Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E

Percentage Accurate: 99.7% → 99.8%

Time: 13.1s

Alternatives: 13

Speedup: 1.0×

• 20.9% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot z \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (* (- y x) 6.0) z)))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (((y - x) * 6.0d0) * z)
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * z);
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * z)

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * z))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * z);
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(y - x, 6 \cdot z, x\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (- y x) (* 6.0 z) x))

C

double code(double x, double y, double z) {
	return fma((y - x), (6.0 * z), x);
}

Julia

function code(x, y, z)
	return fma(Float64(y - x), Float64(6.0 * z), x)
end

Wolfram

code[x_, y_, z_] := N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision] + x), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. +-commutative 99.1%

      \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot z + x} \]

   2. associate-*l* 99.8%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} + x \]

   3. fma-define 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot z, x\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 2: 61.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-54} \lor \neg \left(z \leq 2.4 \cdot 10^{-28}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -5.6e+17)
   (* -6.0 (* x z))
   (if (or (<= z -3.2e-54) (not (<= z 2.4e-28))) (* y (* 6.0 z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+17) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -3.2e-54) || !(z <= 2.4e-28)) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-5.6d+17)) then
        tmp = (-6.0d0) * (x * z)
    else if ((z <= (-3.2d-54)) .or. (.not. (z <= 2.4d-28))) then
        tmp = y * (6.0d0 * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -5.6e+17) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -3.2e-54) || !(z <= 2.4e-28)) {
		tmp = y * (6.0 * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -5.6e+17:
		tmp = -6.0 * (x * z)
	elif (z <= -3.2e-54) or not (z <= 2.4e-28):
		tmp = y * (6.0 * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -5.6e+17)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif ((z <= -3.2e-54) || !(z <= 2.4e-28))
		tmp = Float64(y * Float64(6.0 * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -5.6e+17)
		tmp = -6.0 * (x * z);
	elseif ((z <= -3.2e-54) || ~((z <= 2.4e-28)))
		tmp = y * (6.0 * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -5.6e+17], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -3.2e-54], N[Not[LessEqual[z, 2.4e-28]], $MachinePrecision]], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -5.6e17

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around 0 56.1%

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

      1. *-commutative 56.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 56.1%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -5.6e17 < z < -3.19999999999999998e-54 or 2.4000000000000002e-28 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 88.8%

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

      1. associate-*r* 89.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 89.0%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 89.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 89.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around inf 57.9%

      \[\leadsto \color{blue}{y} \cdot \left(z \cdot 6\right) \]

   if -3.19999999999999998e-54 < z < 2.4000000000000002e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 71.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.6 \cdot 10^{+17}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.2 \cdot 10^{-54} \lor \neg \left(z \leq 2.4 \cdot 10^{-28}\right):\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+16}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-54} \lor \neg \left(z \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+16)
   (* -6.0 (* x z))
   (if (or (<= z -2.6e-54) (not (<= z 4.5e-28))) (* 6.0 (* y z)) x)))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+16) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -2.6e-54) || !(z <= 4.5e-28)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d+16)) then
        tmp = (-6.0d0) * (x * z)
    else if ((z <= (-2.6d-54)) .or. (.not. (z <= 4.5d-28))) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+16) {
		tmp = -6.0 * (x * z);
	} else if ((z <= -2.6e-54) || !(z <= 4.5e-28)) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+16:
		tmp = -6.0 * (x * z)
	elif (z <= -2.6e-54) or not (z <= 4.5e-28):
		tmp = 6.0 * (y * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+16)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif ((z <= -2.6e-54) || !(z <= 4.5e-28))
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+16)
		tmp = -6.0 * (x * z);
	elseif ((z <= -2.6e-54) || ~((z <= 4.5e-28)))
		tmp = 6.0 * (y * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+16], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[z, -2.6e-54], N[Not[LessEqual[z, 4.5e-28]], $MachinePrecision]], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 3 regimes

2. if z < -2e16

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around 0 56.1%

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

      1. *-commutative 56.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 56.1%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -2e16 < z < -2.60000000000000002e-54 or 4.4999999999999998e-28 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in y around inf 57.7%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]

   if -2.60000000000000002e-54 < z < 4.4999999999999998e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 71.4%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+16}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{-54} \lor \neg \left(z \leq 4.5 \cdot 10^{-28}\right):\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e+16)
   (* z (* x -6.0))
   (if (<= z -2.5e-54) (* y (* 6.0 z)) (if (<= z 7.4e-28) x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+16) {
		tmp = z * (x * -6.0);
	} else if (z <= -2.5e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 7.4e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-1.6d+16)) then
        tmp = z * (x * (-6.0d0))
    else if (z <= (-2.5d-54)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 7.4d-28) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e+16) {
		tmp = z * (x * -6.0);
	} else if (z <= -2.5e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 7.4e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e+16:
		tmp = z * (x * -6.0)
	elif z <= -2.5e-54:
		tmp = y * (6.0 * z)
	elif z <= 7.4e-28:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e+16)
		tmp = Float64(z * Float64(x * -6.0));
	elseif (z <= -2.5e-54)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 7.4e-28)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e+16)
		tmp = z * (x * -6.0);
	elseif (z <= -2.5e-54)
		tmp = y * (6.0 * z);
	elseif (z <= 7.4e-28)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e+16], N[(z * N[(x * -6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.5e-54], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.4e-28], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -1.6e16

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around 0 56.1%

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

      1. *-commutative 56.1%

         \[\leadsto \color{blue}{\left(x \cdot z\right) \cdot -6} \]

      2. *-commutative 56.1%

         \[\leadsto \color{blue}{\left(z \cdot x\right)} \cdot -6 \]

      3. associate-*l* 56.2%

         \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   10. Simplified 56.2%

       \[\leadsto \color{blue}{z \cdot \left(x \cdot -6\right)} \]

   if -1.6e16 < z < -2.50000000000000008e-54

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.5%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 68.8%

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

      1. associate-*r* 69.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 69.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around inf 60.1%

      \[\leadsto \color{blue}{y} \cdot \left(z \cdot 6\right) \]

   if -2.50000000000000008e-54 < z < 7.40000000000000039e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 71.4%

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

   if 7.40000000000000039e-28 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in y around inf 57.0%

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

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(6 \cdot y\right) \cdot z} \]

      2. *-commutative 57.2%

         \[\leadsto \color{blue}{\left(y \cdot 6\right)} \cdot z \]

      3. *-commutative 57.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

      4. *-commutative 57.2%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot y\right)} \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{+16}:\\ \;\;\;\;z \cdot \left(x \cdot -6\right)\\ \mathbf{elif}\;z \leq -2.5 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.4 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+15}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -2e+15)
   (* -6.0 (* x z))
   (if (<= z -3e-54) (* y (* 6.0 z)) (if (<= z 7.2e-28) x (* z (* y 6.0))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+15) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 7.2e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (z <= (-2d+15)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-3d-54)) then
        tmp = y * (6.0d0 * z)
    else if (z <= 7.2d-28) then
        tmp = x
    else
        tmp = z * (y * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -2e+15) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3e-54) {
		tmp = y * (6.0 * z);
	} else if (z <= 7.2e-28) {
		tmp = x;
	} else {
		tmp = z * (y * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -2e+15:
		tmp = -6.0 * (x * z)
	elif z <= -3e-54:
		tmp = y * (6.0 * z)
	elif z <= 7.2e-28:
		tmp = x
	else:
		tmp = z * (y * 6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -2e+15)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -3e-54)
		tmp = Float64(y * Float64(6.0 * z));
	elseif (z <= 7.2e-28)
		tmp = x;
	else
		tmp = Float64(z * Float64(y * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -2e+15)
		tmp = -6.0 * (x * z);
	elseif (z <= -3e-54)
		tmp = y * (6.0 * z);
	elseif (z <= 7.2e-28)
		tmp = x;
	else
		tmp = z * (y * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -2e+15], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3e-54], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 7.2e-28], x, N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2e15

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 99.7%

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

      1. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 99.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around 0 56.1%

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

      1. *-commutative 56.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 56.1%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -2e15 < z < -3.00000000000000009e-54

   1. Initial program 99.5%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.5%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.6%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 68.8%

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

      1. associate-*r* 69.0%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 69.0%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 69.0%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 69.0%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around inf 60.1%

      \[\leadsto \color{blue}{y} \cdot \left(z \cdot 6\right) \]

   if -3.00000000000000009e-54 < z < 7.1999999999999997e-28

   1. Initial program 98.4%

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

   3. Taylor expanded in z around 0 71.4%

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

   if 7.1999999999999997e-28 < z

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in y around inf 57.0%

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

      1. associate-*r* 57.2%

         \[\leadsto \color{blue}{\left(6 \cdot y\right) \cdot z} \]

      2. *-commutative 57.2%

         \[\leadsto \color{blue}{\left(y \cdot 6\right)} \cdot z \]

      3. *-commutative 57.2%

         \[\leadsto \color{blue}{z \cdot \left(y \cdot 6\right)} \]

      4. *-commutative 57.2%

         \[\leadsto z \cdot \color{blue}{\left(6 \cdot y\right)} \]

   7. Simplified 57.2%

      \[\leadsto \color{blue}{z \cdot \left(6 \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 64.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2 \cdot 10^{+15}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3 \cdot 10^{-54}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-28}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.00086)))
   (* (- y x) (* 6.0 z))
   (+ x (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.00086)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 0.00086d0))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x + (y * (6.0d0 * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 0.00086)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 0.00086):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 0.00086))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 0.00086)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 0.00086]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 8.59999999999999979e-4 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 98.1%

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

      1. associate-*r* 98.2%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 98.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   if -0.165000000000000008 < z < 8.59999999999999979e-4

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

         \[\leadsto x + \color{blue}{\left(y \cdot z\right) \cdot 6} \]

      2. associate-*r* 99.2%

         \[\leadsto x + \color{blue}{y \cdot \left(z \cdot 6\right)} \]

   5. Simplified 99.2%

      \[\leadsto x + \color{blue}{y \cdot \left(z \cdot 6\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.145 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.145) (not (<= z 0.00086)))
   (* (- y x) (* 6.0 z))
   (+ x (* 6.0 (* y z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.145) || !(z <= 0.00086)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.145d0)) .or. (.not. (z <= 0.00086d0))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x + (6.0d0 * (y * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.145) || !(z <= 0.00086)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x + (6.0 * (y * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.145) or not (z <= 0.00086):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x + (6.0 * (y * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.145) || !(z <= 0.00086))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.145) || ~((z <= 0.00086)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x + (6.0 * (y * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.145], N[Not[LessEqual[z, 0.00086]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.14499999999999999 or 8.59999999999999979e-4 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 98.1%

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

      1. associate-*r* 98.2%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 98.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   if -0.14499999999999999 < z < 8.59999999999999979e-4

   1. Initial program 98.5%

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

   3. Taylor expanded in y around inf 99.2%

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

      1. *-commutative 99.2%

         \[\leadsto x + 6 \cdot \color{blue}{\left(z \cdot y\right)} \]

   5. Simplified 99.2%

      \[\leadsto x + \color{blue}{6 \cdot \left(z \cdot y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.145 \lor \neg \left(z \leq 0.00086\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-54} \lor \neg \left(z \leq 0.00044\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.45e-54) (not (<= z 0.00044)))
   (* (- y x) (* 6.0 z))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.45e-54) || !(z <= 0.00044)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-2.45d-54)) .or. (.not. (z <= 0.00044d0))) then
        tmp = (y - x) * (6.0d0 * z)
    else
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.45e-54) || !(z <= 0.00044)) {
		tmp = (y - x) * (6.0 * z);
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.45e-54) or not (z <= 0.00044):
		tmp = (y - x) * (6.0 * z)
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.45e-54) || !(z <= 0.00044))
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	else
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.45e-54) || ~((z <= 0.00044)))
		tmp = (y - x) * (6.0 * z);
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.45e-54], N[Not[LessEqual[z, 0.00044]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -2.4500000000000001e-54 or 4.40000000000000016e-4 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.8%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.8%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 94.9%

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

      1. associate-*r* 95.1%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 95.1%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 95.1%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 95.1%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   if -2.4500000000000001e-54 < z < 4.40000000000000016e-4

   1. Initial program 98.5%

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

   3. Taylor expanded in x around inf 70.8%

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

      1. +-commutative 70.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 70.8%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.45 \cdot 10^{-54} \lor \neg \left(z \leq 0.00044\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 74.0% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+167}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -5.8e+167)
   (* 6.0 (* y z))
   (if (<= y 2.3e+41) (* x (+ (* z -6.0) 1.0)) (* y (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+167) {
		tmp = 6.0 * (y * z);
	} else if (y <= 2.3e+41) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= (-5.8d+167)) then
        tmp = 6.0d0 * (y * z)
    else if (y <= 2.3d+41) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    else
        tmp = y * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= -5.8e+167) {
		tmp = 6.0 * (y * z);
	} else if (y <= 2.3e+41) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = y * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -5.8e+167:
		tmp = 6.0 * (y * z)
	elif y <= 2.3e+41:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = y * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -5.8e+167)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (y <= 2.3e+41)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	else
		tmp = Float64(y * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= -5.8e+167)
		tmp = 6.0 * (y * z);
	elseif (y <= 2.3e+41)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = y * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -5.8e+167], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.3e+41], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.79999999999999949e167

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.8%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in y around inf 82.6%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot z\right)} \]

   if -5.79999999999999949e167 < y < 2.2999999999999998e41

   1. Initial program 99.4%

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

   3. Taylor expanded in x around inf 77.8%

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

      1. +-commutative 77.8%

         \[\leadsto x \cdot \color{blue}{\left(-6 \cdot z + 1\right)} \]

   5. Simplified 77.8%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z + 1\right)} \]

   if 2.2999999999999998e41 < y

   1. Initial program 97.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.9%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.9%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.9%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.7%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 81.6%

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

      1. associate-*r* 81.7%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 81.7%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 81.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 81.7%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around inf 76.2%

      \[\leadsto \color{blue}{y} \cdot \left(z \cdot 6\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 78.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.8 \cdot 10^{+167}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 2.3 \cdot 10^{+41}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 61.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 3350\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 3350.0))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 3350.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.165d0)) .or. (.not. (z <= 3350.0d0))) then
        tmp = (-6.0d0) * (x * z)
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(z <= 3350.0)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.165) or not (z <= 3350.0):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(z <= 3350.0))
		tmp = Float64(-6.0 * Float64(x * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.165) || ~((z <= 3350.0)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.165], N[Not[LessEqual[z, 3350.0]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -0.165000000000000008 or 3350 < z

   1. Initial program 99.7%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. associate-*r* 99.7%

         \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

      2. +-commutative 99.7%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right) + x} \]

      3. *-commutative 99.7%

         \[\leadsto \left(y - x\right) \cdot \color{blue}{\left(z \cdot 6\right)} + x \]

      4. associate-*r* 99.6%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot z\right) \cdot 6} + x \]

      5. fma-define 99.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\left(y - x\right) \cdot z, 6, x\right)} \]

   5. Taylor expanded in z around inf 98.1%

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

      1. associate-*r* 98.2%

         \[\leadsto \color{blue}{\left(6 \cdot z\right) \cdot \left(y - x\right)} \]

      2. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(z \cdot 6\right)} \cdot \left(y - x\right) \]

      3. *-commutative 98.2%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   7. Simplified 98.2%

      \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(z \cdot 6\right)} \]

   8. Taylor expanded in y around 0 49.1%

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

      1. *-commutative 49.1%

         \[\leadsto -6 \cdot \color{blue}{\left(z \cdot x\right)} \]

   10. Simplified 49.1%

       \[\leadsto \color{blue}{-6 \cdot \left(z \cdot x\right)} \]

   if -0.165000000000000008 < z < 3350

   1. Initial program 98.6%

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

   3. Taylor expanded in z around 0 67.0%

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

4. Final simplification 59.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 3350\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(y - x\right) \cdot \left(6 \cdot z\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* (- y x) (* 6.0 z))))

C

double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * z));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((y - x) * (6.0d0 * z))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((y - x) * (6.0 * z));
}

Python

def code(x, y, z):
	return x + ((y - x) * (6.0 * z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(y - x) * Float64(6.0 * z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((y - x) * (6.0 * z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
2. Step-by-step derivation

   1. associate-*l* 99.8%

      \[\leadsto x + \color{blue}{\left(y - x\right) \cdot \left(6 \cdot z\right)} \]

3. Simplified 99.8%

   \[\leadsto \color{blue}{x + \left(y - x\right) \cdot \left(6 \cdot z\right)} \]
4. Add Preprocessing
5. Add Preprocessing

Alternative 12: 99.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + z \cdot \left(\left(y - x\right) \cdot 6\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (+ x (* z (* (- y x) 6.0))))

C

double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + (z * ((y - x) * 6.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + (z * ((y - x) * 6.0));
}

Python

def code(x, y, z):
	return x + (z * ((y - x) * 6.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(z * Float64(Float64(y - x) * 6.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (z * ((y - x) * 6.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(z * N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.1%

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

3. Final simplification 99.1%

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

Alternative 13: 36.4% accurate, 9.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 x)

C

double code(double x, double y, double z) {
	return x;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x
end function

Java

public static double code(double x, double y, double z) {
	return x;
}

Python

def code(x, y, z):
	return x

Julia

function code(x, y, z)
	return x
end

MATLAB

function tmp = code(x, y, z)
	tmp = x;
end

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.1%

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

3. Taylor expanded in z around 0 38.7%

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

Developer Target 1: 99.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x - \left(6 \cdot z\right) \cdot \left(x - y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (- x (* (* 6.0 z) (- x y))))

C

double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x - ((6.0d0 * z) * (x - y))
end function

Java

public static double code(double x, double y, double z) {
	return x - ((6.0 * z) * (x - y));
}

Python

def code(x, y, z):
	return x - ((6.0 * z) * (x - y))

Julia

function code(x, y, z)
	return Float64(x - Float64(Float64(6.0 * z) * Float64(x - y)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x - ((6.0 * z) * (x - y));
end

Wolfram

code[x_, y_, z_] := N[(x - N[(N[(6.0 * z), $MachinePrecision] * N[(x - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024152 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (! :herbie-platform default (- x (* (* 6 z) (- x y))))

  (+ x (* (* (- y x) 6.0) z)))