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

Percentage Accurate: 99.7% → 99.8%

Time: 8.2s

Alternatives: 11

Speedup: 1.0×

• 20.4% 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, 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 99.4%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot z \]
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 2: 58.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49} \lor \neg \left(z \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))))
   (if (<= z -3.3e+90)
     (* z (* y 6.0))
     (if (<= z -470.0)
       t_1
       (if (<= z -4.2e-119)
         t_0
         (if (<= z 5.7e-86)
           x
           (if (<= z 5.2e-20)
             t_0
             (if (<= z 0.17)
               x
               (if (or (<= z 7.5e+49) (not (<= z 2.15e+83))) t_1 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.3e+90) {
		tmp = z * (y * 6.0);
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 5.2e-20) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 7.5e+49) || !(z <= 2.15e+83)) {
		tmp = t_1;
	} else {
		tmp = t_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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-3.3d+90)) then
        tmp = z * (y * 6.0d0)
    else if (z <= (-470.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-119)) then
        tmp = t_0
    else if (z <= 5.7d-86) then
        tmp = x
    else if (z <= 5.2d-20) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 7.5d+49) .or. (.not. (z <= 2.15d+83))) then
        tmp = t_1
    else
        tmp = t_0
    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 = x * (z * -6.0);
	double tmp;
	if (z <= -3.3e+90) {
		tmp = z * (y * 6.0);
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 5.2e-20) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 7.5e+49) || !(z <= 2.15e+83)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -3.3e+90:
		tmp = z * (y * 6.0)
	elif z <= -470.0:
		tmp = t_1
	elif z <= -4.2e-119:
		tmp = t_0
	elif z <= 5.7e-86:
		tmp = x
	elif z <= 5.2e-20:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	elif (z <= 7.5e+49) or not (z <= 2.15e+83):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.3e+90)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 5.2e-20)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 7.5e+49) || !(z <= 2.15e+83))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.3e+90)
		tmp = z * (y * 6.0);
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 5.2e-20)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 7.5e+49) || ~((z <= 2.15e+83)))
		tmp = t_1;
	else
		tmp = t_0;
	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[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.3e+90], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, -4.2e-119], t$95$0, If[LessEqual[z, 5.7e-86], x, If[LessEqual[z, 5.2e-20], t$95$0, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 7.5e+49], N[Not[LessEqual[z, 2.15e+83]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.30000000000000008e90

   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 66.8%

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

      1. *-commutative 66.8%

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

      2. associate-*r* 66.9%

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

   5. Simplified 66.9%

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

   6. Taylor expanded in z around inf 66.9%

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

      1. fma-define 66.9%

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

   8. Simplified 66.9%

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

   9. Taylor expanded in z around inf 66.3%

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

       1. associate-*r* 66.4%

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

       2. *-commutative 66.4%

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

   11. Simplified 66.4%

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

   if -3.30000000000000008e90 < z < -470 or 0.170000000000000012 < z < 7.4999999999999995e49 or 2.15e83 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 63.4%

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

   8. Simplified 63.4%

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

   if -470 < z < -4.2e-119 or 5.7000000000000004e-86 < z < 5.1999999999999999e-20 or 7.4999999999999995e49 < z < 2.15e83

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 97.4%

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

      1. *-commutative 97.4%

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

      2. associate-*r* 97.3%

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

   5. Simplified 97.3%

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

   6. Taylor expanded in z around inf 88.6%

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

      1. fma-define 88.7%

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

   8. Simplified 88.7%

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

   9. Taylor expanded in z around inf 65.8%

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

   if -4.2e-119 < z < 5.7000000000000004e-86 or 5.1999999999999999e-20 < z < 0.170000000000000012

   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 89.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.3 \cdot 10^{+90}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-20}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 7.5 \cdot 10^{+49} \lor \neg \left(z \leq 2.15 \cdot 10^{+83}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 58.4% accurate, 0.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := x \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-19}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+49} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* x (* z -6.0))))
   (if (<= z -3.4e+90)
     t_0
     (if (<= z -470.0)
       t_1
       (if (<= z -1.05e-119)
         t_0
         (if (<= z 5.7e-86)
           x
           (if (<= z 1.35e-19)
             t_0
             (if (<= z 0.17)
               x
               (if (or (<= z 2e+49) (not (<= z 9.5e+78))) t_1 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = 6.0 * (y * z);
	double t_1 = x * (z * -6.0);
	double tmp;
	if (z <= -3.4e+90) {
		tmp = t_0;
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -1.05e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 1.35e-19) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 2e+49) || !(z <= 9.5e+78)) {
		tmp = t_1;
	} else {
		tmp = t_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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = x * (z * (-6.0d0))
    if (z <= (-3.4d+90)) then
        tmp = t_0
    else if (z <= (-470.0d0)) then
        tmp = t_1
    else if (z <= (-1.05d-119)) then
        tmp = t_0
    else if (z <= 5.7d-86) then
        tmp = x
    else if (z <= 1.35d-19) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 2d+49) .or. (.not. (z <= 9.5d+78))) then
        tmp = t_1
    else
        tmp = t_0
    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 = x * (z * -6.0);
	double tmp;
	if (z <= -3.4e+90) {
		tmp = t_0;
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -1.05e-119) {
		tmp = t_0;
	} else if (z <= 5.7e-86) {
		tmp = x;
	} else if (z <= 1.35e-19) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 2e+49) || !(z <= 9.5e+78)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = x * (z * -6.0)
	tmp = 0
	if z <= -3.4e+90:
		tmp = t_0
	elif z <= -470.0:
		tmp = t_1
	elif z <= -1.05e-119:
		tmp = t_0
	elif z <= 5.7e-86:
		tmp = x
	elif z <= 1.35e-19:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	elif (z <= 2e+49) or not (z <= 9.5e+78):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(6.0 * Float64(y * z))
	t_1 = Float64(x * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -3.4e+90)
		tmp = t_0;
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -1.05e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 1.35e-19)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 2e+49) || !(z <= 9.5e+78))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = 6.0 * (y * z);
	t_1 = x * (z * -6.0);
	tmp = 0.0;
	if (z <= -3.4e+90)
		tmp = t_0;
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -1.05e-119)
		tmp = t_0;
	elseif (z <= 5.7e-86)
		tmp = x;
	elseif (z <= 1.35e-19)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 2e+49) || ~((z <= 9.5e+78)))
		tmp = t_1;
	else
		tmp = t_0;
	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[(x * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+90], t$95$0, If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, -1.05e-119], t$95$0, If[LessEqual[z, 5.7e-86], x, If[LessEqual[z, 1.35e-19], t$95$0, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 2e+49], N[Not[LessEqual[z, 9.5e+78]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.40000000000000018e90 or -470 < z < -1.05e-119 or 5.7000000000000004e-86 < z < 1.35e-19 or 1.99999999999999989e49 < z < 9.5000000000000006e78

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 80.6%

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

      1. *-commutative 80.6%

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

      2. associate-*r* 80.6%

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

   5. Simplified 80.6%

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

   6. Taylor expanded in z around inf 76.7%

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

      1. fma-define 76.7%

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

   8. Simplified 76.7%

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

   9. Taylor expanded in z around inf 66.1%

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

   if -3.40000000000000018e90 < z < -470 or 0.170000000000000012 < z < 1.99999999999999989e49 or 9.5000000000000006e78 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around inf 62.3%

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

      1. associate-*r* 62.3%

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

      2. *-commutative 62.3%

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

      3. associate-*r* 63.4%

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

   8. Simplified 63.4%

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

   if -1.05e-119 < z < 5.7000000000000004e-86 or 1.35e-19 < z < 0.170000000000000012

   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 89.0%

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

4. Final simplification 71.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+90}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{-119}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 5.7 \cdot 10^{-86}:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-19}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 2 \cdot 10^{+49} \lor \neg \left(z \leq 9.5 \cdot 10^{+78}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 59.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 6 \cdot \left(y \cdot z\right)\\ t_1 := -6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+48} \lor \neg \left(z \leq 1.4 \cdot 10^{+85}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* 6.0 (* y z))) (t_1 (* -6.0 (* x z))))
   (if (<= z -3.6e+90)
     t_0
     (if (<= z -470.0)
       t_1
       (if (<= z -4.2e-119)
         t_0
         (if (<= z 0.17)
           x
           (if (or (<= z 8.5e+48) (not (<= z 1.4e+85))) t_1 t_0)))))))

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 <= -3.6e+90) {
		tmp = t_0;
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 8.5e+48) || !(z <= 1.4e+85)) {
		tmp = t_1;
	} else {
		tmp = t_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) :: t_1
    real(8) :: tmp
    t_0 = 6.0d0 * (y * z)
    t_1 = (-6.0d0) * (x * z)
    if (z <= (-3.6d+90)) then
        tmp = t_0
    else if (z <= (-470.0d0)) then
        tmp = t_1
    else if (z <= (-4.2d-119)) then
        tmp = t_0
    else if (z <= 0.17d0) then
        tmp = x
    else if ((z <= 8.5d+48) .or. (.not. (z <= 1.4d+85))) then
        tmp = t_1
    else
        tmp = t_0
    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 <= -3.6e+90) {
		tmp = t_0;
	} else if (z <= -470.0) {
		tmp = t_1;
	} else if (z <= -4.2e-119) {
		tmp = t_0;
	} else if (z <= 0.17) {
		tmp = x;
	} else if ((z <= 8.5e+48) || !(z <= 1.4e+85)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = 6.0 * (y * z)
	t_1 = -6.0 * (x * z)
	tmp = 0
	if z <= -3.6e+90:
		tmp = t_0
	elif z <= -470.0:
		tmp = t_1
	elif z <= -4.2e-119:
		tmp = t_0
	elif z <= 0.17:
		tmp = x
	elif (z <= 8.5e+48) or not (z <= 1.4e+85):
		tmp = t_1
	else:
		tmp = t_0
	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 <= -3.6e+90)
		tmp = t_0;
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 8.5e+48) || !(z <= 1.4e+85))
		tmp = t_1;
	else
		tmp = t_0;
	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 <= -3.6e+90)
		tmp = t_0;
	elseif (z <= -470.0)
		tmp = t_1;
	elseif (z <= -4.2e-119)
		tmp = t_0;
	elseif (z <= 0.17)
		tmp = x;
	elseif ((z <= 8.5e+48) || ~((z <= 1.4e+85)))
		tmp = t_1;
	else
		tmp = t_0;
	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, -3.6e+90], t$95$0, If[LessEqual[z, -470.0], t$95$1, If[LessEqual[z, -4.2e-119], t$95$0, If[LessEqual[z, 0.17], x, If[Or[LessEqual[z, 8.5e+48], N[Not[LessEqual[z, 1.4e+85]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.6e90 or -470 < z < -4.2e-119 or 8.5000000000000001e48 < z < 1.4e85

   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 77.0%

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

      1. *-commutative 77.0%

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

      2. associate-*r* 76.9%

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

   5. Simplified 76.9%

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

   6. Taylor expanded in z around inf 74.6%

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

      1. fma-define 74.6%

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

   8. Simplified 74.6%

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

   9. Taylor expanded in z around inf 66.7%

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

   if -3.6e90 < z < -470 or 0.170000000000000012 < z < 8.5000000000000001e48 or 1.4e85 < z

   1. Initial program 99.7%

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

   3. Taylor expanded in x around inf 65.0%

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

      1. +-commutative 65.0%

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

   5. Simplified 65.0%

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

   6. Taylor expanded in z around inf 62.3%

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

   if -4.2e-119 < z < 0.170000000000000012

   1. Initial program 98.8%

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

   3. Taylor expanded in z around 0 80.1%

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

4. Final simplification 69.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.6 \cdot 10^{+90}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -470:\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.2 \cdot 10^{-119}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq 0.17:\\ \;\;\;\;x\\ \mathbf{elif}\;z \leq 8.5 \cdot 10^{+48} \lor \neg \left(z \leq 1.4 \cdot 10^{+85}\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{if}\;x \leq -6.4 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-74} \lor \neg \left(x \leq 7.6 \cdot 10^{-50}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z -6.0) 1.0))))
   (if (<= x -6.4e-28)
     t_0
     (if (<= x 2.8e-122)
       (* z (* y 6.0))
       (if (or (<= x 9e-74) (not (<= x 7.6e-50))) t_0 (* 6.0 (* y z)))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (x <= -6.4e-28) {
		tmp = t_0;
	} else if (x <= 2.8e-122) {
		tmp = z * (y * 6.0);
	} else if ((x <= 9e-74) || !(x <= 7.6e-50)) {
		tmp = t_0;
	} else {
		tmp = 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) :: t_0
    real(8) :: tmp
    t_0 = x * ((z * (-6.0d0)) + 1.0d0)
    if (x <= (-6.4d-28)) then
        tmp = t_0
    else if (x <= 2.8d-122) then
        tmp = z * (y * 6.0d0)
    else if ((x <= 9d-74) .or. (.not. (x <= 7.6d-50))) then
        tmp = t_0
    else
        tmp = 6.0d0 * (y * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (x <= -6.4e-28) {
		tmp = t_0;
	} else if (x <= 2.8e-122) {
		tmp = z * (y * 6.0);
	} else if ((x <= 9e-74) || !(x <= 7.6e-50)) {
		tmp = t_0;
	} else {
		tmp = 6.0 * (y * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * -6.0) + 1.0)
	tmp = 0
	if x <= -6.4e-28:
		tmp = t_0
	elif x <= 2.8e-122:
		tmp = z * (y * 6.0)
	elif (x <= 9e-74) or not (x <= 7.6e-50):
		tmp = t_0
	else:
		tmp = 6.0 * (y * z)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * -6.0) + 1.0))
	tmp = 0.0
	if (x <= -6.4e-28)
		tmp = t_0;
	elseif (x <= 2.8e-122)
		tmp = Float64(z * Float64(y * 6.0));
	elseif ((x <= 9e-74) || !(x <= 7.6e-50))
		tmp = t_0;
	else
		tmp = Float64(6.0 * Float64(y * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * -6.0) + 1.0);
	tmp = 0.0;
	if (x <= -6.4e-28)
		tmp = t_0;
	elseif (x <= 2.8e-122)
		tmp = z * (y * 6.0);
	elseif ((x <= 9e-74) || ~((x <= 7.6e-50)))
		tmp = t_0;
	else
		tmp = 6.0 * (y * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -6.4e-28], t$95$0, If[LessEqual[x, 2.8e-122], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 9e-74], N[Not[LessEqual[x, 7.6e-50]], $MachinePrecision]], t$95$0, N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < -6.39999999999999964e-28 or 2.7999999999999999e-122 < x < 8.9999999999999998e-74 or 7.5999999999999998e-50 < x

   1. Initial program 99.2%

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

   3. Taylor expanded in x around inf 84.7%

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

      1. +-commutative 84.7%

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

   5. Simplified 84.7%

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

   if -6.39999999999999964e-28 < x < 2.7999999999999999e-122

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*r* 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf 91.3%

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

      1. fma-define 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in z around inf 71.9%

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

       1. associate-*r* 72.0%

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

       2. *-commutative 72.0%

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

   11. Simplified 72.0%

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

   if 8.9999999999999998e-74 < x < 7.5999999999999998e-50

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*r* 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in z around inf 86.2%

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

      1. fma-define 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around inf 86.5%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6.4 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{-122}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 9 \cdot 10^{-74} \lor \neg \left(x \leq 7.6 \cdot 10^{-50}\right):\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 75.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{if}\;x \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-52}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ (* z -6.0) 1.0))))
   (if (<= x -1.8e-28)
     t_0
     (if (<= x 2.3e-121)
       (* z (* y 6.0))
       (if (<= x 2.3e-75)
         t_0
         (if (<= x 6.3e-52) (* 6.0 (* y z)) (+ x (* -6.0 (* x z)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (x <= -1.8e-28) {
		tmp = t_0;
	} else if (x <= 2.3e-121) {
		tmp = z * (y * 6.0);
	} else if (x <= 2.3e-75) {
		tmp = t_0;
	} else if (x <= 6.3e-52) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x + (-6.0 * (x * 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) :: t_0
    real(8) :: tmp
    t_0 = x * ((z * (-6.0d0)) + 1.0d0)
    if (x <= (-1.8d-28)) then
        tmp = t_0
    else if (x <= 2.3d-121) then
        tmp = z * (y * 6.0d0)
    else if (x <= 2.3d-75) then
        tmp = t_0
    else if (x <= 6.3d-52) then
        tmp = 6.0d0 * (y * z)
    else
        tmp = x + ((-6.0d0) * (x * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * ((z * -6.0) + 1.0);
	double tmp;
	if (x <= -1.8e-28) {
		tmp = t_0;
	} else if (x <= 2.3e-121) {
		tmp = z * (y * 6.0);
	} else if (x <= 2.3e-75) {
		tmp = t_0;
	} else if (x <= 6.3e-52) {
		tmp = 6.0 * (y * z);
	} else {
		tmp = x + (-6.0 * (x * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * ((z * -6.0) + 1.0)
	tmp = 0
	if x <= -1.8e-28:
		tmp = t_0
	elif x <= 2.3e-121:
		tmp = z * (y * 6.0)
	elif x <= 2.3e-75:
		tmp = t_0
	elif x <= 6.3e-52:
		tmp = 6.0 * (y * z)
	else:
		tmp = x + (-6.0 * (x * z))
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(Float64(z * -6.0) + 1.0))
	tmp = 0.0
	if (x <= -1.8e-28)
		tmp = t_0;
	elseif (x <= 2.3e-121)
		tmp = Float64(z * Float64(y * 6.0));
	elseif (x <= 2.3e-75)
		tmp = t_0;
	elseif (x <= 6.3e-52)
		tmp = Float64(6.0 * Float64(y * z));
	else
		tmp = Float64(x + Float64(-6.0 * Float64(x * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * ((z * -6.0) + 1.0);
	tmp = 0.0;
	if (x <= -1.8e-28)
		tmp = t_0;
	elseif (x <= 2.3e-121)
		tmp = z * (y * 6.0);
	elseif (x <= 2.3e-75)
		tmp = t_0;
	elseif (x <= 6.3e-52)
		tmp = 6.0 * (y * z);
	else
		tmp = x + (-6.0 * (x * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -1.8e-28], t$95$0, If[LessEqual[x, 2.3e-121], N[(z * N[(y * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-75], t$95$0, If[LessEqual[x, 6.3e-52], N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(-6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -1.7999999999999999e-28 or 2.30000000000000012e-121 < x < 2.3e-75

   1. Initial program 98.6%

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

   3. Taylor expanded in x around inf 83.2%

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

      1. +-commutative 83.2%

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

   5. Simplified 83.2%

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

   if -1.7999999999999999e-28 < x < 2.30000000000000012e-121

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 91.3%

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

      1. *-commutative 91.3%

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

      2. associate-*r* 91.3%

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

   5. Simplified 91.3%

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

   6. Taylor expanded in z around inf 91.3%

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

      1. fma-define 91.4%

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

   8. Simplified 91.4%

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

   9. Taylor expanded in z around inf 71.9%

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

       1. associate-*r* 72.0%

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

       2. *-commutative 72.0%

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

   11. Simplified 72.0%

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

   if 2.3e-75 < x < 6.3000000000000003e-52

   1. Initial program 99.1%

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

   3. Taylor expanded in y around inf 87.1%

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

      1. *-commutative 87.1%

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

      2. associate-*r* 87.1%

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

   5. Simplified 87.1%

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

   6. Taylor expanded in z around inf 86.2%

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

      1. fma-define 86.2%

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

   8. Simplified 86.2%

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

   9. Taylor expanded in z around inf 86.5%

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

   if 6.3000000000000003e-52 < x

   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 0 86.1%

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

4. Final simplification 79.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.8 \cdot 10^{-28}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-121}:\\ \;\;\;\;z \cdot \left(y \cdot 6\right)\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-75}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{elif}\;x \leq 6.3 \cdot 10^{-52}:\\ \;\;\;\;6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + -6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-16} \lor \neg \left(y \leq 2.8 \cdot 10^{-77}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= y -3.2e-16) (not (<= y 2.8e-77)))
   (+ x (* 6.0 (* y z)))
   (* x (+ (* z -6.0) 1.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((y <= -3.2e-16) || !(y <= 2.8e-77)) {
		tmp = x + (6.0 * (y * 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 ((y <= (-3.2d-16)) .or. (.not. (y <= 2.8d-77))) then
        tmp = x + (6.0d0 * (y * 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 ((y <= -3.2e-16) || !(y <= 2.8e-77)) {
		tmp = x + (6.0 * (y * z));
	} else {
		tmp = x * ((z * -6.0) + 1.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (y <= -3.2e-16) or not (y <= 2.8e-77):
		tmp = x + (6.0 * (y * z))
	else:
		tmp = x * ((z * -6.0) + 1.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((y <= -3.2e-16) || !(y <= 2.8e-77))
		tmp = Float64(x + Float64(6.0 * Float64(y * 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 ((y <= -3.2e-16) || ~((y <= 2.8e-77)))
		tmp = x + (6.0 * (y * z));
	else
		tmp = x * ((z * -6.0) + 1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[y, -3.2e-16], N[Not[LessEqual[y, 2.8e-77]], $MachinePrecision]], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.20000000000000023e-16 or 2.7999999999999999e-77 < y

   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 88.5%

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

      1. *-commutative 88.5%

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

   5. Simplified 88.5%

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

   if -3.20000000000000023e-16 < y < 2.7999999999999999e-77

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 88.2%

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

      1. +-commutative 88.2%

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

   5. Simplified 88.2%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.2 \cdot 10^{-16} \lor \neg \left(y \leq 2.8 \cdot 10^{-77}\right):\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 87.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-16}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y -1.35e-16)
   (+ x (* 6.0 (* y z)))
   (if (<= y 1.2e-76) (* x (+ (* z -6.0) 1.0)) (+ x (* y (* 6.0 z))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= -1.35e-16) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.2e-76) {
		tmp = x * ((z * -6.0) + 1.0);
	} 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 (y <= (-1.35d-16)) then
        tmp = x + (6.0d0 * (y * z))
    else if (y <= 1.2d-76) then
        tmp = x * ((z * (-6.0d0)) + 1.0d0)
    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 (y <= -1.35e-16) {
		tmp = x + (6.0 * (y * z));
	} else if (y <= 1.2e-76) {
		tmp = x * ((z * -6.0) + 1.0);
	} else {
		tmp = x + (y * (6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= -1.35e-16:
		tmp = x + (6.0 * (y * z))
	elif y <= 1.2e-76:
		tmp = x * ((z * -6.0) + 1.0)
	else:
		tmp = x + (y * (6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= -1.35e-16)
		tmp = Float64(x + Float64(6.0 * Float64(y * z)));
	elseif (y <= 1.2e-76)
		tmp = Float64(x * Float64(Float64(z * -6.0) + 1.0));
	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 (y <= -1.35e-16)
		tmp = x + (6.0 * (y * z));
	elseif (y <= 1.2e-76)
		tmp = x * ((z * -6.0) + 1.0);
	else
		tmp = x + (y * (6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, -1.35e-16], N[(x + N[(6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.2e-76], N[(x * N[(N[(z * -6.0), $MachinePrecision] + 1.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(y * N[(6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.35e-16

   1. Initial program 99.7%

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

   3. Taylor expanded in y around inf 87.6%

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

      1. *-commutative 87.6%

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

   5. Simplified 87.6%

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

   if -1.35e-16 < y < 1.20000000000000007e-76

   1. Initial program 98.9%

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

   3. Taylor expanded in x around inf 88.2%

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

      1. +-commutative 88.2%

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

   5. Simplified 88.2%

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

   if 1.20000000000000007e-76 < y

   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 89.4%

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

      1. *-commutative 89.4%

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

      2. associate-*r* 89.6%

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

   5. Simplified 89.6%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.35 \cdot 10^{-16}:\\ \;\;\;\;x + 6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;y \leq 1.2 \cdot 10^{-76}:\\ \;\;\;\;x \cdot \left(z \cdot -6 + 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \left(6 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 60.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.165) (not (<= z 0.17))) (* -6.0 (* x z)) x))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.165) || !(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 <= (-0.165d0)) .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 <= -0.165) || !(z <= 0.17)) {
		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 <= 0.17):
		tmp = -6.0 * (x * z)
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.165) || !(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 <= -0.165) || ~((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, -0.165], 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 < -0.165000000000000008 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 x around inf 53.8%

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

      1. +-commutative 53.8%

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

   5. Simplified 53.8%

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

   6. Taylor expanded in z around inf 52.1%

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

   if -0.165000000000000008 < z < 0.170000000000000012

   1. Initial program 98.9%

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

   3. Taylor expanded in z around 0 72.5%

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

4. Final simplification 60.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.165 \lor \neg \left(z \leq 0.17\right):\\ \;\;\;\;-6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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 99.4%

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

3. Final simplification 99.4%

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

Alternative 11: 37.2% 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 99.4%

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

3. Taylor expanded in z around 0 32.4%

   \[\leadsto \color{blue}{x} \]
4. 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 2024085 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, E"
  :precision binary64

  :alt
  (- x (* (* 6.0 z) (- x y)))

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