Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 6.3s

Alternatives: 7

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, 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. Add Preprocessing

Alternative 2: 62.6% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.9 \cdot 10^{+121}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -1 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{-6}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.8 \cdot 10^{+25}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 10^{+182}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.9e+121)
   (* x y)
   (if (<= y -1e-21)
     y
     (if (<= y 4.4e-6)
       (- x)
       (if (<= y 1.8e+25) y (if (<= y 1e+182) (* x y) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+121) {
		tmp = x * y;
	} else if (y <= -1e-21) {
		tmp = y;
	} else if (y <= 4.4e-6) {
		tmp = -x;
	} else if (y <= 1.8e+25) {
		tmp = y;
	} else if (y <= 1e+182) {
		tmp = x * y;
	} 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 <= (-2.9d+121)) then
        tmp = x * y
    else if (y <= (-1d-21)) then
        tmp = y
    else if (y <= 4.4d-6) then
        tmp = -x
    else if (y <= 1.8d+25) then
        tmp = y
    else if (y <= 1d+182) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.9e+121) {
		tmp = x * y;
	} else if (y <= -1e-21) {
		tmp = y;
	} else if (y <= 4.4e-6) {
		tmp = -x;
	} else if (y <= 1.8e+25) {
		tmp = y;
	} else if (y <= 1e+182) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.9e+121:
		tmp = x * y
	elif y <= -1e-21:
		tmp = y
	elif y <= 4.4e-6:
		tmp = -x
	elif y <= 1.8e+25:
		tmp = y
	elif y <= 1e+182:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.9e+121)
		tmp = Float64(x * y);
	elseif (y <= -1e-21)
		tmp = y;
	elseif (y <= 4.4e-6)
		tmp = Float64(-x);
	elseif (y <= 1.8e+25)
		tmp = y;
	elseif (y <= 1e+182)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.9e+121)
		tmp = x * y;
	elseif (y <= -1e-21)
		tmp = y;
	elseif (y <= 4.4e-6)
		tmp = -x;
	elseif (y <= 1.8e+25)
		tmp = y;
	elseif (y <= 1e+182)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.9e+121], N[(x * y), $MachinePrecision], If[LessEqual[y, -1e-21], y, If[LessEqual[y, 4.4e-6], (-x), If[LessEqual[y, 1.8e+25], y, If[LessEqual[y, 1e+182], N[(x * y), $MachinePrecision], y]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.8999999999999999e121 or 1.80000000000000008e25 < y < 1.0000000000000001e182

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in y around inf 66.4%

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

   if -2.8999999999999999e121 < y < -9.99999999999999908e-22 or 4.4000000000000002e-6 < y < 1.80000000000000008e25 or 1.0000000000000001e182 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 67.2%

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

   4. Taylor expanded in y around inf 64.1%

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

   if -9.99999999999999908e-22 < y < 4.4000000000000002e-6

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. neg-mul-1 87.2%

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

   5. Simplified 87.2%

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

Alternative 3: 75.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.1 \cdot 10^{+123}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 3.5 \cdot 10^{+25}:\\ \;\;\;\;y - x\\ \mathbf{elif}\;y \leq 6.4 \cdot 10^{+180}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.1e+123)
   (* x y)
   (if (<= y 3.5e+25) (- y x) (if (<= y 6.4e+180) (* x y) y))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+123) {
		tmp = x * y;
	} else if (y <= 3.5e+25) {
		tmp = y - x;
	} else if (y <= 6.4e+180) {
		tmp = x * y;
	} 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 <= (-2.1d+123)) then
        tmp = x * y
    else if (y <= 3.5d+25) then
        tmp = y - x
    else if (y <= 6.4d+180) then
        tmp = x * y
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -2.1e+123) {
		tmp = x * y;
	} else if (y <= 3.5e+25) {
		tmp = y - x;
	} else if (y <= 6.4e+180) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.1e+123:
		tmp = x * y
	elif y <= 3.5e+25:
		tmp = y - x
	elif y <= 6.4e+180:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.1e+123)
		tmp = Float64(x * y);
	elseif (y <= 3.5e+25)
		tmp = Float64(y - x);
	elseif (y <= 6.4e+180)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.1e+123)
		tmp = x * y;
	elseif (y <= 3.5e+25)
		tmp = y - x;
	elseif (y <= 6.4e+180)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.1e+123], N[(x * y), $MachinePrecision], If[LessEqual[y, 3.5e+25], N[(y - x), $MachinePrecision], If[LessEqual[y, 6.4e+180], N[(x * y), $MachinePrecision], y]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.09999999999999994e123 or 3.49999999999999999e25 < y < 6.39999999999999987e180

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 66.4%

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

      1. *-commutative 66.4%

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

   5. Simplified 66.4%

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

   6. Taylor expanded in y around inf 66.4%

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

   if -2.09999999999999994e123 < y < 3.49999999999999999e25

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 93.5%

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

   if 6.39999999999999987e180 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 62.1%

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

   4. Taylor expanded in y around inf 62.1%

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

Alternative 4: 98.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -62000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -62000000000.0) (not (<= x 1.0))) (- (* x y) x) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -62000000000.0) || !(x <= 1.0)) {
		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 <= (-62000000000.0d0)) .or. (.not. (x <= 1.0d0))) 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 <= -62000000000.0) || !(x <= 1.0)) {
		tmp = (x * y) - x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -62000000000.0) or not (x <= 1.0):
		tmp = (x * y) - x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -62000000000.0) || !(x <= 1.0))
		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 <= -62000000000.0) || ~((x <= 1.0)))
		tmp = (x * y) - x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -62000000000.0], N[Not[LessEqual[x, 1.0]], $MachinePrecision]], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.2e10 or 1 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 99.8%

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

      1. *-commutative 99.8%

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

   5. Simplified 99.8%

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

   if -6.2e10 < x < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 99.3%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -62000000000 \lor \neg \left(x \leq 1\right):\\ \;\;\;\;x \cdot y - x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 3.3 \cdot 10^{-9}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e-21) y (if (<= y 3.3e-9) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e-21) {
		tmp = y;
	} else if (y <= 3.3e-9) {
		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 <= (-1.25d-21)) then
        tmp = y
    else if (y <= 3.3d-9) 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 <= -1.25e-21) {
		tmp = y;
	} else if (y <= 3.3e-9) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e-21:
		tmp = y
	elif y <= 3.3e-9:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e-21)
		tmp = y;
	elseif (y <= 3.3e-9)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e-21)
		tmp = y;
	elseif (y <= 3.3e-9)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e-21], y, If[LessEqual[y, 3.3e-9], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -1.24999999999999993e-21 or 3.30000000000000018e-9 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 51.1%

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

   4. Taylor expanded in y around inf 49.5%

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

   if -1.24999999999999993e-21 < y < 3.30000000000000018e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 87.2%

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

      1. neg-mul-1 87.2%

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

   5. Simplified 87.2%

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

Alternative 6: 38.3% 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 75.5%

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

4. Taylor expanded in y around inf 32.7%

   \[\leadsto \color{blue}{y} \]
5. Add Preprocessing

Alternative 7: 2.6% accurate, 7.0× 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 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. Add Preprocessing

3. Taylor expanded in y around 0 45.7%

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

   1. neg-mul-1 45.7%

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

5. Simplified 45.7%

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

   1. neg-sub0 45.7%

      \[\leadsto \color{blue}{0 - x} \]

   2. sub-neg 45.7%

      \[\leadsto \color{blue}{0 + \left(-x\right)} \]

   3. add-sqr-sqrt 25.1%

      \[\leadsto 0 + \color{blue}{\sqrt{-x} \cdot \sqrt{-x}} \]

   4. sqrt-unprod 17.8%

      \[\leadsto 0 + \color{blue}{\sqrt{\left(-x\right) \cdot \left(-x\right)}} \]

   5. sqr-neg 17.8%

      \[\leadsto 0 + \sqrt{\color{blue}{x \cdot x}} \]

   6. sqrt-unprod 1.2%

      \[\leadsto 0 + \color{blue}{\sqrt{x} \cdot \sqrt{x}} \]

   7. add-sqr-sqrt 2.4%

      \[\leadsto 0 + \color{blue}{x} \]

7. Applied egg-rr 2.4%

   \[\leadsto \color{blue}{0 + x} \]
8. Step-by-step derivation

   1. +-lft-identity 2.4%

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

9. Simplified 2.4%

   \[\leadsto \color{blue}{x} \]
10. Add Preprocessing

Reproduce

herbie shell --seed 2024137 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))