Data.Colour.SRGB:transferFunction from colour-2.3.3

Percentage Accurate: 100.0% → 100.0%

Time: 5.0s

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

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = y + (x * (y + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return y + (x * (y + -1.0));
}

Python

def code(x, y):
	return y + (x * (y + -1.0))

Julia

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

MATLAB

function tmp = code(x, y)
	tmp = y + (x * (y + -1.0));
end

Wolfram

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

Derivation

1. Initial program 100.0%

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

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

      \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

Alternative 2: 61.7% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -7.8e+25)
   (* y x)
   (if (<= y -3.1e-9)
     y
     (if (<= y 6.2e-92) (- 0.0 x) (if (<= y 2.65e+14) y (* y x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -7.8e+25) {
		tmp = y * x;
	} else if (y <= -3.1e-9) {
		tmp = y;
	} else if (y <= 6.2e-92) {
		tmp = 0.0 - x;
	} else if (y <= 2.65e+14) {
		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 <= (-7.8d+25)) then
        tmp = y * x
    else if (y <= (-3.1d-9)) then
        tmp = y
    else if (y <= 6.2d-92) then
        tmp = 0.0d0 - x
    else if (y <= 2.65d+14) 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 <= -7.8e+25) {
		tmp = y * x;
	} else if (y <= -3.1e-9) {
		tmp = y;
	} else if (y <= 6.2e-92) {
		tmp = 0.0 - x;
	} else if (y <= 2.65e+14) {
		tmp = y;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -7.8e+25:
		tmp = y * x
	elif y <= -3.1e-9:
		tmp = y
	elif y <= 6.2e-92:
		tmp = 0.0 - x
	elif y <= 2.65e+14:
		tmp = y
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -7.8e+25)
		tmp = Float64(y * x);
	elseif (y <= -3.1e-9)
		tmp = y;
	elseif (y <= 6.2e-92)
		tmp = Float64(0.0 - x);
	elseif (y <= 2.65e+14)
		tmp = y;
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -7.8e+25)
		tmp = y * x;
	elseif (y <= -3.1e-9)
		tmp = y;
	elseif (y <= 6.2e-92)
		tmp = 0.0 - x;
	elseif (y <= 2.65e+14)
		tmp = y;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -7.8e+25], N[(y * x), $MachinePrecision], If[LessEqual[y, -3.1e-9], y, If[LessEqual[y, 6.2e-92], N[(0.0 - x), $MachinePrecision], If[LessEqual[y, 2.65e+14], y, N[(y * x), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -7.8000000000000004e25 or 2.65e14 < y

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]
   9. Step-by-step derivation

   10. Simplified 63.9%

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

   if -7.8000000000000004e25 < y < -3.10000000000000005e-9 or 6.2000000000000002e-92 < y < 2.65e14

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 70.0%

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

   if -3.10000000000000005e-9 < y < 6.2000000000000002e-92

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 81.3%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 81.3%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 81.3%

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

4. Final simplification 72.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -7.8 \cdot 10^{+25}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq -3.1 \cdot 10^{-9}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 6.2 \cdot 10^{-92}:\\ \;\;\;\;0 - x\\ \mathbf{elif}\;y \leq 2.65 \cdot 10^{+14}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 98.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(x + 1\right)\\ \mathbf{if}\;y \leq -205:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (+ x 1.0))))
   (if (<= y -205.0) t_0 (if (<= y 1.0) (- y x) t_0))))

C

double code(double x, double y) {
	double t_0 = y * (x + 1.0);
	double tmp;
	if (y <= -205.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (x + 1.0d0)
    if (y <= (-205.0d0)) then
        tmp = t_0
    else if (y <= 1.0d0) then
        tmp = y - x
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (x + 1.0);
	double tmp;
	if (y <= -205.0) {
		tmp = t_0;
	} else if (y <= 1.0) {
		tmp = y - x;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (x + 1.0)
	tmp = 0
	if y <= -205.0:
		tmp = t_0
	elif y <= 1.0:
		tmp = y - x
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(x + 1.0))
	tmp = 0.0
	if (y <= -205.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = Float64(y - x);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (x + 1.0);
	tmp = 0.0;
	if (y <= -205.0)
		tmp = t_0;
	elseif (y <= 1.0)
		tmp = y - x;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(x + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -205.0], t$95$0, If[LessEqual[y, 1.0], N[(y - x), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -205 or 1 < y

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 98.9%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 98.9%

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

   if -205 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 99.3%

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

Alternative 4: 75.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.65 \cdot 10^{+22}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 69000000000:\\ \;\;\;\;y - x\\ \mathbf{else}:\\ \;\;\;\;y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.65e+22) (* y x) (if (<= y 69000000000.0) (- y x) (* y x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.65e+22) {
		tmp = y * x;
	} else if (y <= 69000000000.0) {
		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 (y <= (-1.65d+22)) then
        tmp = y * x
    else if (y <= 69000000000.0d0) 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 (y <= -1.65e+22) {
		tmp = y * x;
	} else if (y <= 69000000000.0) {
		tmp = y - x;
	} else {
		tmp = y * x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.65e+22:
		tmp = y * x
	elif y <= 69000000000.0:
		tmp = y - x
	else:
		tmp = y * x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.65e+22)
		tmp = Float64(y * x);
	elseif (y <= 69000000000.0)
		tmp = Float64(y - x);
	else
		tmp = Float64(y * x);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.65e+22)
		tmp = y * x;
	elseif (y <= 69000000000.0)
		tmp = y - x;
	else
		tmp = y * x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.65e+22], N[(y * x), $MachinePrecision], If[LessEqual[y, 69000000000.0], N[(y - x), $MachinePrecision], N[(y * x), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.6499999999999999e22 or 6.9e10 < y

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around inf

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

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{\left(1 + x\right)}\right) \]

      2. +-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(y, \left(x + \color{blue}{1}\right)\right) \]

      3. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{*.f64}\left(y, \mathsf{+.f64}\left(x, \color{blue}{1}\right)\right) \]

   7. Simplified 100.0%

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

   8. Taylor expanded in x around inf

      \[\leadsto \mathsf{*.f64}\left(y, \color{blue}{x}\right) \]
   9. Step-by-step derivation

   10. Simplified 63.9%

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

   if -1.6499999999999999e22 < y < 6.9e10

   1. Initial program 100.0%

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

   3. Taylor expanded in x around 0

      \[\leadsto \mathsf{\_.f64}\left(\color{blue}{y}, x\right) \]
   4. Step-by-step derivation

   5. Simplified 98.1%

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

Alternative 5: 61.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-91}:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.5e-12) y (if (<= y 1.1e-91) (- 0.0 x) y)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.5e-12) {
		tmp = y;
	} else if (y <= 1.1e-91) {
		tmp = 0.0 - 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 <= (-4.5d-12)) then
        tmp = y
    else if (y <= 1.1d-91) then
        tmp = 0.0d0 - x
    else
        tmp = y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.5e-12) {
		tmp = y;
	} else if (y <= 1.1e-91) {
		tmp = 0.0 - x;
	} else {
		tmp = y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.5e-12:
		tmp = y
	elif y <= 1.1e-91:
		tmp = 0.0 - x
	else:
		tmp = y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.5e-12)
		tmp = y;
	elseif (y <= 1.1e-91)
		tmp = Float64(0.0 - x);
	else
		tmp = y;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.5e-12)
		tmp = y;
	elseif (y <= 1.1e-91)
		tmp = 0.0 - x;
	else
		tmp = y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.5e-12], y, If[LessEqual[y, 1.1e-91], N[(0.0 - x), $MachinePrecision], y]]

Derivation

1. Split input into 2 regimes

2. if y < -4.49999999999999981e-12 or 1.1e-91 < y

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0

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

   7. Simplified 45.3%

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

   if -4.49999999999999981e-12 < y < 1.1e-91

   1. Initial program 100.0%

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

      1. sub-neg N/A

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

      2. distribute-rgt1-in N/A

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

      3. *-commutative N/A

         \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

      4. associate-+l+ N/A

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

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

      6. neg-mul-1 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

      7. distribute-rgt-out N/A

         \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

      8. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

      9. +-lowering-+.f64 100.0%

         \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0

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

      1. mul-1-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-sub0 N/A

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

      3. --lowering--.f64 81.3%

         \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

   7. Simplified 81.3%

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

      1. sub0-neg N/A

         \[\leadsto \mathsf{neg}\left(x\right) \]

      2. neg-lowering-neg.f64 81.3%

         \[\leadsto \mathsf{neg.f64}\left(x\right) \]

   9. Applied egg-rr 81.3%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.5 \cdot 10^{-12}:\\ \;\;\;\;y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{-91}:\\ \;\;\;\;0 - x\\ \mathbf{else}:\\ \;\;\;\;y\\ \end{array} \]
5. 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. Step-by-step derivation

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

      \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in x around 0

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

7. Simplified 33.8%

   \[\leadsto \color{blue}{y} \]
8. 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. Step-by-step derivation

   1. sub-neg N/A

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

   2. distribute-rgt1-in N/A

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

   3. *-commutative N/A

      \[\leadsto \left(y + y \cdot x\right) + \left(\mathsf{neg}\left(x\right)\right) \]

   4. associate-+l+ N/A

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

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \color{blue}{\left(y \cdot x + \left(\mathsf{neg}\left(x\right)\right)\right)}\right) \]

   6. neg-mul-1 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(y \cdot x + -1 \cdot \color{blue}{x}\right)\right) \]

   7. distribute-rgt-out N/A

      \[\leadsto \mathsf{+.f64}\left(y, \left(x \cdot \color{blue}{\left(y + -1\right)}\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \color{blue}{\left(y + -1\right)}\right)\right) \]

   9. +-lowering-+.f64 100.0%

      \[\leadsto \mathsf{+.f64}\left(y, \mathsf{*.f64}\left(x, \mathsf{+.f64}\left(y, \color{blue}{-1}\right)\right)\right) \]

3. Simplified 100.0%

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

5. Taylor expanded in y around 0

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

   1. mul-1-neg N/A

      \[\leadsto \mathsf{neg}\left(x\right) \]

   2. neg-sub0 N/A

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

   3. --lowering--.f64 40.8%

      \[\leadsto \mathsf{\_.f64}\left(0, \color{blue}{x}\right) \]

7. Simplified 40.8%

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

   1. sub0-neg N/A

      \[\leadsto \mathsf{neg}\left(x\right) \]

   2. neg-lowering-neg.f64 40.8%

      \[\leadsto \mathsf{neg.f64}\left(x\right) \]

9. Applied egg-rr 40.8%

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

    1. neg-sub0 N/A

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

    2. flip3-- N/A

       \[\leadsto \frac{{0}^{3} - {x}^{3}}{\color{blue}{0 \cdot 0 + \left(x \cdot x + 0 \cdot x\right)}} \]

    3. metadata-eval N/A

       \[\leadsto \frac{0 - {x}^{3}}{\color{blue}{0} \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

    4. neg-sub0 N/A

       \[\leadsto \frac{\mathsf{neg}\left({x}^{3}\right)}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    5. cube-neg N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(x\right)\right)}^{3}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    6. sqr-pow N/A

       \[\leadsto \frac{{\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\mathsf{neg}\left(x\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    7. unpow-prod-down N/A

       \[\leadsto \frac{{\left(\left(\mathsf{neg}\left(x\right)\right) \cdot \left(\mathsf{neg}\left(x\right)\right)\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    8. sqr-neg N/A

       \[\leadsto \frac{{\left(x \cdot x\right)}^{\left(\frac{3}{2}\right)}}{\color{blue}{0} \cdot 0 + \left(x \cdot x + 0 \cdot x\right)} \]

    9. pow-prod-down N/A

       \[\leadsto \frac{{x}^{\left(\frac{3}{2}\right)} \cdot {x}^{\left(\frac{3}{2}\right)}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    10. sqr-pow N/A

        \[\leadsto \frac{{x}^{3}}{\color{blue}{0 \cdot 0} + \left(x \cdot x + 0 \cdot x\right)} \]

    11. metadata-eval N/A

        \[\leadsto \frac{{x}^{3}}{0 + \left(\color{blue}{x \cdot x} + 0 \cdot x\right)} \]

    12. +-lft-identity N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot x + \color{blue}{0 \cdot x}} \]

    13. distribute-rgt-out N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot \color{blue}{\left(x + 0\right)}} \]

    14. +-commutative N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot \left(0 + \color{blue}{x}\right)} \]

    15. +-lft-identity N/A

        \[\leadsto \frac{{x}^{3}}{x \cdot x} \]

    16. pow2 N/A

        \[\leadsto \frac{{x}^{3}}{{x}^{\color{blue}{2}}} \]

    17. pow-div N/A

        \[\leadsto {x}^{\color{blue}{\left(3 - 2\right)}} \]

    18. metadata-eval N/A

        \[\leadsto {x}^{1} \]

    19. unpow1 2.7%

        \[\leadsto x \]

11. Applied egg-rr 2.7%

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

Reproduce

herbie shell --seed 2024145 
(FPCore (x y)
  :name "Data.Colour.SRGB:transferFunction from colour-2.3.3"
  :precision binary64
  (- (* (+ x 1.0) y) x))