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

Percentage Accurate: 99.5% → 99.8%

Time: 10.2s

Alternatives: 16

Speedup: 1.2×

• 21.7% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - 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) * ((2.0d0 / 3.0d0) - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * ((2.0 / 3.0) - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(Float64(2.0 / 3.0) - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * ((2.0 / 3.0) - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(N[(2.0 / 3.0), $MachinePrecision] - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ x + \left(-6 \cdot \left(z \cdot \left(y - x\right)\right) + \left(y - x\right) \cdot 4\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (+ (* -6.0 (* z (- y x))) (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

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 + (((-6.0d0) * (z * (y - x))) + ((y - x) * 4.0d0))
end function

Java

public static double code(double x, double y, double z) {
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
}

Python

def code(x, y, z):
	return x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(-6.0 * Float64(z * Float64(y - x))) + Float64(Float64(y - x) * 4.0)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + ((-6.0 * (z * (y - x))) + ((y - x) * 4.0));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in z around 0 99.8%

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

5. Final simplification 99.8%

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

Alternative 2: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -8.8 \cdot 10^{+266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168} \lor \neg \left(z \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -8.8e+266)
     t_0
     (if (<= z -7.2e+170)
       t_1
       (if (<= z -7.2e+89)
         t_0
         (if (<= z -1.1e+42)
           t_1
           (if (<= z -3.4e-11)
             t_0
             (if (<= z -2.3e-176)
               (* y 4.0)
               (if (<= z -1.3e-232)
                 (* x -3.0)
                 (if (<= z 2.5e-301)
                   (* y 4.0)
                   (if (<= z 1.36e-127)
                     (* x -3.0)
                     (if (<= z 5.4e-108)
                       (* y 4.0)
                       (if (<= z 0.5)
                         (* x -3.0)
                         (if (or (<= z 6.9e+168) (not (<= z 4.1e+207)))
                           t_1
                           t_0))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.8e+266) {
		tmp = t_0;
	} else if (z <= -7.2e+170) {
		tmp = t_1;
	} else if (z <= -7.2e+89) {
		tmp = t_0;
	} else if (z <= -1.1e+42) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -2.3e-176) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-232) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.36e-127) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 6.9e+168) || !(z <= 4.1e+207)) {
		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) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-8.8d+266)) then
        tmp = t_0
    else if (z <= (-7.2d+170)) then
        tmp = t_1
    else if (z <= (-7.2d+89)) then
        tmp = t_0
    else if (z <= (-1.1d+42)) then
        tmp = t_1
    else if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-2.3d-176)) then
        tmp = y * 4.0d0
    else if (z <= (-1.3d-232)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-301) then
        tmp = y * 4.0d0
    else if (z <= 1.36d-127) then
        tmp = x * (-3.0d0)
    else if (z <= 5.4d-108) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if ((z <= 6.9d+168) .or. (.not. (z <= 4.1d+207))) 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 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -8.8e+266) {
		tmp = t_0;
	} else if (z <= -7.2e+170) {
		tmp = t_1;
	} else if (z <= -7.2e+89) {
		tmp = t_0;
	} else if (z <= -1.1e+42) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -2.3e-176) {
		tmp = y * 4.0;
	} else if (z <= -1.3e-232) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.36e-127) {
		tmp = x * -3.0;
	} else if (z <= 5.4e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if ((z <= 6.9e+168) || !(z <= 4.1e+207)) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -8.8e+266:
		tmp = t_0
	elif z <= -7.2e+170:
		tmp = t_1
	elif z <= -7.2e+89:
		tmp = t_0
	elif z <= -1.1e+42:
		tmp = t_1
	elif z <= -3.4e-11:
		tmp = t_0
	elif z <= -2.3e-176:
		tmp = y * 4.0
	elif z <= -1.3e-232:
		tmp = x * -3.0
	elif z <= 2.5e-301:
		tmp = y * 4.0
	elif z <= 1.36e-127:
		tmp = x * -3.0
	elif z <= 5.4e-108:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif (z <= 6.9e+168) or not (z <= 4.1e+207):
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -8.8e+266)
		tmp = t_0;
	elseif (z <= -7.2e+170)
		tmp = t_1;
	elseif (z <= -7.2e+89)
		tmp = t_0;
	elseif (z <= -1.1e+42)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -2.3e-176)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.3e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.36e-127)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.4e-108)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif ((z <= 6.9e+168) || !(z <= 4.1e+207))
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -8.8e+266)
		tmp = t_0;
	elseif (z <= -7.2e+170)
		tmp = t_1;
	elseif (z <= -7.2e+89)
		tmp = t_0;
	elseif (z <= -1.1e+42)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -2.3e-176)
		tmp = y * 4.0;
	elseif (z <= -1.3e-232)
		tmp = x * -3.0;
	elseif (z <= 2.5e-301)
		tmp = y * 4.0;
	elseif (z <= 1.36e-127)
		tmp = x * -3.0;
	elseif (z <= 5.4e-108)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif ((z <= 6.9e+168) || ~((z <= 4.1e+207)))
		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[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -8.8e+266], t$95$0, If[LessEqual[z, -7.2e+170], t$95$1, If[LessEqual[z, -7.2e+89], t$95$0, If[LessEqual[z, -1.1e+42], t$95$1, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -2.3e-176], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.3e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.36e-127], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.4e-108], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[Or[LessEqual[z, 6.9e+168], N[Not[LessEqual[z, 4.1e+207]], $MachinePrecision]], t$95$1, t$95$0]]]]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -8.7999999999999996e266 or -7.1999999999999999e170 < z < -7.2e89 or -1.1000000000000001e42 < z < -3.3999999999999999e-11 or 6.8999999999999998e168 < z < 4.1e207

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 93.3%

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

      1. associate-*r* 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

   10. Simplified 79.2%

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

   if -8.7999999999999996e266 < z < -7.1999999999999999e170 or -7.2e89 < z < -1.1000000000000001e42 or 0.5 < z < 6.8999999999999998e168 or 4.1e207 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.9%

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

      1. associate-*r* 97.8%

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

      2. *-commutative 97.8%

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

      3. associate-*l* 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0 72.5%

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

   if -3.3999999999999999e-11 < z < -2.3000000000000001e-176 or -1.29999999999999998e-232 < z < 2.50000000000000006e-301 or 1.3599999999999999e-127 < z < 5.4000000000000001e-108

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -2.3000000000000001e-176 < z < -1.29999999999999998e-232 or 2.50000000000000006e-301 < z < 1.3599999999999999e-127 or 5.4000000000000001e-108 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -8.8 \cdot 10^{+266}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+170}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7.2 \cdot 10^{+89}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.1 \cdot 10^{+42}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.3 \cdot 10^{-176}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.36 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.4 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168} \lor \neg \left(z \leq 4.1 \cdot 10^{+207}\right):\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 3: 50.5% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.6 \cdot 10^{+266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+95}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -2.6e+266)
     t_0
     (if (<= z -2.6e+172)
       t_1
       (if (<= z -4.9e+95)
         t_0
         (if (<= z -1.05e+42)
           t_1
           (if (<= z -3.4e-11)
             t_0
             (if (<= z -2.7e-180)
               (* y 4.0)
               (if (<= z -1.36e-232)
                 (* x -3.0)
                 (if (<= z 6.5e-301)
                   (* y 4.0)
                   (if (<= z 1.8e-130)
                     (* x -3.0)
                     (if (<= z 6.2e-107)
                       (* y 4.0)
                       (if (<= z 0.5)
                         (* x -3.0)
                         (if (<= z 6.9e+168)
                           (* x (* z 6.0))
                           (if (<= z 5.8e+207) t_0 t_1)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.6e+266) {
		tmp = t_0;
	} else if (z <= -2.6e+172) {
		tmp = t_1;
	} else if (z <= -4.9e+95) {
		tmp = t_0;
	} else if (z <= -1.05e+42) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -2.7e-180) {
		tmp = y * 4.0;
	} else if (z <= -1.36e-232) {
		tmp = x * -3.0;
	} else if (z <= 6.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-130) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.9e+168) {
		tmp = x * (z * 6.0);
	} else if (z <= 5.8e+207) {
		tmp = t_0;
	} 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) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-2.6d+266)) then
        tmp = t_0
    else if (z <= (-2.6d+172)) then
        tmp = t_1
    else if (z <= (-4.9d+95)) then
        tmp = t_0
    else if (z <= (-1.05d+42)) then
        tmp = t_1
    else if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-2.7d-180)) then
        tmp = y * 4.0d0
    else if (z <= (-1.36d-232)) then
        tmp = x * (-3.0d0)
    else if (z <= 6.5d-301) then
        tmp = y * 4.0d0
    else if (z <= 1.8d-130) then
        tmp = x * (-3.0d0)
    else if (z <= 6.2d-107) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 6.9d+168) then
        tmp = x * (z * 6.0d0)
    else if (z <= 5.8d+207) then
        tmp = t_0
    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 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.6e+266) {
		tmp = t_0;
	} else if (z <= -2.6e+172) {
		tmp = t_1;
	} else if (z <= -4.9e+95) {
		tmp = t_0;
	} else if (z <= -1.05e+42) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -2.7e-180) {
		tmp = y * 4.0;
	} else if (z <= -1.36e-232) {
		tmp = x * -3.0;
	} else if (z <= 6.5e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.8e-130) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.9e+168) {
		tmp = x * (z * 6.0);
	} else if (z <= 5.8e+207) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.6e+266:
		tmp = t_0
	elif z <= -2.6e+172:
		tmp = t_1
	elif z <= -4.9e+95:
		tmp = t_0
	elif z <= -1.05e+42:
		tmp = t_1
	elif z <= -3.4e-11:
		tmp = t_0
	elif z <= -2.7e-180:
		tmp = y * 4.0
	elif z <= -1.36e-232:
		tmp = x * -3.0
	elif z <= 6.5e-301:
		tmp = y * 4.0
	elif z <= 1.8e-130:
		tmp = x * -3.0
	elif z <= 6.2e-107:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 6.9e+168:
		tmp = x * (z * 6.0)
	elif z <= 5.8e+207:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.6e+266)
		tmp = t_0;
	elseif (z <= -2.6e+172)
		tmp = t_1;
	elseif (z <= -4.9e+95)
		tmp = t_0;
	elseif (z <= -1.05e+42)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -2.7e-180)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.36e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.5e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.8e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.2e-107)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.9e+168)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= 5.8e+207)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.6e+266)
		tmp = t_0;
	elseif (z <= -2.6e+172)
		tmp = t_1;
	elseif (z <= -4.9e+95)
		tmp = t_0;
	elseif (z <= -1.05e+42)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -2.7e-180)
		tmp = y * 4.0;
	elseif (z <= -1.36e-232)
		tmp = x * -3.0;
	elseif (z <= 6.5e-301)
		tmp = y * 4.0;
	elseif (z <= 1.8e-130)
		tmp = x * -3.0;
	elseif (z <= 6.2e-107)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 6.9e+168)
		tmp = x * (z * 6.0);
	elseif (z <= 5.8e+207)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.6e+266], t$95$0, If[LessEqual[z, -2.6e+172], t$95$1, If[LessEqual[z, -4.9e+95], t$95$0, If[LessEqual[z, -1.05e+42], t$95$1, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -2.7e-180], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.36e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.5e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.8e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.2e-107], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.9e+168], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+207], t$95$0, t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.60000000000000014e266 or -2.6e172 < z < -4.8999999999999999e95 or -1.04999999999999998e42 < z < -3.3999999999999999e-11 or 6.8999999999999998e168 < z < 5.79999999999999994e207

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 93.3%

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

      1. associate-*r* 93.2%

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

      2. *-commutative 93.2%

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

      3. associate-*l* 93.3%

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

   7. Simplified 93.3%

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

   8. Taylor expanded in y around inf 79.2%

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

      1. *-commutative 79.2%

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

   10. Simplified 79.2%

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

   if -2.60000000000000014e266 < z < -2.6e172 or -4.8999999999999999e95 < z < -1.04999999999999998e42 or 5.79999999999999994e207 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 78.4%

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

   if -3.3999999999999999e-11 < z < -2.70000000000000014e-180 or -1.3600000000000001e-232 < z < 6.49999999999999991e-301 or 1.8000000000000001e-130 < z < 6.20000000000000043e-107

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -2.70000000000000014e-180 < z < -1.3600000000000001e-232 or 6.49999999999999991e-301 < z < 1.8000000000000001e-130 or 6.20000000000000043e-107 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.5 < z < 6.8999999999999998e168

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 67.4%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 67.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 67.5%

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

      4. neg-mul-1 67.5%

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

      5. associate-*r* 67.5%

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

      6. *-commutative 67.5%

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

      7. associate-+r+ 67.5%

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

      8. metadata-eval 67.5%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 67.5%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 67.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 67.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around inf 64.2%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.6 \cdot 10^{+266}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -4.9 \cdot 10^{+95}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+42}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.36 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.5 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 4: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+266}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -2.9e+266)
     t_0
     (if (<= z -2.6e+172)
       t_1
       (if (<= z -1.9e+90)
         t_0
         (if (<= z -5.5e+39)
           t_1
           (if (<= z -3.4e-11)
             t_0
             (if (<= z -3.9e-182)
               (* y 4.0)
               (if (<= z -1.7e-232)
                 (* x -3.0)
                 (if (<= z 3.4e-301)
                   (* y 4.0)
                   (if (<= z 2.75e-129)
                     (* x -3.0)
                     (if (<= z 4.5e-108)
                       (* y 4.0)
                       (if (<= z 0.5)
                         (* x -3.0)
                         (if (<= z 7e+168)
                           (* x (* z 6.0))
                           (if (<= z 4.4e+207)
                             (* z (* -6.0 y))
                             t_1)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.9e+266) {
		tmp = t_0;
	} else if (z <= -2.6e+172) {
		tmp = t_1;
	} else if (z <= -1.9e+90) {
		tmp = t_0;
	} else if (z <= -5.5e+39) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -3.9e-182) {
		tmp = y * 4.0;
	} else if (z <= -1.7e-232) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.75e-129) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7e+168) {
		tmp = x * (z * 6.0);
	} else if (z <= 4.4e+207) {
		tmp = z * (-6.0 * y);
	} 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) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-2.9d+266)) then
        tmp = t_0
    else if (z <= (-2.6d+172)) then
        tmp = t_1
    else if (z <= (-1.9d+90)) then
        tmp = t_0
    else if (z <= (-5.5d+39)) then
        tmp = t_1
    else if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-3.9d-182)) then
        tmp = y * 4.0d0
    else if (z <= (-1.7d-232)) then
        tmp = x * (-3.0d0)
    else if (z <= 3.4d-301) then
        tmp = y * 4.0d0
    else if (z <= 2.75d-129) then
        tmp = x * (-3.0d0)
    else if (z <= 4.5d-108) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 7d+168) then
        tmp = x * (z * 6.0d0)
    else if (z <= 4.4d+207) then
        tmp = z * ((-6.0d0) * y)
    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 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -2.9e+266) {
		tmp = t_0;
	} else if (z <= -2.6e+172) {
		tmp = t_1;
	} else if (z <= -1.9e+90) {
		tmp = t_0;
	} else if (z <= -5.5e+39) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -3.9e-182) {
		tmp = y * 4.0;
	} else if (z <= -1.7e-232) {
		tmp = x * -3.0;
	} else if (z <= 3.4e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.75e-129) {
		tmp = x * -3.0;
	} else if (z <= 4.5e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 7e+168) {
		tmp = x * (z * 6.0);
	} else if (z <= 4.4e+207) {
		tmp = z * (-6.0 * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -2.9e+266:
		tmp = t_0
	elif z <= -2.6e+172:
		tmp = t_1
	elif z <= -1.9e+90:
		tmp = t_0
	elif z <= -5.5e+39:
		tmp = t_1
	elif z <= -3.4e-11:
		tmp = t_0
	elif z <= -3.9e-182:
		tmp = y * 4.0
	elif z <= -1.7e-232:
		tmp = x * -3.0
	elif z <= 3.4e-301:
		tmp = y * 4.0
	elif z <= 2.75e-129:
		tmp = x * -3.0
	elif z <= 4.5e-108:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 7e+168:
		tmp = x * (z * 6.0)
	elif z <= 4.4e+207:
		tmp = z * (-6.0 * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -2.9e+266)
		tmp = t_0;
	elseif (z <= -2.6e+172)
		tmp = t_1;
	elseif (z <= -1.9e+90)
		tmp = t_0;
	elseif (z <= -5.5e+39)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -3.9e-182)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.7e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 3.4e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.75e-129)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.5e-108)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e+168)
		tmp = Float64(x * Float64(z * 6.0));
	elseif (z <= 4.4e+207)
		tmp = Float64(z * Float64(-6.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -2.9e+266)
		tmp = t_0;
	elseif (z <= -2.6e+172)
		tmp = t_1;
	elseif (z <= -1.9e+90)
		tmp = t_0;
	elseif (z <= -5.5e+39)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -3.9e-182)
		tmp = y * 4.0;
	elseif (z <= -1.7e-232)
		tmp = x * -3.0;
	elseif (z <= 3.4e-301)
		tmp = y * 4.0;
	elseif (z <= 2.75e-129)
		tmp = x * -3.0;
	elseif (z <= 4.5e-108)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 7e+168)
		tmp = x * (z * 6.0);
	elseif (z <= 4.4e+207)
		tmp = z * (-6.0 * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+266], t$95$0, If[LessEqual[z, -2.6e+172], t$95$1, If[LessEqual[z, -1.9e+90], t$95$0, If[LessEqual[z, -5.5e+39], t$95$1, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -3.9e-182], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.7e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3.4e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.75e-129], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.5e-108], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e+168], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 4.4e+207], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -2.90000000000000017e266 or -2.6e172 < z < -1.9000000000000001e90 or -5.4999999999999997e39 < z < -3.3999999999999999e-11

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 91.3%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-*l* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in y around inf 73.0%

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

      1. *-commutative 73.0%

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

   10. Simplified 73.0%

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

   if -2.90000000000000017e266 < z < -2.6e172 or -1.9000000000000001e90 < z < -5.4999999999999997e39 or 4.40000000000000017e207 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 78.4%

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

   if -3.3999999999999999e-11 < z < -3.9e-182 or -1.7000000000000001e-232 < z < 3.4000000000000002e-301 or 2.75000000000000012e-129 < z < 4.4999999999999997e-108

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -3.9e-182 < z < -1.7000000000000001e-232 or 3.4000000000000002e-301 < z < 2.75000000000000012e-129 or 4.4999999999999997e-108 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.5 < z < 7.0000000000000004e168

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 67.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 67.4%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 67.5%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 67.5%

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

      4. neg-mul-1 67.5%

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

      5. associate-*r* 67.5%

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

      6. *-commutative 67.5%

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

      7. associate-+r+ 67.5%

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

      8. metadata-eval 67.5%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 67.5%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 67.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 67.5%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 67.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around inf 64.2%

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

   if 7.0000000000000004e168 < z < 4.40000000000000017e207

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+266}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -2.6 \cdot 10^{+172}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -1.9 \cdot 10^{+90}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -5.5 \cdot 10^{+39}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.9 \cdot 10^{-182}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.75 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.5 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{+168}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 5: 50.6% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1.35 \cdot 10^{+267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1.35e+267)
     t_0
     (if (<= z -1.5e+172)
       t_1
       (if (<= z -2.8e+86)
         t_0
         (if (<= z -1.85e+43)
           t_1
           (if (<= z -3.4e-11)
             t_0
             (if (<= z -3.3e-175)
               (* y 4.0)
               (if (<= z -3.4e-230)
                 (* x -3.0)
                 (if (<= z 1.75e-301)
                   (* y 4.0)
                   (if (<= z 6.8e-129)
                     (* x -3.0)
                     (if (<= z 2.5e-106)
                       (* y 4.0)
                       (if (<= z 0.5)
                         (* x -3.0)
                         (if (<= z 6.9e+168)
                           (* z (* x 6.0))
                           (if (<= z 5.8e+207)
                             (* z (* -6.0 y))
                             t_1)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.35e+267) {
		tmp = t_0;
	} else if (z <= -1.5e+172) {
		tmp = t_1;
	} else if (z <= -2.8e+86) {
		tmp = t_0;
	} else if (z <= -1.85e+43) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -3.3e-175) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-301) {
		tmp = y * 4.0;
	} else if (z <= 6.8e-129) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-106) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.9e+168) {
		tmp = z * (x * 6.0);
	} else if (z <= 5.8e+207) {
		tmp = z * (-6.0 * y);
	} 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) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1.35d+267)) then
        tmp = t_0
    else if (z <= (-1.5d+172)) then
        tmp = t_1
    else if (z <= (-2.8d+86)) then
        tmp = t_0
    else if (z <= (-1.85d+43)) then
        tmp = t_1
    else if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-3.3d-175)) then
        tmp = y * 4.0d0
    else if (z <= (-3.4d-230)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.75d-301) then
        tmp = y * 4.0d0
    else if (z <= 6.8d-129) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-106) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 6.9d+168) then
        tmp = z * (x * 6.0d0)
    else if (z <= 5.8d+207) then
        tmp = z * ((-6.0d0) * y)
    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 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1.35e+267) {
		tmp = t_0;
	} else if (z <= -1.5e+172) {
		tmp = t_1;
	} else if (z <= -2.8e+86) {
		tmp = t_0;
	} else if (z <= -1.85e+43) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -3.3e-175) {
		tmp = y * 4.0;
	} else if (z <= -3.4e-230) {
		tmp = x * -3.0;
	} else if (z <= 1.75e-301) {
		tmp = y * 4.0;
	} else if (z <= 6.8e-129) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-106) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.9e+168) {
		tmp = z * (x * 6.0);
	} else if (z <= 5.8e+207) {
		tmp = z * (-6.0 * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1.35e+267:
		tmp = t_0
	elif z <= -1.5e+172:
		tmp = t_1
	elif z <= -2.8e+86:
		tmp = t_0
	elif z <= -1.85e+43:
		tmp = t_1
	elif z <= -3.4e-11:
		tmp = t_0
	elif z <= -3.3e-175:
		tmp = y * 4.0
	elif z <= -3.4e-230:
		tmp = x * -3.0
	elif z <= 1.75e-301:
		tmp = y * 4.0
	elif z <= 6.8e-129:
		tmp = x * -3.0
	elif z <= 2.5e-106:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 6.9e+168:
		tmp = z * (x * 6.0)
	elif z <= 5.8e+207:
		tmp = z * (-6.0 * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1.35e+267)
		tmp = t_0;
	elseif (z <= -1.5e+172)
		tmp = t_1;
	elseif (z <= -2.8e+86)
		tmp = t_0;
	elseif (z <= -1.85e+43)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -3.3e-175)
		tmp = Float64(y * 4.0);
	elseif (z <= -3.4e-230)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.75e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 6.8e-129)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-106)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.9e+168)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= 5.8e+207)
		tmp = Float64(z * Float64(-6.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1.35e+267)
		tmp = t_0;
	elseif (z <= -1.5e+172)
		tmp = t_1;
	elseif (z <= -2.8e+86)
		tmp = t_0;
	elseif (z <= -1.85e+43)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -3.3e-175)
		tmp = y * 4.0;
	elseif (z <= -3.4e-230)
		tmp = x * -3.0;
	elseif (z <= 1.75e-301)
		tmp = y * 4.0;
	elseif (z <= 6.8e-129)
		tmp = x * -3.0;
	elseif (z <= 2.5e-106)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 6.9e+168)
		tmp = z * (x * 6.0);
	elseif (z <= 5.8e+207)
		tmp = z * (-6.0 * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1.35e+267], t$95$0, If[LessEqual[z, -1.5e+172], t$95$1, If[LessEqual[z, -2.8e+86], t$95$0, If[LessEqual[z, -1.85e+43], t$95$1, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -3.3e-175], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -3.4e-230], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.75e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 6.8e-129], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-106], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.9e+168], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 5.8e+207], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -1.3500000000000001e267 or -1.5e172 < z < -2.80000000000000004e86 or -1.85e43 < z < -3.3999999999999999e-11

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 91.3%

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

      1. associate-*r* 91.1%

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

      2. *-commutative 91.1%

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

      3. associate-*l* 91.3%

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

   7. Simplified 91.3%

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

   8. Taylor expanded in y around inf 73.0%

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

      1. *-commutative 73.0%

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

   10. Simplified 73.0%

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

   if -1.3500000000000001e267 < z < -1.5e172 or -2.80000000000000004e86 < z < -1.85e43 or 5.79999999999999994e207 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 78.4%

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

   if -3.3999999999999999e-11 < z < -3.29999999999999999e-175 or -3.4e-230 < z < 1.74999999999999996e-301 or 6.80000000000000026e-129 < z < 2.49999999999999991e-106

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -3.29999999999999999e-175 < z < -3.4e-230 or 1.74999999999999996e-301 < z < 6.80000000000000026e-129 or 2.49999999999999991e-106 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.5 < z < 6.8999999999999998e168

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l* 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in y around 0 64.2%

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

      1. associate-*r* 64.2%

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

      2. *-commutative 64.2%

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

   10. Simplified 64.2%

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

   if 6.8999999999999998e168 < z < 5.79999999999999994e207

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 100.0%

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

   10. Simplified 100.0%

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

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1.35 \cdot 10^{+267}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+172}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.8 \cdot 10^{+86}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.85 \cdot 10^{+43}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.3 \cdot 10^{-175}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-230}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.75 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 6.8 \cdot 10^{-129}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.9 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 5.8 \cdot 10^{+207}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 6: 50.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -1 \cdot 10^{+267}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+175}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+94}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{+40}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))) (t_1 (* 6.0 (* x z))))
   (if (<= z -1e+267)
     t_0
     (if (<= z -1.2e+175)
       t_1
       (if (<= z -6e+94)
         t_0
         (if (<= z -3.75e+40)
           t_1
           (if (<= z -3.4e-11)
             (* y (* -6.0 z))
             (if (<= z -1.15e-177)
               (* y 4.0)
               (if (<= z -8.5e-231)
                 (* x -3.0)
                 (if (<= z 7.2e-301)
                   (* y 4.0)
                   (if (<= z 2.15e-128)
                     (* x -3.0)
                     (if (<= z 1.3e-107)
                       (* y 4.0)
                       (if (<= z 0.5)
                         (* x -3.0)
                         (if (<= z 6.6e+168)
                           (* z (* x 6.0))
                           (if (<= z 6e+208)
                             (* z (* -6.0 y))
                             t_1)))))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1e+267) {
		tmp = t_0;
	} else if (z <= -1.2e+175) {
		tmp = t_1;
	} else if (z <= -6e+94) {
		tmp = t_0;
	} else if (z <= -3.75e+40) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = y * (-6.0 * z);
	} else if (z <= -1.15e-177) {
		tmp = y * 4.0;
	} else if (z <= -8.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-128) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.6e+168) {
		tmp = z * (x * 6.0);
	} else if (z <= 6e+208) {
		tmp = z * (-6.0 * y);
	} 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) * (z * y)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-1d+267)) then
        tmp = t_0
    else if (z <= (-1.2d+175)) then
        tmp = t_1
    else if (z <= (-6d+94)) then
        tmp = t_0
    else if (z <= (-3.75d+40)) then
        tmp = t_1
    else if (z <= (-3.4d-11)) then
        tmp = y * ((-6.0d0) * z)
    else if (z <= (-1.15d-177)) then
        tmp = y * 4.0d0
    else if (z <= (-8.5d-231)) then
        tmp = x * (-3.0d0)
    else if (z <= 7.2d-301) then
        tmp = y * 4.0d0
    else if (z <= 2.15d-128) then
        tmp = x * (-3.0d0)
    else if (z <= 1.3d-107) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 6.6d+168) then
        tmp = z * (x * 6.0d0)
    else if (z <= 6d+208) then
        tmp = z * ((-6.0d0) * y)
    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 * (z * y);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -1e+267) {
		tmp = t_0;
	} else if (z <= -1.2e+175) {
		tmp = t_1;
	} else if (z <= -6e+94) {
		tmp = t_0;
	} else if (z <= -3.75e+40) {
		tmp = t_1;
	} else if (z <= -3.4e-11) {
		tmp = y * (-6.0 * z);
	} else if (z <= -1.15e-177) {
		tmp = y * 4.0;
	} else if (z <= -8.5e-231) {
		tmp = x * -3.0;
	} else if (z <= 7.2e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.15e-128) {
		tmp = x * -3.0;
	} else if (z <= 1.3e-107) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 6.6e+168) {
		tmp = z * (x * 6.0);
	} else if (z <= 6e+208) {
		tmp = z * (-6.0 * y);
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -1e+267:
		tmp = t_0
	elif z <= -1.2e+175:
		tmp = t_1
	elif z <= -6e+94:
		tmp = t_0
	elif z <= -3.75e+40:
		tmp = t_1
	elif z <= -3.4e-11:
		tmp = y * (-6.0 * z)
	elif z <= -1.15e-177:
		tmp = y * 4.0
	elif z <= -8.5e-231:
		tmp = x * -3.0
	elif z <= 7.2e-301:
		tmp = y * 4.0
	elif z <= 2.15e-128:
		tmp = x * -3.0
	elif z <= 1.3e-107:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 6.6e+168:
		tmp = z * (x * 6.0)
	elif z <= 6e+208:
		tmp = z * (-6.0 * y)
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -1e+267)
		tmp = t_0;
	elseif (z <= -1.2e+175)
		tmp = t_1;
	elseif (z <= -6e+94)
		tmp = t_0;
	elseif (z <= -3.75e+40)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = Float64(y * Float64(-6.0 * z));
	elseif (z <= -1.15e-177)
		tmp = Float64(y * 4.0);
	elseif (z <= -8.5e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.2e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.15e-128)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.3e-107)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.6e+168)
		tmp = Float64(z * Float64(x * 6.0));
	elseif (z <= 6e+208)
		tmp = Float64(z * Float64(-6.0 * y));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -1e+267)
		tmp = t_0;
	elseif (z <= -1.2e+175)
		tmp = t_1;
	elseif (z <= -6e+94)
		tmp = t_0;
	elseif (z <= -3.75e+40)
		tmp = t_1;
	elseif (z <= -3.4e-11)
		tmp = y * (-6.0 * z);
	elseif (z <= -1.15e-177)
		tmp = y * 4.0;
	elseif (z <= -8.5e-231)
		tmp = x * -3.0;
	elseif (z <= 7.2e-301)
		tmp = y * 4.0;
	elseif (z <= 2.15e-128)
		tmp = x * -3.0;
	elseif (z <= 1.3e-107)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 6.6e+168)
		tmp = z * (x * 6.0);
	elseif (z <= 6e+208)
		tmp = z * (-6.0 * y);
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -1e+267], t$95$0, If[LessEqual[z, -1.2e+175], t$95$1, If[LessEqual[z, -6e+94], t$95$0, If[LessEqual[z, -3.75e+40], t$95$1, If[LessEqual[z, -3.4e-11], N[(y * N[(-6.0 * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -1.15e-177], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -8.5e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.2e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.15e-128], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.3e-107], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.6e+168], N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 6e+208], N[(z * N[(-6.0 * y), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]]]]]]]]]]]

Derivation

1. Split input into 7 regimes

2. if z < -9.9999999999999997e266 or -1.2e175 < z < -6.0000000000000001e94

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around inf 78.5%

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

      1. *-commutative 78.5%

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

   10. Simplified 78.5%

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

   if -9.9999999999999997e266 < z < -1.2e175 or -6.0000000000000001e94 < z < -3.7499999999999998e40 or 5.99999999999999989e208 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 99.7%

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

      2. *-commutative 99.7%

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

      3. associate-*l* 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 78.4%

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

   if -3.7499999999999998e40 < z < -3.3999999999999999e-11

   1. Initial program 99.3%

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

      1. +-commutative 99.3%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.5%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.5%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.5%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.7%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 72.3%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]

   5. Taylor expanded in z around inf 62.1%

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

      1. *-commutative 62.1%

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

      2. associate-*r* 62.1%

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

      3. *-commutative 62.1%

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

   7. Simplified 62.1%

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

   if -3.3999999999999999e-11 < z < -1.15000000000000011e-177 or -8.5e-231 < z < 7.20000000000000015e-301 or 2.14999999999999997e-128 < z < 1.3e-107

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -1.15000000000000011e-177 < z < -8.5e-231 or 7.20000000000000015e-301 < z < 2.14999999999999997e-128 or 1.3e-107 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if 0.5 < z < 6.5999999999999997e168

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.7%

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

   5. Taylor expanded in z around inf 95.1%

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

      1. associate-*r* 95.1%

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

      2. *-commutative 95.1%

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

      3. associate-*l* 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in y around 0 64.2%

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

      1. associate-*r* 64.2%

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

      2. *-commutative 64.2%

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

   10. Simplified 64.2%

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

   if 6.5999999999999997e168 < z < 5.99999999999999989e208

   1. Initial program 100.0%

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

      1. metadata-eval 100.0%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 99.8%

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

      1. associate-*r* 100.0%

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

      2. *-commutative 100.0%

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

      3. associate-*l* 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.8%

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

      1. associate-*r* 100.0%

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

   10. Simplified 100.0%

       \[\leadsto \color{blue}{\left(-6 \cdot y\right) \cdot z} \]
3. Recombined 7 regimes into one program.

4. Final simplification 69.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -1 \cdot 10^{+267}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.2 \cdot 10^{+175}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6 \cdot 10^{+94}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -3.75 \cdot 10^{+40}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;y \cdot \left(-6 \cdot z\right)\\ \mathbf{elif}\;z \leq -1.15 \cdot 10^{-177}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -8.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.2 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.15 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.3 \cdot 10^{-107}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.6 \cdot 10^{+168}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq 6 \cdot 10^{+208}:\\ \;\;\;\;z \cdot \left(-6 \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]

Alternative 7: 73.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z (- y x)))))
   (if (<= z -3.4e-11)
     t_0
     (if (<= z -1.3e-173)
       (* y 4.0)
       (if (<= z -4.3e-232)
         (* x -3.0)
         (if (<= z 1.85e-301)
           (* y 4.0)
           (if (<= z 1.35e-127)
             (* x -3.0)
             (if (<= z 1.52e-108)
               (* y 4.0)
               (if (<= z 0.5) (* x -3.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -1.3e-173) {
		tmp = y * 4.0;
	} else if (z <= -4.3e-232) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-127) {
		tmp = x * -3.0;
	} else if (z <= 1.52e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} 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) :: tmp
    t_0 = (-6.0d0) * (z * (y - x))
    if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-1.3d-173)) then
        tmp = y * 4.0d0
    else if (z <= (-4.3d-232)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.85d-301) then
        tmp = y * 4.0d0
    else if (z <= 1.35d-127) then
        tmp = x * (-3.0d0)
    else if (z <= 1.52d-108) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    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 * (z * (y - x));
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -1.3e-173) {
		tmp = y * 4.0;
	} else if (z <= -4.3e-232) {
		tmp = x * -3.0;
	} else if (z <= 1.85e-301) {
		tmp = y * 4.0;
	} else if (z <= 1.35e-127) {
		tmp = x * -3.0;
	} else if (z <= 1.52e-108) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -3.4e-11:
		tmp = t_0
	elif z <= -1.3e-173:
		tmp = y * 4.0
	elif z <= -4.3e-232:
		tmp = x * -3.0
	elif z <= 1.85e-301:
		tmp = y * 4.0
	elif z <= 1.35e-127:
		tmp = x * -3.0
	elif z <= 1.52e-108:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -1.3e-173)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.3e-232)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.85e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.35e-127)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.52e-108)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -1.3e-173)
		tmp = y * 4.0;
	elseif (z <= -4.3e-232)
		tmp = x * -3.0;
	elseif (z <= 1.85e-301)
		tmp = y * 4.0;
	elseif (z <= 1.35e-127)
		tmp = x * -3.0;
	elseif (z <= 1.52e-108)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -1.3e-173], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.3e-232], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.85e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.35e-127], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.52e-108], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999999e-11 or 0.5 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 96.5%

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

   if -3.3999999999999999e-11 < z < -1.30000000000000002e-173 or -4.2999999999999997e-232 < z < 1.8499999999999999e-301 or 1.35e-127 < z < 1.52000000000000001e-108

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -1.30000000000000002e-173 < z < -4.2999999999999997e-232 or 1.8499999999999999e-301 < z < 1.35e-127 or 1.52000000000000001e-108 < z < 0.5

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

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

4. Final simplification 80.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.3 \cdot 10^{-232}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.85 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.35 \cdot 10^{-127}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.52 \cdot 10^{-108}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 8: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x \cdot \left(-3 + z \cdot 6\right)\\ t_1 := -6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2700000000000:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* x (+ -3.0 (* z 6.0)))) (t_1 (* -6.0 (* z (- y x)))))
   (if (<= z -3.4e-11)
     t_1
     (if (<= z -1.3e-180)
       (* y 4.0)
       (if (<= z -4.5e-231)
         t_0
         (if (<= z 4.3e-301)
           (* y 4.0)
           (if (<= z 2.7e-130)
             (* x -3.0)
             (if (<= z 1.05e-106)
               (* y 4.0)
               (if (<= z 2700000000000.0) t_0 t_1)))))))))

C

double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_1;
	} else if (z <= -1.3e-180) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-231) {
		tmp = t_0;
	} else if (z <= 4.3e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-130) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-106) {
		tmp = y * 4.0;
	} else if (z <= 2700000000000.0) {
		tmp = t_0;
	} 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 = x * ((-3.0d0) + (z * 6.0d0))
    t_1 = (-6.0d0) * (z * (y - x))
    if (z <= (-3.4d-11)) then
        tmp = t_1
    else if (z <= (-1.3d-180)) then
        tmp = y * 4.0d0
    else if (z <= (-4.5d-231)) then
        tmp = t_0
    else if (z <= 4.3d-301) then
        tmp = y * 4.0d0
    else if (z <= 2.7d-130) then
        tmp = x * (-3.0d0)
    else if (z <= 1.05d-106) then
        tmp = y * 4.0d0
    else if (z <= 2700000000000.0d0) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = x * (-3.0 + (z * 6.0));
	double t_1 = -6.0 * (z * (y - x));
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_1;
	} else if (z <= -1.3e-180) {
		tmp = y * 4.0;
	} else if (z <= -4.5e-231) {
		tmp = t_0;
	} else if (z <= 4.3e-301) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-130) {
		tmp = x * -3.0;
	} else if (z <= 1.05e-106) {
		tmp = y * 4.0;
	} else if (z <= 2700000000000.0) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = x * (-3.0 + (z * 6.0))
	t_1 = -6.0 * (z * (y - x))
	tmp = 0
	if z <= -3.4e-11:
		tmp = t_1
	elif z <= -1.3e-180:
		tmp = y * 4.0
	elif z <= -4.5e-231:
		tmp = t_0
	elif z <= 4.3e-301:
		tmp = y * 4.0
	elif z <= 2.7e-130:
		tmp = x * -3.0
	elif z <= 1.05e-106:
		tmp = y * 4.0
	elif z <= 2700000000000.0:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(x * Float64(-3.0 + Float64(z * 6.0)))
	t_1 = Float64(-6.0 * Float64(z * Float64(y - x)))
	tmp = 0.0
	if (z <= -3.4e-11)
		tmp = t_1;
	elseif (z <= -1.3e-180)
		tmp = Float64(y * 4.0);
	elseif (z <= -4.5e-231)
		tmp = t_0;
	elseif (z <= 4.3e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e-130)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.05e-106)
		tmp = Float64(y * 4.0);
	elseif (z <= 2700000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = x * (-3.0 + (z * 6.0));
	t_1 = -6.0 * (z * (y - x));
	tmp = 0.0;
	if (z <= -3.4e-11)
		tmp = t_1;
	elseif (z <= -1.3e-180)
		tmp = y * 4.0;
	elseif (z <= -4.5e-231)
		tmp = t_0;
	elseif (z <= 4.3e-301)
		tmp = y * 4.0;
	elseif (z <= 2.7e-130)
		tmp = x * -3.0;
	elseif (z <= 1.05e-106)
		tmp = y * 4.0;
	elseif (z <= 2700000000000.0)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-11], t$95$1, If[LessEqual[z, -1.3e-180], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -4.5e-231], t$95$0, If[LessEqual[z, 4.3e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e-130], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.05e-106], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2700000000000.0], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.3999999999999999e-11 or 2.7e12 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.8%

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

   if -3.3999999999999999e-11 < z < -1.2999999999999999e-180 or -4.4999999999999998e-231 < z < 4.29999999999999989e-301 or 2.69999999999999991e-130 < z < 1.05000000000000002e-106

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -1.2999999999999999e-180 < z < -4.4999999999999998e-231 or 1.05000000000000002e-106 < z < 2.7e12

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 68.2%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 68.2%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 68.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 68.3%

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

      4. neg-mul-1 68.3%

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

      5. associate-*r* 68.3%

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

      6. *-commutative 68.3%

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

      7. associate-+r+ 68.3%

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

      8. metadata-eval 68.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 68.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 68.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 68.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 68.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if 4.29999999999999989e-301 < z < 2.69999999999999991e-130

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 61.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 61.1%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 61.1%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 61.1%

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

      4. neg-mul-1 61.1%

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

      5. associate-*r* 61.1%

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

      6. *-commutative 61.1%

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

      7. associate-+r+ 61.1%

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

      8. metadata-eval 61.1%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 61.1%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 61.1%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 61.1%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 61.1%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 61.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 61.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 61.1%

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

4. Final simplification 80.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq -1.3 \cdot 10^{-180}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{elif}\;z \leq 4.3 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-130}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.05 \cdot 10^{-106}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2700000000000:\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 9: 49.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(z \cdot y\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* z y))))
   (if (<= z -3.4e-11)
     t_0
     (if (<= z -1.7e-173)
       (* y 4.0)
       (if (<= z -5e-231)
         (* x -3.0)
         (if (<= z 1.8e-301)
           (* y 4.0)
           (if (<= z 4.1e-128)
             (* x -3.0)
             (if (<= z 4.1e-109)
               (* y 4.0)
               (if (<= z 0.55) (* x -3.0) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (z * y);
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -1.7e-173) {
		tmp = y * 4.0;
	} else if (z <= -5e-231) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-301) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-128) {
		tmp = x * -3.0;
	} else if (z <= 4.1e-109) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} 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) :: tmp
    t_0 = (-6.0d0) * (z * y)
    if (z <= (-3.4d-11)) then
        tmp = t_0
    else if (z <= (-1.7d-173)) then
        tmp = y * 4.0d0
    else if (z <= (-5d-231)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d-301) then
        tmp = y * 4.0d0
    else if (z <= 4.1d-128) then
        tmp = x * (-3.0d0)
    else if (z <= 4.1d-109) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) then
        tmp = x * (-3.0d0)
    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 * (z * y);
	double tmp;
	if (z <= -3.4e-11) {
		tmp = t_0;
	} else if (z <= -1.7e-173) {
		tmp = y * 4.0;
	} else if (z <= -5e-231) {
		tmp = x * -3.0;
	} else if (z <= 1.8e-301) {
		tmp = y * 4.0;
	} else if (z <= 4.1e-128) {
		tmp = x * -3.0;
	} else if (z <= 4.1e-109) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (z * y)
	tmp = 0
	if z <= -3.4e-11:
		tmp = t_0
	elif z <= -1.7e-173:
		tmp = y * 4.0
	elif z <= -5e-231:
		tmp = x * -3.0
	elif z <= 1.8e-301:
		tmp = y * 4.0
	elif z <= 4.1e-128:
		tmp = x * -3.0
	elif z <= 4.1e-109:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(z * y))
	tmp = 0.0
	if (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -1.7e-173)
		tmp = Float64(y * 4.0);
	elseif (z <= -5e-231)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e-301)
		tmp = Float64(y * 4.0);
	elseif (z <= 4.1e-128)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.1e-109)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		tmp = Float64(x * -3.0);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (z * y);
	tmp = 0.0;
	if (z <= -3.4e-11)
		tmp = t_0;
	elseif (z <= -1.7e-173)
		tmp = y * 4.0;
	elseif (z <= -5e-231)
		tmp = x * -3.0;
	elseif (z <= 1.8e-301)
		tmp = y * 4.0;
	elseif (z <= 4.1e-128)
		tmp = x * -3.0;
	elseif (z <= 4.1e-109)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		tmp = x * -3.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(z * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e-11], t$95$0, If[LessEqual[z, -1.7e-173], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -5e-231], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e-301], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 4.1e-128], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.1e-109], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -3.3999999999999999e-11 or 0.55000000000000004 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 96.5%

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

      1. associate-*r* 96.5%

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

      2. *-commutative 96.5%

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

      3. associate-*l* 96.5%

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

   7. Simplified 96.5%

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

   8. Taylor expanded in y around inf 46.2%

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

      1. *-commutative 46.2%

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

   10. Simplified 46.2%

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

   if -3.3999999999999999e-11 < z < -1.6999999999999999e-173 or -5.00000000000000023e-231 < z < 1.80000000000000004e-301 or 4.1e-128 < z < 4.1000000000000002e-109

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.9%

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

   5. Taylor expanded in x around 0 67.8%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 67.6%

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

      1. *-commutative 67.6%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 67.6%

      \[\leadsto \color{blue}{y \cdot 4} \]

   if -1.6999999999999999e-173 < z < -5.00000000000000023e-231 or 1.80000000000000004e-301 < z < 4.1e-128 or 4.1000000000000002e-109 < z < 0.55000000000000004

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 64.3%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 64.3%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 64.3%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 64.3%

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

      4. neg-mul-1 64.3%

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

      5. associate-*r* 64.3%

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

      6. *-commutative 64.3%

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

      7. associate-+r+ 64.3%

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

      8. metadata-eval 64.3%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 64.3%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 64.3%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 64.3%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 63.3%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 63.3%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 63.3%

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

4. Final simplification 56.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{-11}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \mathbf{elif}\;z \leq -1.7 \cdot 10^{-173}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -5 \cdot 10^{-231}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{-301}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-128}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.1 \cdot 10^{-109}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(z \cdot y\right)\\ \end{array} \]

Alternative 10: 75.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+28} \lor \neg \left(x \leq -1.45 \cdot 10^{-17} \lor \neg \left(x \leq -2 \cdot 10^{-83}\right) \land x \leq 2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.25e+28)
         (not (or (<= x -1.45e-17) (and (not (<= x -2e-83)) (<= x 2e-22)))))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* -6.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+28) || !((x <= -1.45e-17) || (!(x <= -2e-83) && (x <= 2e-22)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-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 ((x <= (-1.25d+28)) .or. (.not. (x <= (-1.45d-17)) .or. (.not. (x <= (-2d-83))) .and. (x <= 2d-22))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + ((-6.0d0) * z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -1.25e+28) || !((x <= -1.45e-17) || (!(x <= -2e-83) && (x <= 2e-22)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (-6.0 * z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -1.25e+28) or not ((x <= -1.45e-17) or (not (x <= -2e-83) and (x <= 2e-22))):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (-6.0 * z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -1.25e+28) || !((x <= -1.45e-17) || (!(x <= -2e-83) && (x <= 2e-22))))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(-6.0 * z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -1.25e+28) || ~(((x <= -1.45e-17) || (~((x <= -2e-83)) && (x <= 2e-22)))))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (-6.0 * z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -1.25e+28], N[Not[Or[LessEqual[x, -1.45e-17], And[N[Not[LessEqual[x, -2e-83]], $MachinePrecision], LessEqual[x, 2e-22]]]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(-6.0 * z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -1.24999999999999989e28 or -1.4500000000000001e-17 < x < -2.0000000000000001e-83 or 2.0000000000000001e-22 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 84.8%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 84.8%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 84.8%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 84.8%

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

      4. neg-mul-1 84.8%

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

      5. associate-*r* 84.8%

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

      6. *-commutative 84.8%

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

      7. associate-+r+ 84.8%

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

      8. metadata-eval 84.8%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 84.8%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 84.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 84.8%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 84.8%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   if -1.24999999999999989e28 < x < -1.4500000000000001e-17 or -2.0000000000000001e-83 < x < 2.0000000000000001e-22

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

         \[\leadsto \color{blue}{\left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) + x} \]

      2. associate-*l* 99.8%

         \[\leadsto \color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(\frac{2}{3} - z\right)\right)} + x \]

      3. fma-def 99.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(y - x, 6 \cdot \left(\frac{2}{3} - z\right), x\right)} \]

      4. sub-neg 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, 6 \cdot \color{blue}{\left(\frac{2}{3} + \left(-z\right)\right)}, x\right) \]

      5. distribute-rgt-in 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{\frac{2}{3} \cdot 6 + \left(-z\right) \cdot 6}, x\right) \]

      6. metadata-eval 99.8%

         \[\leadsto \mathsf{fma}\left(y - x, \color{blue}{0.6666666666666666} \cdot 6 + \left(-z\right) \cdot 6, x\right) \]

      7. metadata-eval 99.8%

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

      8. distribute-lft-neg-out 99.8%

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

      9. distribute-rgt-neg-in 99.8%

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

      10. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around inf 80.6%

      \[\leadsto \color{blue}{y \cdot \left(4 + -6 \cdot z\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.25 \cdot 10^{+28} \lor \neg \left(x \leq -1.45 \cdot 10^{-17} \lor \neg \left(x \leq -2 \cdot 10^{-83}\right) \land x \leq 2 \cdot 10^{-22}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + -6 \cdot z\right)\\ \end{array} \]

Alternative 11: 97.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.6)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.65) (+ x (* (- y x) 4.0)) (* z (* -6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * (-6.0 * (y - 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 <= (-0.6d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.65d0) then
        tmp = x + ((y - x) * 4.0d0)
    else
        tmp = z * ((-6.0d0) * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.6) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.65) {
		tmp = x + ((y - x) * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.6:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.65:
		tmp = x + ((y - x) * 4.0)
	else:
		tmp = z * (-6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.6)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.65)
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	else
		tmp = Float64(z * Float64(-6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.6)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.65)
		tmp = x + ((y - x) * 4.0);
	else
		tmp = z * (-6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.6], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.65], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.599999999999999978

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.2%

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

   if -0.599999999999999978 < z < 0.650000000000000022

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 98.4%

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

   if 0.650000000000000022 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.3%

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

      1. associate-*r* 97.3%

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

      2. *-commutative 97.3%

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

      3. associate-*l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.6:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.65:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 12: 97.8% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z -0.55)
   (* -6.0 (* z (- y x)))
   (if (<= z 0.58) (+ (* x -3.0) (* y 4.0)) (* z (* -6.0 (- y x))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (-6.0 * (y - 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 <= (-0.55d0)) then
        tmp = (-6.0d0) * (z * (y - x))
    else if (z <= 0.58d0) then
        tmp = (x * (-3.0d0)) + (y * 4.0d0)
    else
        tmp = z * ((-6.0d0) * (y - x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= -0.55) {
		tmp = -6.0 * (z * (y - x));
	} else if (z <= 0.58) {
		tmp = (x * -3.0) + (y * 4.0);
	} else {
		tmp = z * (-6.0 * (y - x));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= -0.55:
		tmp = -6.0 * (z * (y - x))
	elif z <= 0.58:
		tmp = (x * -3.0) + (y * 4.0)
	else:
		tmp = z * (-6.0 * (y - x))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= -0.55)
		tmp = Float64(-6.0 * Float64(z * Float64(y - x)));
	elseif (z <= 0.58)
		tmp = Float64(Float64(x * -3.0) + Float64(y * 4.0));
	else
		tmp = Float64(z * Float64(-6.0 * Float64(y - x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= -0.55)
		tmp = -6.0 * (z * (y - x));
	elseif (z <= 0.58)
		tmp = (x * -3.0) + (y * 4.0);
	else
		tmp = z * (-6.0 * (y - x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, -0.55], N[(-6.0 * N[(z * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, 0.58], N[(N[(x * -3.0), $MachinePrecision] + N[(y * 4.0), $MachinePrecision]), $MachinePrecision], N[(z * N[(-6.0 * N[(y - x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if z < -0.55000000000000004

   1. Initial program 99.6%

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

      1. metadata-eval 99.6%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.2%

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

   if -0.55000000000000004 < z < 0.57999999999999996

   1. Initial program 99.4%

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

      1. metadata-eval 99.4%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.4%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in y around 0 99.4%

      \[\leadsto x + \color{blue}{\left(-6 \cdot x + 6 \cdot y\right)} \cdot \left(0.6666666666666666 - z\right) \]

   5. Taylor expanded in z around 0 97.9%

      \[\leadsto \color{blue}{x + 0.6666666666666666 \cdot \left(-6 \cdot x + 6 \cdot y\right)} \]
   6. Step-by-step derivation

      1. distribute-rgt-in 97.9%

         \[\leadsto x + \color{blue}{\left(\left(-6 \cdot x\right) \cdot 0.6666666666666666 + \left(6 \cdot y\right) \cdot 0.6666666666666666\right)} \]

      2. associate-+r+ 98.0%

         \[\leadsto \color{blue}{\left(x + \left(-6 \cdot x\right) \cdot 0.6666666666666666\right) + \left(6 \cdot y\right) \cdot 0.6666666666666666} \]

      3. *-commutative 98.0%

         \[\leadsto \left(x + \color{blue}{0.6666666666666666 \cdot \left(-6 \cdot x\right)}\right) + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      4. associate-*r* 98.2%

         \[\leadsto \left(x + \color{blue}{\left(0.6666666666666666 \cdot -6\right) \cdot x}\right) + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      5. metadata-eval 98.2%

         \[\leadsto \left(x + \color{blue}{-4} \cdot x\right) + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      6. distribute-rgt1-in 98.2%

         \[\leadsto \color{blue}{\left(-4 + 1\right) \cdot x} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      7. metadata-eval 98.2%

         \[\leadsto \color{blue}{-3} \cdot x + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      8. *-commutative 98.2%

         \[\leadsto \color{blue}{x \cdot -3} + \left(6 \cdot y\right) \cdot 0.6666666666666666 \]

      9. *-commutative 98.2%

         \[\leadsto x \cdot -3 + \color{blue}{\left(y \cdot 6\right)} \cdot 0.6666666666666666 \]

      10. associate-*l* 98.4%

          \[\leadsto x \cdot -3 + \color{blue}{y \cdot \left(6 \cdot 0.6666666666666666\right)} \]

      11. metadata-eval 98.4%

          \[\leadsto x \cdot -3 + y \cdot \color{blue}{4} \]

   7. Simplified 98.4%

      \[\leadsto \color{blue}{x \cdot -3 + y \cdot 4} \]

   if 0.57999999999999996 < z

   1. Initial program 99.8%

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

      1. metadata-eval 99.8%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in z around inf 97.3%

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

      1. associate-*r* 97.3%

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

      2. *-commutative 97.3%

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

      3. associate-*l* 97.3%

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

   7. Simplified 97.3%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.55:\\ \;\;\;\;-6 \cdot \left(z \cdot \left(y - x\right)\right)\\ \mathbf{elif}\;z \leq 0.58:\\ \;\;\;\;x \cdot -3 + y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(-6 \cdot \left(y - x\right)\right)\\ \end{array} \]

Alternative 13: 99.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (+ x (* (* (- y x) 6.0) (- 0.6666666666666666 z))))

C

double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - 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) * (0.6666666666666666d0 - z))
end function

Java

public static double code(double x, double y, double z) {
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z));
}

Python

def code(x, y, z):
	return x + (((y - x) * 6.0) * (0.6666666666666666 - z))

Julia

function code(x, y, z)
	return Float64(x + Float64(Float64(Float64(y - x) * 6.0) * Float64(0.6666666666666666 - z)))
end

MATLAB

function tmp = code(x, y, z)
	tmp = x + (((y - x) * 6.0) * (0.6666666666666666 - z));
end

Wolfram

code[x_, y_, z_] := N[(x + N[(N[(N[(y - x), $MachinePrecision] * 6.0), $MachinePrecision] * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Final simplification 99.5%

   \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) \]

Alternative 14: 36.3% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-83}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -1.75e-83) (* x -3.0) (if (<= x 9.6e-79) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-83) {
		tmp = x * -3.0;
	} else if (x <= 9.6e-79) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	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 (x <= (-1.75d-83)) then
        tmp = x * (-3.0d0)
    else if (x <= 9.6d-79) then
        tmp = y * 4.0d0
    else
        tmp = x * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (x <= -1.75e-83) {
		tmp = x * -3.0;
	} else if (x <= 9.6e-79) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -1.75e-83:
		tmp = x * -3.0
	elif x <= 9.6e-79:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -1.75e-83)
		tmp = Float64(x * -3.0);
	elseif (x <= 9.6e-79)
		tmp = Float64(y * 4.0);
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -1.75e-83)
		tmp = x * -3.0;
	elseif (x <= 9.6e-79)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -1.75e-83], N[(x * -3.0), $MachinePrecision], If[LessEqual[x, 9.6e-79], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -1.75000000000000015e-83 or 9.60000000000000023e-79 < x

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in x around inf 77.6%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   5. Step-by-step derivation

      1. sub-neg 77.6%

         \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

      2. distribute-rgt-in 77.6%

         \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

      3. metadata-eval 77.6%

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

      4. neg-mul-1 77.6%

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

      5. associate-*r* 77.6%

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

      6. *-commutative 77.6%

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

      7. associate-+r+ 77.6%

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

      8. metadata-eval 77.6%

         \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

      9. associate-*r* 77.6%

         \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

      10. metadata-eval 77.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

      11. *-commutative 77.6%

          \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

   6. Simplified 77.6%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

   7. Taylor expanded in z around 0 40.1%

      \[\leadsto \color{blue}{-3 \cdot x} \]
   8. Step-by-step derivation

      1. *-commutative 40.1%

         \[\leadsto \color{blue}{x \cdot -3} \]

   9. Simplified 40.1%

      \[\leadsto \color{blue}{x \cdot -3} \]

   if -1.75000000000000015e-83 < x < 9.60000000000000023e-79

   1. Initial program 99.5%

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

      1. metadata-eval 99.5%

         \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

   4. Taylor expanded in z around 0 99.8%

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

   5. Taylor expanded in x around 0 85.5%

      \[\leadsto \color{blue}{-6 \cdot \left(y \cdot z\right) + 4 \cdot y} \]

   6. Taylor expanded in z around 0 52.7%

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

      1. *-commutative 52.7%

         \[\leadsto \color{blue}{y \cdot 4} \]

   8. Simplified 52.7%

      \[\leadsto \color{blue}{y \cdot 4} \]
3. Recombined 2 regimes into one program.

4. Final simplification 45.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.75 \cdot 10^{-83}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;x \leq 9.6 \cdot 10^{-79}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]

Alternative 15: 26.2% accurate, 4.3× speedup

Math

\[\begin{array}{l} \\ x \cdot -3 \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (* x -3.0))

C

double code(double x, double y, double z) {
	return x * -3.0;
}

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 * (-3.0d0)
end function

Java

public static double code(double x, double y, double z) {
	return x * -3.0;
}

Python

def code(x, y, z):
	return x * -3.0

Julia

function code(x, y, z)
	return Float64(x * -3.0)
end

MATLAB

function tmp = code(x, y, z)
	tmp = x * -3.0;
end

Wolfram

code[x_, y_, z_] := N[(x * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in x around inf 53.3%

   \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
5. Step-by-step derivation

   1. sub-neg 53.3%

      \[\leadsto x \cdot \left(1 + -6 \cdot \color{blue}{\left(0.6666666666666666 + \left(-z\right)\right)}\right) \]

   2. distribute-rgt-in 53.3%

      \[\leadsto x \cdot \left(1 + \color{blue}{\left(0.6666666666666666 \cdot -6 + \left(-z\right) \cdot -6\right)}\right) \]

   3. metadata-eval 53.3%

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

   4. neg-mul-1 53.3%

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

   5. associate-*r* 53.3%

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

   6. *-commutative 53.3%

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

   7. associate-+r+ 53.3%

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

   8. metadata-eval 53.3%

      \[\leadsto x \cdot \left(\color{blue}{-3} + -1 \cdot \left(-6 \cdot z\right)\right) \]

   9. associate-*r* 53.3%

      \[\leadsto x \cdot \left(-3 + \color{blue}{\left(-1 \cdot -6\right) \cdot z}\right) \]

   10. metadata-eval 53.3%

       \[\leadsto x \cdot \left(-3 + \color{blue}{6} \cdot z\right) \]

   11. *-commutative 53.3%

       \[\leadsto x \cdot \left(-3 + \color{blue}{z \cdot 6}\right) \]

6. Simplified 53.3%

   \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]

7. Taylor expanded in z around 0 27.2%

   \[\leadsto \color{blue}{-3 \cdot x} \]
8. Step-by-step derivation

   1. *-commutative 27.2%

      \[\leadsto \color{blue}{x \cdot -3} \]

9. Simplified 27.2%

   \[\leadsto \color{blue}{x \cdot -3} \]

10. Final simplification 27.2%

    \[\leadsto x \cdot -3 \]

Alternative 16: 2.6% accurate, 13.0× 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 99.5%

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

   1. metadata-eval 99.5%

      \[\leadsto x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\color{blue}{0.6666666666666666} - z\right) \]

3. Simplified 99.5%

   \[\leadsto \color{blue}{x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} \]

4. Taylor expanded in z around inf 47.3%

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

5. Taylor expanded in z around 0 2.8%

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

6. Final simplification 2.8%

   \[\leadsto x \]

Reproduce

herbie shell --seed 2023271 
(FPCore (x y z)
  :name "Data.Colour.RGBSpace.HSL:hsl from colour-2.3.3, D"
  :precision binary64
  (+ x (* (* (- y x) 6.0) (- (/ 2.0 3.0) z))))