Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 2.0s

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. Final simplification 100.0%

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

Alternative 2: 62.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.27:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+45}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+109} \lor \neg \left(x \leq 4.8 \cdot 10^{+222}\right) \land x \leq 4.2 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.27)
   (- x)
   (if (<= x 4.4e-85)
     y
     (if (<= x 1.6e+45)
       (- x)
       (if (or (<= x 1.25e+109) (and (not (<= x 4.8e+222)) (<= x 4.2e+248)))
         (* x y)
         (- x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.27) {
		tmp = -x;
	} else if (x <= 4.4e-85) {
		tmp = y;
	} else if (x <= 1.6e+45) {
		tmp = -x;
	} else if ((x <= 1.25e+109) || (!(x <= 4.8e+222) && (x <= 4.2e+248))) {
		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 <= (-0.27d0)) then
        tmp = -x
    else if (x <= 4.4d-85) then
        tmp = y
    else if (x <= 1.6d+45) then
        tmp = -x
    else if ((x <= 1.25d+109) .or. (.not. (x <= 4.8d+222)) .and. (x <= 4.2d+248)) 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 <= -0.27) {
		tmp = -x;
	} else if (x <= 4.4e-85) {
		tmp = y;
	} else if (x <= 1.6e+45) {
		tmp = -x;
	} else if ((x <= 1.25e+109) || (!(x <= 4.8e+222) && (x <= 4.2e+248))) {
		tmp = x * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.27:
		tmp = -x
	elif x <= 4.4e-85:
		tmp = y
	elif x <= 1.6e+45:
		tmp = -x
	elif (x <= 1.25e+109) or (not (x <= 4.8e+222) and (x <= 4.2e+248)):
		tmp = x * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.27)
		tmp = Float64(-x);
	elseif (x <= 4.4e-85)
		tmp = y;
	elseif (x <= 1.6e+45)
		tmp = Float64(-x);
	elseif ((x <= 1.25e+109) || (!(x <= 4.8e+222) && (x <= 4.2e+248)))
		tmp = Float64(x * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.27)
		tmp = -x;
	elseif (x <= 4.4e-85)
		tmp = y;
	elseif (x <= 1.6e+45)
		tmp = -x;
	elseif ((x <= 1.25e+109) || (~((x <= 4.8e+222)) && (x <= 4.2e+248)))
		tmp = x * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.27], (-x), If[LessEqual[x, 4.4e-85], y, If[LessEqual[x, 1.6e+45], (-x), If[Or[LessEqual[x, 1.25e+109], And[N[Not[LessEqual[x, 4.8e+222]], $MachinePrecision], LessEqual[x, 4.2e+248]]], N[(x * y), $MachinePrecision], (-x)]]]]

Derivation

1. Split input into 3 regimes

2. if x < -0.27000000000000002 or 4.4e-85 < x < 1.6000000000000001e45 or 1.25e109 < x < 4.8000000000000002e222 or 4.19999999999999977e248 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 62.1%

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

      1. neg-mul-1 62.1%

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

   4. Simplified 62.1%

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

   if -0.27000000000000002 < x < 4.4e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.1%

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

   if 1.6000000000000001e45 < x < 1.25e109 or 4.8000000000000002e222 < x < 4.19999999999999977e248

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

   3. Taylor expanded in y around inf 87.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.27:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{elif}\;x \leq 1.6 \cdot 10^{+45}:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+109} \lor \neg \left(x \leq 4.8 \cdot 10^{+222}\right) \land x \leq 4.2 \cdot 10^{+248}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 3: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-82} \lor \neg \left(y \leq 1.6 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.05e-82) (not (<= y 1.6e-12))) (* (+ x 1.0) y) (- x)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e-82) || !(y <= 1.6e-12)) {
		tmp = (x + 1.0) * 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 <= (-1.05d-82)) .or. (.not. (y <= 1.6d-12))) then
        tmp = (x + 1.0d0) * y
    else
        tmp = -x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.05e-82) || !(y <= 1.6e-12)) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.05e-82) or not (y <= 1.6e-12):
		tmp = (x + 1.0) * y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.05e-82) || !(y <= 1.6e-12))
		tmp = Float64(Float64(x + 1.0) * y);
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.05e-82) || ~((y <= 1.6e-12)))
		tmp = (x + 1.0) * y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.05e-82], N[Not[LessEqual[y, 1.6e-12]], $MachinePrecision]], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision], (-x)]

Derivation

1. Split input into 2 regimes

2. if y < -1.05e-82 or 1.6e-12 < y

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 93.1%

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

   if -1.05e-82 < y < 1.6e-12

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 77.9%

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

      1. neg-mul-1 77.9%

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

   4. Simplified 77.9%

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

4. Final simplification 86.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.05 \cdot 10^{-82} \lor \neg \left(y \leq 1.6 \cdot 10^{-12}\right):\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 4: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.36 \lor \neg \left(x \leq 5.5 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -0.36) (not (<= x 5.5e-110))) (* x (+ y -1.0)) (* (+ x 1.0) y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -0.36) || !(x <= 5.5e-110)) {
		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 <= (-0.36d0)) .or. (.not. (x <= 5.5d-110))) 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 <= -0.36) || !(x <= 5.5e-110)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = (x + 1.0) * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -0.36) or not (x <= 5.5e-110):
		tmp = x * (y + -1.0)
	else:
		tmp = (x + 1.0) * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -0.36) || !(x <= 5.5e-110))
		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 <= -0.36) || ~((x <= 5.5e-110)))
		tmp = x * (y + -1.0);
	else
		tmp = (x + 1.0) * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -0.36], N[Not[LessEqual[x, 5.5e-110]], $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 < -0.35999999999999999 or 5.4999999999999998e-110 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 92.9%

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

   if -0.35999999999999999 < x < 5.4999999999999998e-110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.8%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.36 \lor \neg \left(x \leq 5.5 \cdot 10^{-110}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \end{array} \]

Alternative 5: 86.2% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -390:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-110}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -390.0)
   (- (* x y) x)
   (if (<= x 5.5e-110) (* (+ x 1.0) y) (* x (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -390.0) {
		tmp = (x * y) - x;
	} else if (x <= 5.5e-110) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = x * (y + -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 <= (-390.0d0)) then
        tmp = (x * y) - x
    else if (x <= 5.5d-110) then
        tmp = (x + 1.0d0) * y
    else
        tmp = x * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= -390.0) {
		tmp = (x * y) - x;
	} else if (x <= 5.5e-110) {
		tmp = (x + 1.0) * y;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -390.0:
		tmp = (x * y) - x
	elif x <= 5.5e-110:
		tmp = (x + 1.0) * y
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -390.0)
		tmp = Float64(Float64(x * y) - x);
	elseif (x <= 5.5e-110)
		tmp = Float64(Float64(x + 1.0) * y);
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -390.0)
		tmp = (x * y) - x;
	elseif (x <= 5.5e-110)
		tmp = (x + 1.0) * y;
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -390.0], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 5.5e-110], N[(N[(x + 1.0), $MachinePrecision] * y), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -390

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-out-- 100.0%

         \[\leadsto \color{blue}{x \cdot y - x \cdot 1} \]

      3. *-commutative 100.0%

         \[\leadsto \color{blue}{y \cdot x} - x \cdot 1 \]

      4. cancel-sign-sub-inv 100.0%

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

      5. *-rgt-identity 100.0%

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

      6. sub-neg 100.0%

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

   4. Simplified 100.0%

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

   if -390 < x < 5.4999999999999998e-110

   1. Initial program 100.0%

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

   2. Taylor expanded in y around inf 81.8%

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

   if 5.4999999999999998e-110 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in x around inf 88.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -390:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 5.5 \cdot 10^{-110}:\\ \;\;\;\;\left(x + 1\right) \cdot y\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 6: 62.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -0.27:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -0.27) (- x) (if (<= x 4.4e-85) y (- x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -0.27) {
		tmp = -x;
	} else if (x <= 4.4e-85) {
		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 <= (-0.27d0)) then
        tmp = -x
    else if (x <= 4.4d-85) 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 <= -0.27) {
		tmp = -x;
	} else if (x <= 4.4e-85) {
		tmp = y;
	} else {
		tmp = -x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -0.27:
		tmp = -x
	elif x <= 4.4e-85:
		tmp = y
	else:
		tmp = -x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -0.27)
		tmp = Float64(-x);
	elseif (x <= 4.4e-85)
		tmp = y;
	else
		tmp = Float64(-x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -0.27)
		tmp = -x;
	elseif (x <= 4.4e-85)
		tmp = y;
	else
		tmp = -x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -0.27], (-x), If[LessEqual[x, 4.4e-85], y, (-x)]]

Derivation

1. Split input into 2 regimes

2. if x < -0.27000000000000002 or 4.4e-85 < x

   1. Initial program 100.0%

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

   2. Taylor expanded in y around 0 57.2%

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

      1. neg-mul-1 57.2%

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

   4. Simplified 57.2%

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

   if -0.27000000000000002 < x < 4.4e-85

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 80.1%

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

4. Final simplification 67.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -0.27:\\ \;\;\;\;-x\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{-85}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;-x\\ \end{array} \]

Alternative 7: 38.9% 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 41.3%

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

3. Final simplification 41.3%

   \[\leadsto y \]

Reproduce

herbie shell --seed 2023182 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))