Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 3.1s

Alternatives: 9

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

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

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 Float64(fma(x, y, y) - x)
end

Wolfram

code[x_, y_] := N[(N[(x * y + y), $MachinePrecision] - x), $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. distribute-rgt-in 100.0%

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

   3. fma-def 100.0%

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

   4. *-lft-identity 100.0%

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

3. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 62.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+272}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.027:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.9e+272)
   y
   (if (<= y -0.027)
     (* x y)
     (if (<= y 1.0) (- x) (if (<= y 8.8e+117) (* x y) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.9e+272) {
		tmp = y;
	} else if (y <= -0.027) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = -x;
	} else if (y <= 8.8e+117) {
		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 <= (-4.9d+272)) then
        tmp = y
    else if (y <= (-0.027d0)) then
        tmp = x * y
    else if (y <= 1.0d0) then
        tmp = -x
    else if (y <= 8.8d+117) 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 <= -4.9e+272) {
		tmp = y;
	} else if (y <= -0.027) {
		tmp = x * y;
	} else if (y <= 1.0) {
		tmp = -x;
	} else if (y <= 8.8e+117) {
		tmp = x * y;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.9e+272:
		tmp = y
	elif y <= -0.027:
		tmp = x * y
	elif y <= 1.0:
		tmp = -x
	elif y <= 8.8e+117:
		tmp = x * y
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.9e+272)
		tmp = y;
	elseif (y <= -0.027)
		tmp = Float64(x * y);
	elseif (y <= 1.0)
		tmp = Float64(-x);
	elseif (y <= 8.8e+117)
		tmp = Float64(x * y);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.9e+272)
		tmp = y;
	elseif (y <= -0.027)
		tmp = x * y;
	elseif (y <= 1.0)
		tmp = -x;
	elseif (y <= 8.8e+117)
		tmp = x * y;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.9e+272], y, If[LessEqual[y, -0.027], N[(x * y), $MachinePrecision], If[LessEqual[y, 1.0], (-x), If[LessEqual[y, 8.8e+117], N[(x * y), $MachinePrecision], y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.9000000000000002e272 or 8.80000000000000056e117 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 64.4%

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

   if -4.9000000000000002e272 < y < -0.0269999999999999997 or 1 < y < 8.80000000000000056e117

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 96.7%

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

   3. Taylor expanded in x around 0 96.7%

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

   4. Taylor expanded in x around inf 60.5%

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

   if -0.0269999999999999997 < y < 1

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.1%

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

      1. neg-mul-1 77.1%

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

   4. Simplified 77.1%

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

4. Final simplification 69.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.9 \cdot 10^{+272}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -0.027:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 8.8 \cdot 10^{+117}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]

Alternative 3: 87.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-45} \lor \neg \left(y \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -7.2e-45) (not (<= y 3.4e-11))) (* y (+ x 1.0)) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -7.2e-45) || !(y <= 3.4e-11)) {
		tmp = y * (x + 1.0);
	} 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 <= (-7.2d-45)) .or. (.not. (y <= 3.4d-11))) then
        tmp = y * (x + 1.0d0)
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -7.2e-45) || !(y <= 3.4e-11)) {
		tmp = y * (x + 1.0);
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -7.2e-45) or not (y <= 3.4e-11):
		tmp = y * (x + 1.0)
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -7.2e-45) || !(y <= 3.4e-11))
		tmp = Float64(y * Float64(x + 1.0));
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -7.2e-45) || ~((y <= 3.4e-11)))
		tmp = y * (x + 1.0);
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -7.2e-45], N[Not[LessEqual[y, 3.4e-11]], $MachinePrecision]], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -7.20000000000000001e-45 or 3.3999999999999999e-11 < y

   1. Initial program 99.9%

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

   2. Taylor expanded in y around inf 96.6%

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

   if -7.20000000000000001e-45 < y < 3.3999999999999999e-11

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 80.1%

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

      1. neg-mul-1 80.1%

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

   4. Simplified 80.1%

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

4. Final simplification 89.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.2 \cdot 10^{-45} \lor \neg \left(y \leq 3.4 \cdot 10^{-11}\right):\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+15} \lor \neg \left(x \leq 135\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.1e+15) (not (<= x 135.0))) (* x (+ y -1.0)) (* y (+ x 1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.1e+15) || !(x <= 135.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y * (x + 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 ((x <= (-4.1d+15)) .or. (.not. (x <= 135.0d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y * (x + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.1e+15) || !(x <= 135.0)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y * (x + 1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.1e+15) or not (x <= 135.0):
		tmp = x * (y + -1.0)
	else:
		tmp = y * (x + 1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.1e+15) || !(x <= 135.0))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y * Float64(x + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.1e+15) || ~((x <= 135.0)))
		tmp = x * (y + -1.0);
	else
		tmp = y * (x + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.1e+15], N[Not[LessEqual[x, 135.0]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e15 or 135 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -4.1e15 < x < 135

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+15} \lor \neg \left(x \leq 135\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 1\right)\\ \end{array} \]

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+15} \lor \neg \left(x \leq 0.0115\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -4.1e+15) (not (<= x 0.0115))) (* x (+ y -1.0)) (+ y (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -4.1e+15) || !(x <= 0.0115)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y + (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 <= (-4.1d+15)) .or. (.not. (x <= 0.0115d0))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -4.1e+15) || !(x <= 0.0115)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -4.1e+15) or not (x <= 0.0115):
		tmp = x * (y + -1.0)
	else:
		tmp = y + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -4.1e+15) || !(x <= 0.0115))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -4.1e+15) || ~((x <= 0.0115)))
		tmp = x * (y + -1.0);
	else
		tmp = y + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -4.1e+15], N[Not[LessEqual[x, 0.0115]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1e15 or 0.0115 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   if -4.1e15 < x < 0.0115

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 79.0%

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

   3. Taylor expanded in x around 0 79.0%

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

4. Final simplification 90.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.1 \cdot 10^{+15} \lor \neg \left(x \leq 0.0115\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y + x \cdot y\\ \end{array} \]

Alternative 6: 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 7: 100.0% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

2. Taylor expanded in x around 0 100.0%

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

3. Final simplification 100.0%

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

Alternative 8: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-34}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.0042:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -9.5e-34) (- x) (if (<= x 0.0042) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -9.5e-34) {
		tmp = -x;
	} else if (x <= 0.0042) {
		tmp = 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 <= (-9.5d-34)) then
        tmp = -x
    else if (x <= 0.0042d0) then
        tmp = y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -9.5e-34) {
		tmp = -x;
	} else if (x <= 0.0042) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -9.5e-34:
		tmp = -x
	elif x <= 0.0042:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -9.5e-34)
		tmp = Float64(-x);
	elseif (x <= 0.0042)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -9.5e-34)
		tmp = -x;
	elseif (x <= 0.0042)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -9.5e-34], (-x), If[LessEqual[x, 0.0042], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -9.49999999999999985e-34 or 0.00419999999999999974 < x

   1. Initial program 99.9%

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

   2. Taylor expanded in y around 0 51.5%

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

      1. neg-mul-1 51.5%

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

   4. Simplified 51.5%

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

   if -9.49999999999999985e-34 < x < 0.00419999999999999974

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.7%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.5 \cdot 10^{-34}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 0.0042:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 9: 37.7% 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. Taylor expanded in x around 0 36.4%

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

3. Final simplification 36.4%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023208 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))