Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.3s

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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg 100.0%

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

   2. distribute-rgt1-in 100.0%

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

   3. *-commutative 100.0%

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

   4. associate-+l+ 100.0%

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

   5. *-commutative 100.0%

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

   6. +-commutative 100.0%

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

   7. *-commutative 100.0%

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

   8. neg-mul-1 100.0%

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

   9. distribute-rgt-out 100.0%

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

   10. fma-define 100.0%

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

3. Simplified 100.0%

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

5. Final simplification 100.0%

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

Alternative 2: 62.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -900:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -3.3e+84)
   y
   (if (<= y -4.4e+17)
     (* x y)
     (if (<= y -900.0) y (if (<= y 5.5e-7) (- x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -3.3e+84) {
		tmp = y;
	} else if (y <= -4.4e+17) {
		tmp = x * y;
	} else if (y <= -900.0) {
		tmp = y;
	} else if (y <= 5.5e-7) {
		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 <= (-3.3d+84)) then
        tmp = y
    else if (y <= (-4.4d+17)) then
        tmp = x * y
    else if (y <= (-900.0d0)) then
        tmp = y
    else if (y <= 5.5d-7) 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 <= -3.3e+84) {
		tmp = y;
	} else if (y <= -4.4e+17) {
		tmp = x * y;
	} else if (y <= -900.0) {
		tmp = y;
	} else if (y <= 5.5e-7) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -3.3e+84:
		tmp = y
	elif y <= -4.4e+17:
		tmp = x * y
	elif y <= -900.0:
		tmp = y
	elif y <= 5.5e-7:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -3.3e+84)
		tmp = y;
	elseif (y <= -4.4e+17)
		tmp = Float64(x * y);
	elseif (y <= -900.0)
		tmp = y;
	elseif (y <= 5.5e-7)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -3.3e+84)
		tmp = y;
	elseif (y <= -4.4e+17)
		tmp = x * y;
	elseif (y <= -900.0)
		tmp = y;
	elseif (y <= 5.5e-7)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -3.3e+84], y, If[LessEqual[y, -4.4e+17], N[(x * y), $MachinePrecision], If[LessEqual[y, -900.0], y, If[LessEqual[y, 5.5e-7], (-x), y]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.30000000000000017e84 or -4.4e17 < y < -900 or 5.5000000000000003e-7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 62.7%

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

   if -3.30000000000000017e84 < y < -4.4e17

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 100.0%

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

      1. distribute-lft-in 100.0%

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

      2. *-rgt-identity 100.0%

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

      3. +-commutative 100.0%

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

   5. Applied egg-rr 100.0%

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

   6. Taylor expanded in x around inf 66.1%

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

      1. *-commutative 66.1%

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

   8. Simplified 66.1%

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

   if -900 < y < 5.5000000000000003e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.3 \cdot 10^{+84}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq -4.4 \cdot 10^{+17}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq -900:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5.5 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x -1.0) (not (<= x 1.75e-6))) (* x (+ y -1.0)) (- y x)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.75e-6)) {
		tmp = x * (y + -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 ((x <= (-1.0d0)) .or. (.not. (x <= 1.75d-6))) then
        tmp = x * (y + (-1.0d0))
    else
        tmp = y - x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= -1.0) || !(x <= 1.75e-6)) {
		tmp = x * (y + -1.0);
	} else {
		tmp = y - x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= -1.0) or not (x <= 1.75e-6):
		tmp = x * (y + -1.0)
	else:
		tmp = y - x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= -1.0) || !(x <= 1.75e-6))
		tmp = Float64(x * Float64(y + -1.0));
	else
		tmp = Float64(y - x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= -1.0) || ~((x <= 1.75e-6)))
		tmp = x * (y + -1.0);
	else
		tmp = y - x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, -1.0], N[Not[LessEqual[x, 1.75e-6]], $MachinePrecision]], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(y - x), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1 or 1.74999999999999997e-6 < x

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 97.8%

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

   if -1 < x < 1.74999999999999997e-6

   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 99.5%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1 \lor \neg \left(x \leq 1.75 \cdot 10^{-6}\right):\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;y - x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x -1.0) (- (* x y) x) (if (<= x 1.75e-6) (- y x) (* x (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= -1.0) {
		tmp = (x * y) - x;
	} else if (x <= 1.75e-6) {
		tmp = y - x;
	} 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 <= (-1.0d0)) then
        tmp = (x * y) - x
    else if (x <= 1.75d-6) then
        tmp = y - x
    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 <= -1.0) {
		tmp = (x * y) - x;
	} else if (x <= 1.75e-6) {
		tmp = y - x;
	} else {
		tmp = x * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= -1.0:
		tmp = (x * y) - x
	elif x <= 1.75e-6:
		tmp = y - x
	else:
		tmp = x * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= -1.0)
		tmp = Float64(Float64(x * y) - x);
	elseif (x <= 1.75e-6)
		tmp = Float64(y - x);
	else
		tmp = Float64(x * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= -1.0)
		tmp = (x * y) - x;
	elseif (x <= 1.75e-6)
		tmp = y - x;
	else
		tmp = x * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, -1.0], N[(N[(x * y), $MachinePrecision] - x), $MachinePrecision], If[LessEqual[x, 1.75e-6], N[(y - x), $MachinePrecision], N[(x * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 98.9%

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

      1. *-commutative 98.9%

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

   5. Simplified 98.9%

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

   if -1 < x < 1.74999999999999997e-6

   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 99.5%

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

   if 1.74999999999999997e-6 < x

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf 96.4%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1:\\ \;\;\;\;x \cdot y - x\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-6}:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.35 \cdot 10^{+53} \lor \neg \left(x \leq 3.05 \cdot 10^{+122}\right):\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= x 3.35e+53) (not (<= x 3.05e+122))) (- y x) (* x y)))

C

double code(double x, double y) {
	double tmp;
	if ((x <= 3.35e+53) || !(x <= 3.05e+122)) {
		tmp = y - 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 <= 3.35d+53) .or. (.not. (x <= 3.05d+122))) then
        tmp = y - x
    else
        tmp = x * y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((x <= 3.35e+53) || !(x <= 3.05e+122)) {
		tmp = y - x;
	} else {
		tmp = x * y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (x <= 3.35e+53) or not (x <= 3.05e+122):
		tmp = y - x
	else:
		tmp = x * y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((x <= 3.35e+53) || !(x <= 3.05e+122))
		tmp = Float64(y - x);
	else
		tmp = Float64(x * y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((x <= 3.35e+53) || ~((x <= 3.05e+122)))
		tmp = y - x;
	else
		tmp = x * y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[x, 3.35e+53], N[Not[LessEqual[x, 3.05e+122]], $MachinePrecision]], N[(y - x), $MachinePrecision], N[(x * y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.3499999999999999e53 or 3.0499999999999999e122 < x

   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 79.6%

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

   if 3.3499999999999999e53 < x < 3.0499999999999999e122

   1. Initial program 100.0%

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

   3. Taylor expanded in y around inf 77.8%

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

      1. distribute-lft-in 77.8%

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

      2. *-rgt-identity 77.8%

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

      3. +-commutative 77.8%

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

   5. Applied egg-rr 77.8%

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

   6. Taylor expanded in x around inf 77.8%

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

      1. *-commutative 77.8%

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

   8. Simplified 77.8%

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

4. Final simplification 79.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.35 \cdot 10^{+53} \lor \neg \left(x \leq 3.05 \cdot 10^{+122}\right):\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;x \cdot y\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 62.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -900.0) y (if (<= y 5e-7) (- x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -900.0) {
		tmp = y;
	} else if (y <= 5e-7) {
		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 <= (-900.0d0)) then
        tmp = y
    else if (y <= 5d-7) 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 <= -900.0) {
		tmp = y;
	} else if (y <= 5e-7) {
		tmp = -x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -900.0:
		tmp = y
	elif y <= 5e-7:
		tmp = -x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -900.0)
		tmp = y;
	elseif (y <= 5e-7)
		tmp = Float64(-x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -900.0)
		tmp = y;
	elseif (y <= 5e-7)
		tmp = -x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -900.0], y, If[LessEqual[y, 5e-7], (-x), y]]

Derivation

1. Split input into 2 regimes

2. if y < -900 or 4.99999999999999977e-7 < y

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0 59.0%

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

   if -900 < y < 4.99999999999999977e-7

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0 82.2%

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

      1. neg-mul-1 82.2%

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

   5. Simplified 82.2%

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

4. Final simplification 69.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-7}:\\ \;\;\;\;-x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
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: 39.3% 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 40.0%

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

4. Final simplification 40.0%

   \[\leadsto y \]
5. Add Preprocessing

Reproduce

herbie shell --seed 2024076 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))