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

Percentage Accurate: 99.7% → 99.7%

Time: 8.4s

Alternatives: 10

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: 99.7% 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]

Derivation

1. Initial program 99.8%

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

3. Final simplification 99.8%

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

Alternative 2: 61.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+24}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-21}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -3.2e+171)
     t_0
     (if (<= z -5.6e+24)
       t_1
       (if (<= z -1.2e-21) t_0 (if (<= z 0.17) x t_1))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.2e+171) {
		tmp = t_0;
	} else if (z <= -5.6e+24) {
		tmp = t_1;
	} else if (z <= -1.2e-21) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-3.2d+171)) then
        tmp = t_0
    else if (z <= (-5.6d+24)) then
        tmp = t_1
    else if (z <= (-1.2d-21)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = -6.0 * (x * z);
	double tmp;
	if (z <= -3.2e+171) {
		tmp = t_0;
	} else if (z <= -5.6e+24) {
		tmp = t_1;
	} else if (z <= -1.2e-21) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -3.2e+171:
		tmp = t_0
	elif z <= -5.6e+24:
		tmp = t_1
	elif z <= -1.2e-21:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(-6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -3.2e+171)
		tmp = t_0;
	elseif (z <= -5.6e+24)
		tmp = t_1;
	elseif (z <= -1.2e-21)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = -6.0 * (x * z);
	tmp = 0.0;
	if (z <= -3.2e+171)
		tmp = t_0;
	elseif (z <= -5.6e+24)
		tmp = t_1;
	elseif (z <= -1.2e-21)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+171], t$95$0, If[LessEqual[z, -5.6e+24], t$95$1, If[LessEqual[z, -1.2e-21], t$95$0, If[LessEqual[z, 0.17], x, t$95$1]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.20000000000000011e171 or -5.6000000000000003e24 < z < -1.2e-21

   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* 97.3%

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

      2. +-commutative 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 99.8%

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

      5. fma-def 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 y around inf 64.6%

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

      1. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   if -3.20000000000000011e171 < z < -5.6000000000000003e24 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 65.5%

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

   4. Taylor expanded in z around inf 63.6%

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

   if -1.2e-21 < z < 0.170000000000000012

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -5.6 \cdot 10^{+24}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{-21}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+30}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))))
   (if (<= z -3.2e+171)
     t_0
     (if (<= z -1.2e+30)
       (* -6.0 (* x z))
       (if (<= z -3.7e-17) t_0 (if (<= z 0.17) x (* x (* z -6.0))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.2e+171) {
		tmp = t_0;
	} else if (z <= -1.2e+30) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.7e-17) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -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) :: t_0
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    if (z <= (-3.2d+171)) then
        tmp = t_0
    else if (z <= (-1.2d+30)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-3.7d-17)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double tmp;
	if (z <= -3.2e+171) {
		tmp = t_0;
	} else if (z <= -1.2e+30) {
		tmp = -6.0 * (x * z);
	} else if (z <= -3.7e-17) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	tmp = 0
	if z <= -3.2e+171:
		tmp = t_0
	elif z <= -1.2e+30:
		tmp = -6.0 * (x * z)
	elif z <= -3.7e-17:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -3.2e+171)
		tmp = t_0;
	elseif (z <= -1.2e+30)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -3.7e-17)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	tmp = 0.0;
	if (z <= -3.2e+171)
		tmp = t_0;
	elseif (z <= -1.2e+30)
		tmp = -6.0 * (x * z);
	elseif (z <= -3.7e-17)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.2e+171], t$95$0, If[LessEqual[z, -1.2e+30], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -3.7e-17], t$95$0, If[LessEqual[z, 0.17], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.20000000000000011e171 or -1.2e30 < z < -3.6999999999999997e-17

   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* 97.3%

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

      2. +-commutative 97.3%

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

      3. *-commutative 97.3%

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

      4. associate-*r* 99.8%

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

      5. fma-def 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 y around inf 64.6%

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

      1. *-commutative 64.6%

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

   7. Simplified 64.6%

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

   if -3.20000000000000011e171 < z < -1.2e30

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 64.5%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -3.6999999999999997e-17 < z < 0.170000000000000012

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.1%

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

   if 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 66.0%

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

   4. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.1%

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

      3. *-commutative 63.1%

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

   6. Simplified 63.1%

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

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.2 \cdot 10^{+171}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+30}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.7 \cdot 10^{-17}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.4% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-23}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -3.1e+171)
   (* z (* y 6.0))
   (if (<= z -5.8e+28)
     (* -6.0 (* x z))
     (if (<= z -7.9e-23)
       (* 6.0 (* y z))
       (if (<= z 0.17) x (* x (* z -6.0)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+171) {
		tmp = z * (y * 6.0);
	} else if (z <= -5.8e+28) {
		tmp = -6.0 * (x * z);
	} else if (z <= -7.9e-23) {
		tmp = 6.0 * (y * z);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -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 <= (-3.1d+171)) then
        tmp = z * (y * 6.0d0)
    else if (z <= (-5.8d+28)) then
        tmp = (-6.0d0) * (x * z)
    else if (z <= (-7.9d-23)) then
        tmp = 6.0d0 * (y * z)
    else if (z <= 0.17d0) then
        tmp = x
    else
        tmp = x * (z * (-6.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -3.1e+171) {
		tmp = z * (y * 6.0);
	} else if (z <= -5.8e+28) {
		tmp = -6.0 * (x * z);
	} else if (z <= -7.9e-23) {
		tmp = 6.0 * (y * z);
	} else if (z <= 0.17) {
		tmp = x;
	} else {
		tmp = x * (z * -6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -3.1e+171:
		tmp = z * (y * 6.0)
	elif z <= -5.8e+28:
		tmp = -6.0 * (x * z)
	elif z <= -7.9e-23:
		tmp = 6.0 * (y * z)
	elif z <= 0.17:
		tmp = x
	else:
		tmp = x * (z * -6.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -3.1e+171)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= -5.8e+28)
		tmp = Float64(-6.0 * Float64(x * z));
	elseif (z <= -7.9e-23)
		tmp = Float64(6.0 * Float64(y * z));
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = Float64(x * Float64(z * -6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -3.1e+171)
		tmp = z * (y * 6.0);
	elseif (z <= -5.8e+28)
		tmp = -6.0 * (x * z);
	elseif (z <= -7.9e-23)
		tmp = 6.0 * (y * z);
	elseif (z <= 0.17)
		tmp = x;
	else
		tmp = x * (z * -6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -3.1e+171], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -5.8e+28], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -7.9e-23], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.17], x, N[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -3.0999999999999999e171

   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* 96.9%

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

      2. +-commutative 96.9%

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

      3. *-commutative 96.9%

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

      4. associate-*r* 99.8%

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

      5. fma-def 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 y around inf 61.6%

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

      1. associate-*r* 61.7%

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

      2. *-commutative 61.7%

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

   7. Simplified 61.7%

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

   if -3.0999999999999999e171 < z < -5.8000000000000002e28

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 64.5%

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

   4. Taylor expanded in z around inf 64.5%

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

   if -5.8000000000000002e28 < z < -7.90000000000000041e-23

   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* 99.3%

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

      2. +-commutative 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-*r* 100.0%

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

      5. fma-def 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 y around inf 78.3%

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

      1. *-commutative 78.3%

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

   7. Simplified 78.3%

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

   if -7.90000000000000041e-23 < z < 0.170000000000000012

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 75.1%

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

   if 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 66.0%

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

   4. Taylor expanded in z around inf 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.1%

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

      3. *-commutative 63.1%

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

   6. Simplified 63.1%

      \[\leadsto \color{blue}{x \cdot \left(-6 \cdot z\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 69.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.1 \cdot 10^{+171}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -5.8 \cdot 10^{+28}:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.9 \cdot 10^{-23}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-20} \lor \neg \left(z \leq 2.3 \cdot 10^{-35}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -2.35e-20) (not (<= z 2.3e-35))) (* 6.0 (* (- y x) z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -2.35e-20) || !(z <= 2.3e-35)) {
		tmp = 6.0 * ((y - 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 <= (-2.35d-20)) .or. (.not. (z <= 2.3d-35))) then
        tmp = 6.0d0 * ((y - 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 <= -2.35e-20) || !(z <= 2.3e-35)) {
		tmp = 6.0 * ((y - x) * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -2.35e-20) or not (z <= 2.3e-35):
		tmp = 6.0 * ((y - x) * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -2.35e-20) || !(z <= 2.3e-35))
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -2.35e-20) || ~((z <= 2.3e-35)))
		tmp = 6.0 * ((y - x) * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -2.35e-20], N[Not[LessEqual[z, 2.3e-35]], $MachinePrecision]], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -2.35000000000000007e-20 or 2.2999999999999999e-35 < 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* 99.1%

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

      2. +-commutative 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-*r* 99.8%

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

      5. fma-def 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 97.2%

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

   if -2.35000000000000007e-20 < z < 2.2999999999999999e-35

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.4%

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

4. Final simplification 88.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.35 \cdot 10^{-20} \lor \neg \left(z \leq 2.3 \cdot 10^{-35}\right):\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 84.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1.6e-17)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.45e-32) x (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e-17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.45e-32) {
		tmp = x;
	} else {
		tmp = (y - x) * (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 <= (-1.6d-17)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.45d-32) then
        tmp = x
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1.6e-17) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.45e-32) {
		tmp = x;
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1.6e-17:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.45e-32:
		tmp = x
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1.6e-17)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.45e-32)
		tmp = x;
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1.6e-17)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.45e-32)
		tmp = x;
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1.6e-17], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.45e-32], x, N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.6000000000000001e-17

   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* 98.5%

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

      2. +-commutative 98.5%

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

      3. *-commutative 98.5%

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

      4. associate-*r* 99.9%

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

      5. fma-def 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 98.8%

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

   if -1.6000000000000001e-17 < z < 1.44999999999999998e-32

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 77.4%

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

   if 1.44999999999999998e-32 < 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-def 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 95.5%

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

      1. *-commutative 95.5%

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

      2. *-commutative 95.5%

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

      3. associate-*r* 95.7%

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

   7. Simplified 95.7%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.6 \cdot 10^{-17}:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.45 \cdot 10^{-32}:\\ \;\;\;\;x\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1160000000:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-23}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -1160000000.0)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.05e-23) (+ x (* 6.0 (* y z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -1160000000.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.05e-23) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (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 <= (-1160000000.0d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.05d-23) then
        tmp = x + (6.0d0 * (y * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -1160000000.0) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.05e-23) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -1160000000.0:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.05e-23:
		tmp = x + (6.0 * (y * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -1160000000.0)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.05e-23)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -1160000000.0)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.05e-23)
		tmp = x + (6.0 * (y * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -1160000000.0], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-23], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -1.16e9

   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* 98.4%

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

      2. +-commutative 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-*r* 99.9%

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

      5. fma-def 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 99.9%

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

   if -1.16e9 < z < 1.05e-23

   1. Initial program 99.8%

      \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
   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%

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

   if 1.05e-23 < 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* 99.7%

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

      5. fma-def 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 96.8%

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

      1. *-commutative 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*r* 96.9%

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

   7. Simplified 96.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000000:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-23}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.18:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.18)
   (* 6.0 (* (- y x) z))
   (if (<= z 1.05e-23) (+ x (* y (* 6.0 z))) (* (- y x) (* 6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.18) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.05e-23) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = (y - x) * (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 <= (-0.18d0)) then
        tmp = 6.0d0 * ((y - x) * z)
    else if (z <= 1.05d-23) then
        tmp = x + (y * (6.0d0 * z))
    else
        tmp = (y - x) * (6.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.18) {
		tmp = 6.0 * ((y - x) * z);
	} else if (z <= 1.05e-23) {
		tmp = x + (y * (6.0 * z));
	} else {
		tmp = (y - x) * (6.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.18:
		tmp = 6.0 * ((y - x) * z)
	elif z <= 1.05e-23:
		tmp = x + (y * (6.0 * z))
	else:
		tmp = (y - x) * (6.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.18)
		tmp = Float64(6.0 * Float64(Float64(y - x) * z));
	elseif (z <= 1.05e-23)
		tmp = Float64(x + Float64(y * Float64(6.0 * z)));
	else
		tmp = Float64(Float64(y - x) * Float64(6.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.18)
		tmp = 6.0 * ((y - x) * z);
	elseif (z <= 1.05e-23)
		tmp = x + (y * (6.0 * z));
	else
		tmp = (y - x) * (6.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.18], N[(6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 1.05e-23], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(y - x), $MachinePrecision] * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.17999999999999999

   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* 98.4%

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

      2. +-commutative 98.4%

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

      3. *-commutative 98.4%

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

      4. associate-*r* 99.9%

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

      5. fma-def 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 99.9%

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

   if -0.17999999999999999 < z < 1.05e-23

   1. Initial program 99.9%

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

   3. Taylor expanded in y around inf 99.2%

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

   4. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.2%

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

      2. *-commutative 99.2%

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

      3. associate-*r* 99.2%

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

   6. Simplified 99.2%

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

   if 1.05e-23 < 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* 99.7%

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

      5. fma-def 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 96.8%

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

      1. *-commutative 96.8%

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

      2. *-commutative 96.8%

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

      3. associate-*r* 96.9%

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

   7. Simplified 96.9%

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

4. Final simplification 98.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.18:\\ \;\;\;\;6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-23}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;\left(y - x\right) \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 61.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -1160000000.0) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -1160000000.0) || !(z <= 0.17)) {
		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 <= (-1160000000.0d0)) .or. (.not. (z <= 0.17d0))) 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 <= -1160000000.0) || !(z <= 0.17)) {
		tmp = -6.0 * (x * z);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -1160000000.0) or not (z <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -1160000000.0) || !(z <= 0.17))
		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 <= -1160000000.0) || ~((z <= 0.17)))
		tmp = -6.0 * (x * z);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -1160000000.0], N[Not[LessEqual[z, 0.17]], $MachinePrecision]], N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if z < -1.16e9 or 0.170000000000000012 < z

   1. Initial program 99.8%

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

   3. Taylor expanded in y around 0 60.0%

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

   4. Taylor expanded in z around inf 58.6%

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

   if -1.16e9 < z < 0.170000000000000012

   1. Initial program 99.8%

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

   3. Taylor expanded in z around 0 72.2%

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

4. Final simplification 65.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1160000000 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 36.3% 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 99.8%

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

3. Taylor expanded in z around 0 35.9%

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

4. Final simplification 35.9%

   \[\leadsto x \]
5. Add Preprocessing

Developer target: 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 2024027 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :herbie-target
  (- x (* (* 6.0 z) (- x y)))

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