Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 4.3s

Alternatives: 8

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.5% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+101} \lor \neg \left(y \leq 6.5 \cdot 10^{+202}\right) \land y \leq 9.8 \cdot 10^{+294}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -9e+19)
   (* y x)
   (if (<= y -3.1e-21)
     y
     (if (<= y 5.2e-78)
       (- x)
       (if (or (<= y 1.55e+101) (and (not (<= y 6.5e+202)) (<= y 9.8e+294)))
         y
         (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -9e+19) {
		tmp = y * x;
	} else if (y <= -3.1e-21) {
		tmp = y;
	} else if (y <= 5.2e-78) {
		tmp = -x;
	} else if ((y <= 1.55e+101) || (!(y <= 6.5e+202) && (y <= 9.8e+294))) {
		tmp = 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 (y <= (-9d+19)) then
        tmp = y * x
    else if (y <= (-3.1d-21)) then
        tmp = y
    else if (y <= 5.2d-78) then
        tmp = -x
    else if ((y <= 1.55d+101) .or. (.not. (y <= 6.5d+202)) .and. (y <= 9.8d+294)) then
        tmp = y
    else
        tmp = y * x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -9e+19) {
		tmp = y * x;
	} else if (y <= -3.1e-21) {
		tmp = y;
	} else if (y <= 5.2e-78) {
		tmp = -x;
	} else if ((y <= 1.55e+101) || (!(y <= 6.5e+202) && (y <= 9.8e+294))) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -9e+19:
		tmp = y * x
	elif y <= -3.1e-21:
		tmp = y
	elif y <= 5.2e-78:
		tmp = -x
	elif (y <= 1.55e+101) or (not (y <= 6.5e+202) and (y <= 9.8e+294)):
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -9e+19)
		tmp = Float64(y * x);
	elseif (y <= -3.1e-21)
		tmp = y;
	elseif (y <= 5.2e-78)
		tmp = Float64(-x);
	elseif ((y <= 1.55e+101) || (!(y <= 6.5e+202) && (y <= 9.8e+294)))
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -9e+19)
		tmp = y * x;
	elseif (y <= -3.1e-21)
		tmp = y;
	elseif (y <= 5.2e-78)
		tmp = -x;
	elseif ((y <= 1.55e+101) || (~((y <= 6.5e+202)) && (y <= 9.8e+294)))
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -9e+19], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.1e-21], y, If[LessEqual[y, 5.2e-78], (-x), If[Or[LessEqual[y, 1.55e+101], And[N[Not[LessEqual[y, 6.5e+202]], $MachinePrecision], LessEqual[y, 9.8e+294]]], y, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e19 or 1.55e101 < y < 6.4999999999999996e202 or 9.7999999999999995e294 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 62.6%

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

      1. *-commutative 62.6%

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

   5. Simplified 62.6%

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

   6. Taylor expanded in y around inf 62.6%

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

   if -9e19 < y < -3.0999999999999998e-21 or 5.2000000000000002e-78 < y < 1.55e101 or 6.4999999999999996e202 < y < 9.7999999999999995e294

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 67.8%

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

   if -3.0999999999999998e-21 < y < 5.2000000000000002e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

   5. Simplified 82.9%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+19}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-21}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+101} \lor \neg \left(y \leq 6.5 \cdot 10^{+202}\right) \land y \leq 9.8 \cdot 10^{+294}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 73.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 4.6 \cdot 10^{+213}\right) \land x \leq 1.15 \cdot 10^{+260}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -2.0) (and (not (<= x 4.6e+213)) (<= x 1.15e+260)))
   (* y x)
   (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -2.0) || (!(x <= 4.6e+213) && (x <= 1.15e+260))) {
		tmp = 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 <= (-2.0d0)) .or. (.not. (x <= 4.6d+213)) .and. (x <= 1.15d+260)) then
        tmp = 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 <= -2.0) || (!(x <= 4.6e+213) && (x <= 1.15e+260))) {
		tmp = y * x;
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -2.0) or (not (x <= 4.6e+213) and (x <= 1.15e+260)):
		tmp = y * x
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -2.0) || (!(x <= 4.6e+213) && (x <= 1.15e+260)))
		tmp = Float64(y * x);
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -2.0) || (~((x <= 4.6e+213)) && (x <= 1.15e+260)))
		tmp = y * x;
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -2.0], And[N[Not[LessEqual[x, 4.6e+213]], $MachinePrecision], LessEqual[x, 1.15e+260]]], N[(y * x), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2 or 4.59999999999999996e213 < x < 1.15000000000000005e260

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.0%

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

      1. *-commutative 98.0%

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

   5. Simplified 98.0%

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

   6. Taylor expanded in y around inf 63.6%

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

   if -2 < x < 4.59999999999999996e213 or 1.15000000000000005e260 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 85.5%

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

4. Final simplification 78.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2 \lor \neg \left(x \leq 4.6 \cdot 10^{+213}\right) \land x \leq 1.15 \cdot 10^{+260}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.8% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 99.4%

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

      1. +-commutative 99.4%

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

   7. Simplified 99.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.6%

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

4. Final simplification 99.1%

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

Alternative 5: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) (+ y (* y x)) (if (<= y 1.0) (- y x) (* y (+ x 1.0)))))

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 98.9%

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

      1. +-commutative 98.9%

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

   7. Simplified 98.9%

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

      1. distribute-lft-in 98.9%

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

      2. *-rgt-identity 98.9%

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

   9. Applied egg-rr 98.9%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 98.6%

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

   if 1 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.1%

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

Alternative 6: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -2.6e-20) y (if (<= y 5.2e-78) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -2.6e-20) {
		tmp = y;
	} else if (y <= 5.2e-78) {
		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 <= (-2.6d-20)) then
        tmp = y
    else if (y <= 5.2d-78) 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 <= -2.6e-20) {
		tmp = y;
	} else if (y <= 5.2e-78) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -2.6e-20:
		tmp = y
	elif y <= 5.2e-78:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -2.6e-20)
		tmp = y;
	elseif (y <= 5.2e-78)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -2.6e-20)
		tmp = y;
	elseif (y <= 5.2e-78)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -2.6e-20], y, If[LessEqual[y, 5.2e-78], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -2.59999999999999995e-20 or 5.2000000000000002e-78 < y

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. distribute-lft-in 100.0%

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

      3. *-commutative 100.0%

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

      4. *-un-lft-identity 100.0%

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

   4. Applied egg-rr 100.0%

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

   5. Taylor expanded in x around 0 49.1%

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

   if -2.59999999999999995e-20 < y < 5.2000000000000002e-78

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.9%

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

      1. mul-1-neg 82.9%

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

   5. Simplified 82.9%

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

4. Final simplification 61.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2.6 \cdot 10^{-20}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.2 \cdot 10^{-78}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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. Add Preprocessing

3. Final simplification 100.0%

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

Alternative 8: 37.4% 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. Step-by-step derivation

   1. *-commutative 100.0%

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

   2. distribute-lft-in 100.0%

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

   3. *-commutative 100.0%

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

   4. *-un-lft-identity 100.0%

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

4. Applied egg-rr 100.0%

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

5. Taylor expanded in x around 0 37.9%

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

6. Final simplification 37.9%

   \[\leadsto y \]
7. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))