not. (x <= 1.6d-94))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -5e-16) || !(x <= 1.6e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -5e-16) or not (x <= 1.6e-94):
		tmp = x * (y + -1.0)
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -5e-16) || !(x <= 1.6e-94))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -5e-16) || ~((x <= 1.6e-94)))
		tmp = x * (y + -1.0);
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -5e-16], N[Not[LessEqual[x, 1.6e-94]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], y]

Derivation

1. Split input into 2 regimes

2. if x < -5.0000000000000004e-16 or 1.59999999999999998e-94 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 96.2%

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

   if -5.0000000000000004e-16 < x < 1.59999999999999998e-94

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 80.6%

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

4. Final simplification 89.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5 \cdot 10^{-16} \lor \neg \left(x \leq 1.6 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 86.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -620 \lor \neg \left(x \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -620.0) (not (<= x 3.7e-94))) (* x (+ y -1.0)) (* (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -620.0) || !(x <= 3.7e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((x <= (-620.0d0)) .or. (.not. (x <= 3.7d-94))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = (x + 1.0d0) * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -620.0) || !(x <= 3.7e-94)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -620.0) or not (x <= 3.7e-94):
		tmp = x * (y + -1.0)
	else:
		tmp = (x + 1.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -620.0) || !(x <= 3.7e-94))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(Float64(x + 1.0) * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -620.0) || ~((x <= 3.7e-94)))
		tmp = x * (y + -1.0);
	else
		tmp = (x + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -620.0], N[Not[LessEqual[x, 3.7e-94]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -620 or 3.6999999999999998e-94 < x

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around inf 97.3%

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

   if -620 < x < 3.6999999999999998e-94

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in y around inf 80.3%

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

      1. +-commutative 80.3%

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

   5. Simplified 80.3%

      \[\leadsto \color{blue}{y \cdot \left(x + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -620 \lor \neg \left(x \leq 3.7 \cdot 10^{-94}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 60.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6e-35) y (if (<= y 8.2e-126) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6e-35) {
		tmp = y;
	} else if (y <= 8.2e-126) {
		tmp = -x;
	} else {
		tmp = 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 <= (-6d-35)) then
        tmp = y
    else if (y <= 8.2d-126) then
        tmp = -x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -6e-35) {
		tmp = y;
	} else if (y <= 8.2e-126) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6e-35:
		tmp = y
	elif y <= 8.2e-126:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6e-35)
		tmp = y;
	elseif (y <= 8.2e-126)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6e-35)
		tmp = y;
	elseif (y <= 8.2e-126)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6e-35], y, If[LessEqual[y, 8.2e-126], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -5.99999999999999978e-35 or 8.1999999999999995e-126 < y

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in x around 0 53.4%

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

   if -5.99999999999999978e-35 < y < 8.1999999999999995e-126

   1. Initial program 100.0%

      \[\left(x + 1\right) \cdot y - x \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 86.1%

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

      1. neg-mul-1 86.1%

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

   5. Simplified 86.1%

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

4. Final simplification 65.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -6 \cdot 10^{-35}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-126}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 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]

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Final simplification 100.0%

   \[\leadsto \left(x + 1\right) \cdot y - x \]
4. Add Preprocessing

Alternative 7: 38.5% accurate, 7.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 y)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return y

Julia

function code(x, y)
	return y
end

MATLAB

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

Wolfram

code[x_, y_] := y

Derivation

1. Initial program 100.0%

   \[\left(x + 1\right) \cdot y - x \]
2. Add Preprocessing

3. Taylor expanded in x around 0 39.4%

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

4. Final simplification 39.4%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024059 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))