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

Percentage Accurate: 99.5% → 99.8%

Time: 15.0s

Alternatives: 17

Speedup: 1.2×

• 20.7% 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, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

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. +-commutative 99.6%

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

   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-define 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. Add Preprocessing

5. Final simplification 99.8%

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

Alternative 2: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -4.5e+68)
     t_0
     (if (<= z -1.5e+28)
       t_1
       (if (<= z -7e-15)
         (* y 4.0)
         (if (<= z -1e-228)
           (* x -3.0)
           (if (<= z 5.6e-273)
             (* y 4.0)
             (if (<= z 1.4e-81)
               (* x -3.0)
               (if (<= z 1.5e-20)
                 (* y 4.0)
                 (if (<= z 0.52)
                   (* x -3.0)
                   (if (<= z 9e+125) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.5e+68) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = t_1;
	} else if (z <= -7e-15) {
		tmp = y * 4.0;
	} else if (z <= -1e-228) {
		tmp = x * -3.0;
	} else if (z <= 5.6e-273) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-81) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-20) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 9e+125) {
		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) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-4.5d+68)) then
        tmp = t_0
    else if (z <= (-1.5d+28)) then
        tmp = t_1
    else if (z <= (-7d-15)) then
        tmp = y * 4.0d0
    else if (z <= (-1d-228)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.6d-273) then
        tmp = y * 4.0d0
    else if (z <= 1.4d-81) then
        tmp = x * (-3.0d0)
    else if (z <= 1.5d-20) then
        tmp = y * 4.0d0
    else if (z <= 0.52d0) then
        tmp = x * (-3.0d0)
    else if (z <= 9d+125) 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 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -4.5e+68) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = t_1;
	} else if (z <= -7e-15) {
		tmp = y * 4.0;
	} else if (z <= -1e-228) {
		tmp = x * -3.0;
	} else if (z <= 5.6e-273) {
		tmp = y * 4.0;
	} else if (z <= 1.4e-81) {
		tmp = x * -3.0;
	} else if (z <= 1.5e-20) {
		tmp = y * 4.0;
	} else if (z <= 0.52) {
		tmp = x * -3.0;
	} else if (z <= 9e+125) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -4.5e+68:
		tmp = t_0
	elif z <= -1.5e+28:
		tmp = t_1
	elif z <= -7e-15:
		tmp = y * 4.0
	elif z <= -1e-228:
		tmp = x * -3.0
	elif z <= 5.6e-273:
		tmp = y * 4.0
	elif z <= 1.4e-81:
		tmp = x * -3.0
	elif z <= 1.5e-20:
		tmp = y * 4.0
	elif z <= 0.52:
		tmp = x * -3.0
	elif z <= 9e+125:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -4.5e+68)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = t_1;
	elseif (z <= -7e-15)
		tmp = Float64(y * 4.0);
	elseif (z <= -1e-228)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.6e-273)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.4e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.5e-20)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.52)
		tmp = Float64(x * -3.0);
	elseif (z <= 9e+125)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -4.5e+68)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = t_1;
	elseif (z <= -7e-15)
		tmp = y * 4.0;
	elseif (z <= -1e-228)
		tmp = x * -3.0;
	elseif (z <= 5.6e-273)
		tmp = y * 4.0;
	elseif (z <= 1.4e-81)
		tmp = x * -3.0;
	elseif (z <= 1.5e-20)
		tmp = y * 4.0;
	elseif (z <= 0.52)
		tmp = x * -3.0;
	elseif (z <= 9e+125)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.5e+68], t$95$0, If[LessEqual[z, -1.5e+28], t$95$1, If[LessEqual[z, -7e-15], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1e-228], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.6e-273], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.4e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.5e-20], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.52], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 9e+125], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -4.5000000000000003e68 or 0.52000000000000002 < z < 9.0000000000000001e125

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.6%

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

   7. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   9. Simplified 63.6%

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

   if -4.5000000000000003e68 < z < -1.5e28 or 9.0000000000000001e125 < z

   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. Add Preprocessing

   5. Taylor expanded in x around inf 66.4%

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

      1. sub-neg 66.4%

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

      2. distribute-rgt-in 66.4%

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

      3. metadata-eval 66.4%

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

      4. metadata-eval 66.4%

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

      5. neg-mul-1 66.4%

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

      6. associate-*r* 66.4%

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

      7. *-commutative 66.4%

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

      8. distribute-lft-in 66.4%

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

      9. distribute-lft-in 66.4%

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

      10. metadata-eval 66.4%

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

      11. metadata-eval 66.4%

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

      12. associate-+r+ 66.4%

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

      13. metadata-eval 66.4%

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

      14. metadata-eval 66.4%

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

      15. associate-*r* 66.4%

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

      16. metadata-eval 66.4%

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

      17. *-commutative 66.4%

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

   7. Simplified 66.4%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   8. Step-by-step derivation

      1. flip-+ 64.3%

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

      2. associate-*r/ 55.5%

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

      3. metadata-eval 55.5%

         \[\leadsto \frac{x \cdot \left(\color{blue}{9} - \left(z \cdot 6\right) \cdot \left(z \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      4. swap-sqr 55.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(6 \cdot 6\right)}\right)}{-3 - z \cdot 6} \]

      5. pow2 55.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(6 \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      6. metadata-eval 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{-3 - z \cdot 6} \]

      7. *-commutative 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 - \color{blue}{6 \cdot z}} \]

      8. cancel-sign-sub-inv 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{-3 + \left(-6\right) \cdot z}} \]

      9. metadata-eval 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + \color{blue}{-6} \cdot z} \]

   9. Applied egg-rr 55.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + -6 \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 64.3%

          \[\leadsto \color{blue}{\frac{x}{\frac{-3 + -6 \cdot z}{9 - {z}^{2} \cdot 36}}} \]

       2. +-commutative 64.3%

          \[\leadsto \frac{x}{\frac{\color{blue}{-6 \cdot z + -3}}{9 - {z}^{2} \cdot 36}} \]

       3. *-commutative 64.3%

          \[\leadsto \frac{x}{\frac{\color{blue}{z \cdot -6} + -3}{9 - {z}^{2} \cdot 36}} \]

   11. Simplified 64.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot -6 + -3}{9 - {z}^{2} \cdot 36}}} \]

   12. Taylor expanded in z around inf 66.4%

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

   if -1.5e28 < z < -7.0000000000000001e-15 or -1.00000000000000003e-228 < z < 5.59999999999999971e-273 or 1.3999999999999999e-81 < z < 1.50000000000000014e-20

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 62.6%

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

   8. Taylor expanded in z around 0 57.2%

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

      1. *-commutative 57.2%

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

   10. Simplified 57.2%

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

   if -7.0000000000000001e-15 < z < -1.00000000000000003e-228 or 5.59999999999999971e-273 < z < 1.3999999999999999e-81 or 1.50000000000000014e-20 < z < 0.52000000000000002

   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. Add Preprocessing

   5. Taylor expanded in x around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. distribute-rgt-in 63.5%

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

      3. metadata-eval 63.5%

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

      4. metadata-eval 63.5%

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

      5. neg-mul-1 63.5%

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

      6. associate-*r* 63.5%

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

      7. *-commutative 63.5%

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

      8. distribute-lft-in 63.5%

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

      9. distribute-lft-in 63.5%

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

      10. metadata-eval 63.5%

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

      11. metadata-eval 63.5%

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

      12. associate-+r+ 63.5%

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

      13. metadata-eval 63.5%

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

      14. metadata-eval 63.5%

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

      15. associate-*r* 63.5%

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

      16. metadata-eval 63.5%

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

      17. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. *-commutative 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.5 \cdot 10^{+68}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1 \cdot 10^{-228}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.6 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.5 \cdot 10^{-20}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.52:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 9 \cdot 10^{+125}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 50.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.9e+72)
     t_0
     (if (<= z -1.5e+28)
       (* 6.0 (* x z))
       (if (<= z -6.4e-16)
         (* y 4.0)
         (if (<= z -1.4e-229)
           (* x -3.0)
           (if (<= z 5.2e-273)
             (* y 4.0)
             (if (<= z 7.8e-82)
               (* x -3.0)
               (if (<= z 5e-21)
                 (* y 4.0)
                 (if (<= z 0.55)
                   (* x -3.0)
                   (if (<= z 6.2e+126) t_0 (* x (* z 6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.9e+72) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.4e-16) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-229) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-273) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-82) {
		tmp = x * -3.0;
	} else if (z <= 5e-21) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else if (z <= 6.2e+126) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    if (z <= (-2.9d+72)) then
        tmp = t_0
    else if (z <= (-1.5d+28)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-6.4d-16)) then
        tmp = y * 4.0d0
    else if (z <= (-1.4d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 5.2d-273) then
        tmp = y * 4.0d0
    else if (z <= 7.8d-82) then
        tmp = x * (-3.0d0)
    else if (z <= 5d-21) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) then
        tmp = x * (-3.0d0)
    else if (z <= 6.2d+126) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.9e+72) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = 6.0 * (x * z);
	} else if (z <= -6.4e-16) {
		tmp = y * 4.0;
	} else if (z <= -1.4e-229) {
		tmp = x * -3.0;
	} else if (z <= 5.2e-273) {
		tmp = y * 4.0;
	} else if (z <= 7.8e-82) {
		tmp = x * -3.0;
	} else if (z <= 5e-21) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else if (z <= 6.2e+126) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.9e+72:
		tmp = t_0
	elif z <= -1.5e+28:
		tmp = 6.0 * (x * z)
	elif z <= -6.4e-16:
		tmp = y * 4.0
	elif z <= -1.4e-229:
		tmp = x * -3.0
	elif z <= 5.2e-273:
		tmp = y * 4.0
	elif z <= 7.8e-82:
		tmp = x * -3.0
	elif z <= 5e-21:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	elif z <= 6.2e+126:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	tmp = 0.0
	if (z <= -2.9e+72)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -6.4e-16)
		tmp = Float64(y * 4.0);
	elseif (z <= -1.4e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 5.2e-273)
		tmp = Float64(y * 4.0);
	elseif (z <= 7.8e-82)
		tmp = Float64(x * -3.0);
	elseif (z <= 5e-21)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.2e+126)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	tmp = 0.0;
	if (z <= -2.9e+72)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = 6.0 * (x * z);
	elseif (z <= -6.4e-16)
		tmp = y * 4.0;
	elseif (z <= -1.4e-229)
		tmp = x * -3.0;
	elseif (z <= 5.2e-273)
		tmp = y * 4.0;
	elseif (z <= 7.8e-82)
		tmp = x * -3.0;
	elseif (z <= 5e-21)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		tmp = x * -3.0;
	elseif (z <= 6.2e+126)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.9e+72], t$95$0, If[LessEqual[z, -1.5e+28], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.4e-16], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -1.4e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5.2e-273], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7.8e-82], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 5e-21], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.2e+126], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.90000000000000017e72 or 0.55000000000000004 < z < 6.2e126

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.6%

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

   7. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

   9. Simplified 63.6%

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

   if -2.90000000000000017e72 < z < -1.5e28

   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. Add Preprocessing

   5. Taylor expanded in x around inf 73.2%

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

      1. sub-neg 73.2%

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

      2. distribute-rgt-in 73.2%

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

      3. metadata-eval 73.2%

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

      4. metadata-eval 73.2%

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

      5. neg-mul-1 73.2%

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

      6. associate-*r* 73.2%

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

      7. *-commutative 73.2%

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

      8. distribute-lft-in 73.2%

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

      9. distribute-lft-in 73.2%

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

      10. metadata-eval 73.2%

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

      11. metadata-eval 73.2%

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

      12. associate-+r+ 73.2%

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

      13. metadata-eval 73.2%

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

      14. metadata-eval 73.2%

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

      15. associate-*r* 73.2%

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

      16. metadata-eval 73.2%

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

      17. *-commutative 73.2%

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

   7. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   8. Step-by-step derivation

      1. flip-+ 73.2%

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

      2. associate-*r/ 56.8%

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

      3. metadata-eval 56.8%

         \[\leadsto \frac{x \cdot \left(\color{blue}{9} - \left(z \cdot 6\right) \cdot \left(z \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      4. swap-sqr 56.9%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(6 \cdot 6\right)}\right)}{-3 - z \cdot 6} \]

      5. pow2 56.9%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(6 \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      6. metadata-eval 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{-3 - z \cdot 6} \]

      7. *-commutative 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 - \color{blue}{6 \cdot z}} \]

      8. cancel-sign-sub-inv 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{-3 + \left(-6\right) \cdot z}} \]

      9. metadata-eval 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + \color{blue}{-6} \cdot z} \]

   9. Applied egg-rr 56.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + -6 \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 73.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{-3 + -6 \cdot z}{9 - {z}^{2} \cdot 36}}} \]

       2. +-commutative 73.2%

          \[\leadsto \frac{x}{\frac{\color{blue}{-6 \cdot z + -3}}{9 - {z}^{2} \cdot 36}} \]

       3. *-commutative 73.2%

          \[\leadsto \frac{x}{\frac{\color{blue}{z \cdot -6} + -3}{9 - {z}^{2} \cdot 36}} \]

   11. Simplified 73.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot -6 + -3}{9 - {z}^{2} \cdot 36}}} \]

   12. Taylor expanded in z around inf 73.4%

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

   if -1.5e28 < z < -6.40000000000000046e-16 or -1.39999999999999995e-229 < z < 5.19999999999999967e-273 or 7.79999999999999947e-82 < z < 4.99999999999999973e-21

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 62.6%

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

   8. Taylor expanded in z around 0 57.2%

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

      1. *-commutative 57.2%

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

   10. Simplified 57.2%

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

   if -6.40000000000000046e-16 < z < -1.39999999999999995e-229 or 5.19999999999999967e-273 < z < 7.79999999999999947e-82 or 4.99999999999999973e-21 < z < 0.55000000000000004

   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. Add Preprocessing

   5. Taylor expanded in x around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. distribute-rgt-in 63.5%

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

      3. metadata-eval 63.5%

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

      4. metadata-eval 63.5%

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

      5. neg-mul-1 63.5%

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

      6. associate-*r* 63.5%

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

      7. *-commutative 63.5%

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

      8. distribute-lft-in 63.5%

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

      9. distribute-lft-in 63.5%

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

      10. metadata-eval 63.5%

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

      11. metadata-eval 63.5%

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

      12. associate-+r+ 63.5%

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

      13. metadata-eval 63.5%

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

      14. metadata-eval 63.5%

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

      15. associate-*r* 63.5%

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

      16. metadata-eval 63.5%

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

      17. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. *-commutative 62.7%

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

   10. Simplified 62.7%

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

   if 6.2e126 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 63.9%

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

      1. sub-neg 63.9%

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

      2. distribute-rgt-in 63.9%

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

      3. metadata-eval 63.9%

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

      4. metadata-eval 63.9%

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

      5. neg-mul-1 63.9%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

      8. distribute-lft-in 63.9%

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

      9. distribute-lft-in 63.9%

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

      10. metadata-eval 63.9%

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

      11. metadata-eval 63.9%

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

      12. associate-+r+ 63.9%

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

      13. metadata-eval 63.9%

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

      14. metadata-eval 63.9%

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

      15. associate-*r* 63.9%

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

      16. metadata-eval 63.9%

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

      17. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in z around inf 63.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.9 \cdot 10^{+72}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -6.4 \cdot 10^{-16}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -1.4 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5.2 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7.8 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 5 \cdot 10^{-21}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{+126}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ \mathbf{if}\;z \leq -2.8 \cdot 10^{+74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+126}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))))
   (if (<= z -2.8e+74)
     t_0
     (if (<= z -1.5e+28)
       (* 6.0 (* x z))
       (if (<= z -2.9e-15)
         (* y 4.0)
         (if (<= z -6.5e-229)
           (* x -3.0)
           (if (<= z 1.6e-271)
             (* y 4.0)
             (if (<= z 3.4e-81)
               (* x -3.0)
               (if (<= z 6.2e-18)
                 (* y 4.0)
                 (if (<= z 0.56)
                   (* x -3.0)
                   (if (<= z 1.95e+126) t_0 (* x (* z 6.0)))))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -2.8e+74) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.9e-15) {
		tmp = y * 4.0;
	} else if (z <= -6.5e-229) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-271) {
		tmp = y * 4.0;
	} else if (z <= 3.4e-81) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-18) {
		tmp = y * 4.0;
	} else if (z <= 0.56) {
		tmp = x * -3.0;
	} else if (z <= 1.95e+126) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (z * (-6.0d0))
    if (z <= (-2.8d+74)) then
        tmp = t_0
    else if (z <= (-1.5d+28)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-2.9d-15)) then
        tmp = y * 4.0d0
    else if (z <= (-6.5d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.6d-271) then
        tmp = y * 4.0d0
    else if (z <= 3.4d-81) then
        tmp = x * (-3.0d0)
    else if (z <= 6.2d-18) then
        tmp = y * 4.0d0
    else if (z <= 0.56d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.95d+126) then
        tmp = t_0
    else
        tmp = x * (z * 6.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double tmp;
	if (z <= -2.8e+74) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = 6.0 * (x * z);
	} else if (z <= -2.9e-15) {
		tmp = y * 4.0;
	} else if (z <= -6.5e-229) {
		tmp = x * -3.0;
	} else if (z <= 1.6e-271) {
		tmp = y * 4.0;
	} else if (z <= 3.4e-81) {
		tmp = x * -3.0;
	} else if (z <= 6.2e-18) {
		tmp = y * 4.0;
	} else if (z <= 0.56) {
		tmp = x * -3.0;
	} else if (z <= 1.95e+126) {
		tmp = t_0;
	} else {
		tmp = x * (z * 6.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	tmp = 0
	if z <= -2.8e+74:
		tmp = t_0
	elif z <= -1.5e+28:
		tmp = 6.0 * (x * z)
	elif z <= -2.9e-15:
		tmp = y * 4.0
	elif z <= -6.5e-229:
		tmp = x * -3.0
	elif z <= 1.6e-271:
		tmp = y * 4.0
	elif z <= 3.4e-81:
		tmp = x * -3.0
	elif z <= 6.2e-18:
		tmp = y * 4.0
	elif z <= 0.56:
		tmp = x * -3.0
	elif z <= 1.95e+126:
		tmp = t_0
	else:
		tmp = x * (z * 6.0)
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	tmp = 0.0
	if (z <= -2.8e+74)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -2.9e-15)
		tmp = Float64(y * 4.0);
	elseif (z <= -6.5e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.6e-271)
		tmp = Float64(y * 4.0);
	elseif (z <= 3.4e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= 6.2e-18)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.56)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.95e+126)
		tmp = t_0;
	else
		tmp = Float64(x * Float64(z * 6.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	tmp = 0.0;
	if (z <= -2.8e+74)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = 6.0 * (x * z);
	elseif (z <= -2.9e-15)
		tmp = y * 4.0;
	elseif (z <= -6.5e-229)
		tmp = x * -3.0;
	elseif (z <= 1.6e-271)
		tmp = y * 4.0;
	elseif (z <= 3.4e-81)
		tmp = x * -3.0;
	elseif (z <= 6.2e-18)
		tmp = y * 4.0;
	elseif (z <= 0.56)
		tmp = x * -3.0;
	elseif (z <= 1.95e+126)
		tmp = t_0;
	else
		tmp = x * (z * 6.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.8e+74], t$95$0, If[LessEqual[z, -1.5e+28], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -2.9e-15], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6.5e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.6e-271], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 3.4e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 6.2e-18], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.56], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.95e+126], t$95$0, N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision]]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.80000000000000002e74 or 0.56000000000000005 < z < 1.94999999999999997e126

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.6%

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

   7. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*l* 63.7%

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

      3. *-commutative 63.7%

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

      4. *-commutative 63.7%

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

   9. Simplified 63.7%

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

   if -2.80000000000000002e74 < z < -1.5e28

   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. Add Preprocessing

   5. Taylor expanded in x around inf 73.2%

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

      1. sub-neg 73.2%

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

      2. distribute-rgt-in 73.2%

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

      3. metadata-eval 73.2%

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

      4. metadata-eval 73.2%

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

      5. neg-mul-1 73.2%

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

      6. associate-*r* 73.2%

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

      7. *-commutative 73.2%

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

      8. distribute-lft-in 73.2%

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

      9. distribute-lft-in 73.2%

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

      10. metadata-eval 73.2%

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

      11. metadata-eval 73.2%

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

      12. associate-+r+ 73.2%

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

      13. metadata-eval 73.2%

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

      14. metadata-eval 73.2%

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

      15. associate-*r* 73.2%

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

      16. metadata-eval 73.2%

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

      17. *-commutative 73.2%

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

   7. Simplified 73.2%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   8. Step-by-step derivation

      1. flip-+ 73.2%

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

      2. associate-*r/ 56.8%

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

      3. metadata-eval 56.8%

         \[\leadsto \frac{x \cdot \left(\color{blue}{9} - \left(z \cdot 6\right) \cdot \left(z \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      4. swap-sqr 56.9%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(6 \cdot 6\right)}\right)}{-3 - z \cdot 6} \]

      5. pow2 56.9%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(6 \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      6. metadata-eval 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{-3 - z \cdot 6} \]

      7. *-commutative 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 - \color{blue}{6 \cdot z}} \]

      8. cancel-sign-sub-inv 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{-3 + \left(-6\right) \cdot z}} \]

      9. metadata-eval 56.9%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + \color{blue}{-6} \cdot z} \]

   9. Applied egg-rr 56.9%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + -6 \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 73.2%

          \[\leadsto \color{blue}{\frac{x}{\frac{-3 + -6 \cdot z}{9 - {z}^{2} \cdot 36}}} \]

       2. +-commutative 73.2%

          \[\leadsto \frac{x}{\frac{\color{blue}{-6 \cdot z + -3}}{9 - {z}^{2} \cdot 36}} \]

       3. *-commutative 73.2%

          \[\leadsto \frac{x}{\frac{\color{blue}{z \cdot -6} + -3}{9 - {z}^{2} \cdot 36}} \]

   11. Simplified 73.2%

       \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot -6 + -3}{9 - {z}^{2} \cdot 36}}} \]

   12. Taylor expanded in z around inf 73.4%

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

   if -1.5e28 < z < -2.90000000000000019e-15 or -6.5e-229 < z < 1.59999999999999989e-271 or 3.3999999999999999e-81 < z < 6.20000000000000014e-18

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 62.6%

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

   8. Taylor expanded in z around 0 57.2%

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

      1. *-commutative 57.2%

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

   10. Simplified 57.2%

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

   if -2.90000000000000019e-15 < z < -6.5e-229 or 1.59999999999999989e-271 < z < 3.3999999999999999e-81 or 6.20000000000000014e-18 < z < 0.56000000000000005

   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. Add Preprocessing

   5. Taylor expanded in x around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. distribute-rgt-in 63.5%

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

      3. metadata-eval 63.5%

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

      4. metadata-eval 63.5%

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

      5. neg-mul-1 63.5%

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

      6. associate-*r* 63.5%

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

      7. *-commutative 63.5%

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

      8. distribute-lft-in 63.5%

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

      9. distribute-lft-in 63.5%

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

      10. metadata-eval 63.5%

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

      11. metadata-eval 63.5%

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

      12. associate-+r+ 63.5%

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

      13. metadata-eval 63.5%

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

      14. metadata-eval 63.5%

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

      15. associate-*r* 63.5%

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

      16. metadata-eval 63.5%

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

      17. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. *-commutative 62.7%

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

   10. Simplified 62.7%

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

   if 1.94999999999999997e126 < z

   1. Initial program 99.9%

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

      1. metadata-eval 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 63.9%

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

      1. sub-neg 63.9%

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

      2. distribute-rgt-in 63.9%

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

      3. metadata-eval 63.9%

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

      4. metadata-eval 63.9%

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

      5. neg-mul-1 63.9%

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

      6. associate-*r* 63.9%

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

      7. *-commutative 63.9%

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

      8. distribute-lft-in 63.9%

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

      9. distribute-lft-in 63.9%

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

      10. metadata-eval 63.9%

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

      11. metadata-eval 63.9%

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

      12. associate-+r+ 63.9%

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

      13. metadata-eval 63.9%

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

      14. metadata-eval 63.9%

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

      15. associate-*r* 63.9%

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

      16. metadata-eval 63.9%

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

      17. *-commutative 63.9%

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

   7. Simplified 63.9%

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

   8. Taylor expanded in z around inf 63.9%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.8 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -2.9 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.5 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 3.4 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 6.2 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.56:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.95 \cdot 10^{+126}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.1% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(z \cdot -6\right)\\ t_1 := z \cdot \left(x \cdot 6\right)\\ \mathbf{if}\;z \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* y (* z -6.0))) (t_1 (* z (* x 6.0))))
   (if (<= z -2.1e+74)
     t_0
     (if (<= z -1.5e+28)
       t_1
       (if (<= z -6.8e-15)
         (* y 4.0)
         (if (<= z -6.2e-229)
           (* x -3.0)
           (if (<= z 2.5e-272)
             (* y 4.0)
             (if (<= z 2.6e-81)
               (* x -3.0)
               (if (<= z 4.4e-17)
                 (* y 4.0)
                 (if (<= z 0.55)
                   (* x -3.0)
                   (if (<= z 1.8e+125) t_0 t_1)))))))))))

C

double code(double x, double y, double z) {
	double t_0 = y * (z * -6.0);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -2.1e+74) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = t_1;
	} else if (z <= -6.8e-15) {
		tmp = y * 4.0;
	} else if (z <= -6.2e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-272) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-81) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-17) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else if (z <= 1.8e+125) {
		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 = y * (z * (-6.0d0))
    t_1 = z * (x * 6.0d0)
    if (z <= (-2.1d+74)) then
        tmp = t_0
    else if (z <= (-1.5d+28)) then
        tmp = t_1
    else if (z <= (-6.8d-15)) then
        tmp = y * 4.0d0
    else if (z <= (-6.2d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.5d-272) then
        tmp = y * 4.0d0
    else if (z <= 2.6d-81) then
        tmp = x * (-3.0d0)
    else if (z <= 4.4d-17) then
        tmp = y * 4.0d0
    else if (z <= 0.55d0) then
        tmp = x * (-3.0d0)
    else if (z <= 1.8d+125) 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 = y * (z * -6.0);
	double t_1 = z * (x * 6.0);
	double tmp;
	if (z <= -2.1e+74) {
		tmp = t_0;
	} else if (z <= -1.5e+28) {
		tmp = t_1;
	} else if (z <= -6.8e-15) {
		tmp = y * 4.0;
	} else if (z <= -6.2e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.5e-272) {
		tmp = y * 4.0;
	} else if (z <= 2.6e-81) {
		tmp = x * -3.0;
	} else if (z <= 4.4e-17) {
		tmp = y * 4.0;
	} else if (z <= 0.55) {
		tmp = x * -3.0;
	} else if (z <= 1.8e+125) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = y * (z * -6.0)
	t_1 = z * (x * 6.0)
	tmp = 0
	if z <= -2.1e+74:
		tmp = t_0
	elif z <= -1.5e+28:
		tmp = t_1
	elif z <= -6.8e-15:
		tmp = y * 4.0
	elif z <= -6.2e-229:
		tmp = x * -3.0
	elif z <= 2.5e-272:
		tmp = y * 4.0
	elif z <= 2.6e-81:
		tmp = x * -3.0
	elif z <= 4.4e-17:
		tmp = y * 4.0
	elif z <= 0.55:
		tmp = x * -3.0
	elif z <= 1.8e+125:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(y * Float64(z * -6.0))
	t_1 = Float64(z * Float64(x * 6.0))
	tmp = 0.0
	if (z <= -2.1e+74)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = t_1;
	elseif (z <= -6.8e-15)
		tmp = Float64(y * 4.0);
	elseif (z <= -6.2e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.5e-272)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.6e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= 4.4e-17)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.55)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.8e+125)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = y * (z * -6.0);
	t_1 = z * (x * 6.0);
	tmp = 0.0;
	if (z <= -2.1e+74)
		tmp = t_0;
	elseif (z <= -1.5e+28)
		tmp = t_1;
	elseif (z <= -6.8e-15)
		tmp = y * 4.0;
	elseif (z <= -6.2e-229)
		tmp = x * -3.0;
	elseif (z <= 2.5e-272)
		tmp = y * 4.0;
	elseif (z <= 2.6e-81)
		tmp = x * -3.0;
	elseif (z <= 4.4e-17)
		tmp = y * 4.0;
	elseif (z <= 0.55)
		tmp = x * -3.0;
	elseif (z <= 1.8e+125)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(y * N[(z * -6.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(z * N[(x * 6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -2.1e+74], t$95$0, If[LessEqual[z, -1.5e+28], t$95$1, If[LessEqual[z, -6.8e-15], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, -6.2e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.5e-272], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.6e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 4.4e-17], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.55], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.8e+125], t$95$0, t$95$1]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -2.0999999999999999e74 or 0.55000000000000004 < z < 1.8000000000000002e125

   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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.6%

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

   7. Taylor expanded in y around inf 63.6%

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

      1. *-commutative 63.6%

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

      2. associate-*l* 63.7%

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

      3. *-commutative 63.7%

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

      4. *-commutative 63.7%

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

   9. Simplified 63.7%

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

   if -2.0999999999999999e74 < z < -1.5e28 or 1.8000000000000002e125 < z

   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. Add Preprocessing

   5. Taylor expanded in x around inf 66.4%

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

      1. sub-neg 66.4%

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

      2. distribute-rgt-in 66.4%

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

      3. metadata-eval 66.4%

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

      4. metadata-eval 66.4%

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

      5. neg-mul-1 66.4%

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

      6. associate-*r* 66.4%

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

      7. *-commutative 66.4%

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

      8. distribute-lft-in 66.4%

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

      9. distribute-lft-in 66.4%

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

      10. metadata-eval 66.4%

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

      11. metadata-eval 66.4%

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

      12. associate-+r+ 66.4%

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

      13. metadata-eval 66.4%

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

      14. metadata-eval 66.4%

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

      15. associate-*r* 66.4%

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

      16. metadata-eval 66.4%

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

      17. *-commutative 66.4%

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

   7. Simplified 66.4%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   8. Step-by-step derivation

      1. flip-+ 64.3%

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

      2. associate-*r/ 55.5%

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

      3. metadata-eval 55.5%

         \[\leadsto \frac{x \cdot \left(\color{blue}{9} - \left(z \cdot 6\right) \cdot \left(z \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      4. swap-sqr 55.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(6 \cdot 6\right)}\right)}{-3 - z \cdot 6} \]

      5. pow2 55.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(6 \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      6. metadata-eval 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{-3 - z \cdot 6} \]

      7. *-commutative 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 - \color{blue}{6 \cdot z}} \]

      8. cancel-sign-sub-inv 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{-3 + \left(-6\right) \cdot z}} \]

      9. metadata-eval 55.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + \color{blue}{-6} \cdot z} \]

   9. Applied egg-rr 55.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + -6 \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 64.3%

          \[\leadsto \color{blue}{\frac{x}{\frac{-3 + -6 \cdot z}{9 - {z}^{2} \cdot 36}}} \]

       2. +-commutative 64.3%

          \[\leadsto \frac{x}{\frac{\color{blue}{-6 \cdot z + -3}}{9 - {z}^{2} \cdot 36}} \]

       3. *-commutative 64.3%

          \[\leadsto \frac{x}{\frac{\color{blue}{z \cdot -6} + -3}{9 - {z}^{2} \cdot 36}} \]

   11. Simplified 64.3%

       \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot -6 + -3}{9 - {z}^{2} \cdot 36}}} \]

   12. Taylor expanded in z around inf 66.4%

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

       1. associate-*r* 66.6%

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

   14. Simplified 66.6%

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

   if -1.5e28 < z < -6.8000000000000001e-15 or -6.2000000000000002e-229 < z < 2.49999999999999991e-272 or 2.5999999999999999e-81 < z < 4.4e-17

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.4%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 62.6%

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

   8. Taylor expanded in z around 0 57.2%

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

      1. *-commutative 57.2%

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

   10. Simplified 57.2%

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

   if -6.8000000000000001e-15 < z < -6.2000000000000002e-229 or 2.49999999999999991e-272 < z < 2.5999999999999999e-81 or 4.4e-17 < z < 0.55000000000000004

   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. Add Preprocessing

   5. Taylor expanded in x around inf 63.4%

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

      1. sub-neg 63.4%

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

      2. distribute-rgt-in 63.5%

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

      3. metadata-eval 63.5%

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

      4. metadata-eval 63.5%

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

      5. neg-mul-1 63.5%

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

      6. associate-*r* 63.5%

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

      7. *-commutative 63.5%

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

      8. distribute-lft-in 63.5%

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

      9. distribute-lft-in 63.5%

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

      10. metadata-eval 63.5%

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

      11. metadata-eval 63.5%

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

      12. associate-+r+ 63.5%

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

      13. metadata-eval 63.5%

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

      14. metadata-eval 63.5%

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

      15. associate-*r* 63.5%

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

      16. metadata-eval 63.5%

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

      17. *-commutative 63.5%

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

   7. Simplified 63.5%

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

   8. Taylor expanded in z around 0 62.7%

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

      1. *-commutative 62.7%

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

   10. Simplified 62.7%

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

4. Final simplification 62.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.1 \cdot 10^{+74}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{elif}\;z \leq -1.5 \cdot 10^{+28}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq -6.2 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.5 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 4.4 \cdot 10^{-17}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.8 \cdot 10^{+125}:\\ \;\;\;\;y \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(x \cdot 6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 74.4% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -3.5:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -3.5)
     t_0
     (if (<= z -8e-17)
       (* 6.0 (* y (- 0.6666666666666666 z)))
       (if (<= z -6.8e-229)
         (* x -3.0)
         (if (<= z 2.3e-273)
           (* y 4.0)
           (if (<= z 7e-82)
             (* x -3.0)
             (if (<= z 1.65e-18)
               (* 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 * ((y - x) * z);
	double tmp;
	if (z <= -3.5) {
		tmp = t_0;
	} else if (z <= -8e-17) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -6.8e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-273) {
		tmp = y * 4.0;
	} else if (z <= 7e-82) {
		tmp = x * -3.0;
	} else if (z <= 1.65e-18) {
		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) * ((y - x) * z)
    if (z <= (-3.5d0)) then
        tmp = t_0
    else if (z <= (-8d-17)) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (z <= (-6.8d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.3d-273) then
        tmp = y * 4.0d0
    else if (z <= 7d-82) then
        tmp = x * (-3.0d0)
    else if (z <= 1.65d-18) 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 * ((y - x) * z);
	double tmp;
	if (z <= -3.5) {
		tmp = t_0;
	} else if (z <= -8e-17) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (z <= -6.8e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.3e-273) {
		tmp = y * 4.0;
	} else if (z <= 7e-82) {
		tmp = x * -3.0;
	} else if (z <= 1.65e-18) {
		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 * ((y - x) * z)
	tmp = 0
	if z <= -3.5:
		tmp = t_0
	elif z <= -8e-17:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif z <= -6.8e-229:
		tmp = x * -3.0
	elif z <= 2.3e-273:
		tmp = y * 4.0
	elif z <= 7e-82:
		tmp = x * -3.0
	elif z <= 1.65e-18:
		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(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -3.5)
		tmp = t_0;
	elseif (z <= -8e-17)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (z <= -6.8e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.3e-273)
		tmp = Float64(y * 4.0);
	elseif (z <= 7e-82)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.65e-18)
		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 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -3.5)
		tmp = t_0;
	elseif (z <= -8e-17)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (z <= -6.8e-229)
		tmp = x * -3.0;
	elseif (z <= 2.3e-273)
		tmp = y * 4.0;
	elseif (z <= 7e-82)
		tmp = x * -3.0;
	elseif (z <= 1.65e-18)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.5], t$95$0, If[LessEqual[z, -8e-17], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -6.8e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.3e-273], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 7e-82], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.65e-18], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -3.5 or 0.5 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.8%

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

   if -3.5 < z < -8.00000000000000057e-17

   1. Initial program 98.8%

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

      1. metadata-eval 98.8%

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

   3. Simplified 98.8%

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

      1. add0 98.8%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.0%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.0%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 85.5%

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

   if -8.00000000000000057e-17 < z < -6.7999999999999998e-229 or 2.29999999999999981e-273 < z < 6.9999999999999997e-82 or 1.6500000000000001e-18 < z < 0.5

   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. Add Preprocessing

   5. Taylor expanded in x around inf 64.1%

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

      1. sub-neg 64.1%

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

      2. distribute-rgt-in 64.1%

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

      3. metadata-eval 64.1%

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

      4. metadata-eval 64.1%

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

      5. neg-mul-1 64.1%

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

      6. associate-*r* 64.1%

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

      7. *-commutative 64.1%

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

      8. distribute-lft-in 64.1%

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

      9. distribute-lft-in 64.1%

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

      10. metadata-eval 64.1%

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

      11. metadata-eval 64.1%

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

      12. associate-+r+ 64.1%

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

      13. metadata-eval 64.1%

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

      14. metadata-eval 64.1%

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

      15. associate-*r* 64.1%

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

      16. metadata-eval 64.1%

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

      17. *-commutative 64.1%

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

   7. Simplified 64.1%

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

   8. Taylor expanded in z around 0 63.4%

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

      1. *-commutative 63.4%

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

   10. Simplified 63.4%

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

   if -6.7999999999999998e-229 < z < 2.29999999999999981e-273 or 6.9999999999999997e-82 < z < 1.6500000000000001e-18

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.5%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 59.6%

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

   8. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

4. Final simplification 78.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.5:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-17}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.3 \cdot 10^{-273}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-82}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.65 \cdot 10^{-18}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 74.1% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{if}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* (- y x) z))))
   (if (<= z -4.8e-9)
     t_0
     (if (<= z -8e-229)
       (* x -3.0)
       (if (<= z 1.42e-272)
         (* y 4.0)
         (if (<= z 1.6e-81)
           (* x -3.0)
           (if (<= z 7e-15) (* 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 * ((y - x) * z);
	double tmp;
	if (z <= -4.8e-9) {
		tmp = t_0;
	} else if (z <= -8e-229) {
		tmp = x * -3.0;
	} else if (z <= 1.42e-272) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-81) {
		tmp = x * -3.0;
	} else if (z <= 7e-15) {
		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) * ((y - x) * z)
    if (z <= (-4.8d-9)) then
        tmp = t_0
    else if (z <= (-8d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.42d-272) then
        tmp = y * 4.0d0
    else if (z <= 1.6d-81) then
        tmp = x * (-3.0d0)
    else if (z <= 7d-15) 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 * ((y - x) * z);
	double tmp;
	if (z <= -4.8e-9) {
		tmp = t_0;
	} else if (z <= -8e-229) {
		tmp = x * -3.0;
	} else if (z <= 1.42e-272) {
		tmp = y * 4.0;
	} else if (z <= 1.6e-81) {
		tmp = x * -3.0;
	} else if (z <= 7e-15) {
		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 * ((y - x) * z)
	tmp = 0
	if z <= -4.8e-9:
		tmp = t_0
	elif z <= -8e-229:
		tmp = x * -3.0
	elif z <= 1.42e-272:
		tmp = y * 4.0
	elif z <= 1.6e-81:
		tmp = x * -3.0
	elif z <= 7e-15:
		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(Float64(y - x) * z))
	tmp = 0.0
	if (z <= -4.8e-9)
		tmp = t_0;
	elseif (z <= -8e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.42e-272)
		tmp = Float64(y * 4.0);
	elseif (z <= 1.6e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= 7e-15)
		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 * ((y - x) * z);
	tmp = 0.0;
	if (z <= -4.8e-9)
		tmp = t_0;
	elseif (z <= -8e-229)
		tmp = x * -3.0;
	elseif (z <= 1.42e-272)
		tmp = y * 4.0;
	elseif (z <= 1.6e-81)
		tmp = x * -3.0;
	elseif (z <= 7e-15)
		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[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -4.8e-9], t$95$0, If[LessEqual[z, -8e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.42e-272], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 1.6e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7e-15], 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 < -4.8e-9 or 0.5 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 97.0%

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

   if -4.8e-9 < z < -8.00000000000000055e-229 or 1.41999999999999997e-272 < z < 1.6e-81 or 7.0000000000000001e-15 < z < 0.5

   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. Add Preprocessing

   5. Taylor expanded in x around inf 61.3%

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

      1. sub-neg 61.3%

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

      2. distribute-rgt-in 61.3%

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

      3. metadata-eval 61.3%

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

      4. metadata-eval 61.3%

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

      5. neg-mul-1 61.3%

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

      6. associate-*r* 61.3%

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

      7. *-commutative 61.3%

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

      8. distribute-lft-in 61.3%

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

      9. distribute-lft-in 61.3%

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

      10. metadata-eval 61.3%

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

      11. metadata-eval 61.3%

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

      12. associate-+r+ 61.3%

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

      13. metadata-eval 61.3%

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

      14. metadata-eval 61.3%

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

      15. associate-*r* 61.3%

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

      16. metadata-eval 61.3%

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

      17. *-commutative 61.3%

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

   7. Simplified 61.3%

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

   8. Taylor expanded in z around 0 60.2%

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

      1. *-commutative 60.2%

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

   10. Simplified 60.2%

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

   if -8.00000000000000055e-229 < z < 1.41999999999999997e-272 or 1.6e-81 < z < 7.0000000000000001e-15

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.5%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 59.6%

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

   8. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

4. Final simplification 76.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -4.8 \cdot 10^{-9}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{elif}\;z \leq -8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.42 \cdot 10^{-272}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 1.6 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7 \cdot 10^{-15}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 50.3% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -26:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -26.0)
     t_0
     (if (<= z -6.8e-229)
       (* x -3.0)
       (if (<= z 2.6e-271)
         (* y 4.0)
         (if (<= z 2.7e-81)
           (* x -3.0)
           (if (<= z 7.6e-19) (* 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 * (y * z);
	double tmp;
	if (z <= -26.0) {
		tmp = t_0;
	} else if (z <= -6.8e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-271) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-81) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-19) {
		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) * (y * z)
    if (z <= (-26.0d0)) then
        tmp = t_0
    else if (z <= (-6.8d-229)) then
        tmp = x * (-3.0d0)
    else if (z <= 2.6d-271) then
        tmp = y * 4.0d0
    else if (z <= 2.7d-81) then
        tmp = x * (-3.0d0)
    else if (z <= 7.6d-19) 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 * (y * z);
	double tmp;
	if (z <= -26.0) {
		tmp = t_0;
	} else if (z <= -6.8e-229) {
		tmp = x * -3.0;
	} else if (z <= 2.6e-271) {
		tmp = y * 4.0;
	} else if (z <= 2.7e-81) {
		tmp = x * -3.0;
	} else if (z <= 7.6e-19) {
		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 * (y * z)
	tmp = 0
	if z <= -26.0:
		tmp = t_0
	elif z <= -6.8e-229:
		tmp = x * -3.0
	elif z <= 2.6e-271:
		tmp = y * 4.0
	elif z <= 2.7e-81:
		tmp = x * -3.0
	elif z <= 7.6e-19:
		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(y * z))
	tmp = 0.0
	if (z <= -26.0)
		tmp = t_0;
	elseif (z <= -6.8e-229)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.6e-271)
		tmp = Float64(y * 4.0);
	elseif (z <= 2.7e-81)
		tmp = Float64(x * -3.0);
	elseif (z <= 7.6e-19)
		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 * (y * z);
	tmp = 0.0;
	if (z <= -26.0)
		tmp = t_0;
	elseif (z <= -6.8e-229)
		tmp = x * -3.0;
	elseif (z <= 2.6e-271)
		tmp = y * 4.0;
	elseif (z <= 2.7e-81)
		tmp = x * -3.0;
	elseif (z <= 7.6e-19)
		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[(y * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -26.0], t$95$0, If[LessEqual[z, -6.8e-229], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.6e-271], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 2.7e-81], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 7.6e-19], 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 < -26 or 0.55000000000000004 < 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. Add Preprocessing

   5. Taylor expanded in z around 0 99.7%

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

   6. Taylor expanded in z around inf 98.4%

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

   7. Taylor expanded in y around inf 56.7%

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

      1. *-commutative 56.7%

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

   9. Simplified 56.7%

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

   if -26 < z < -6.7999999999999998e-229 or 2.6e-271 < z < 2.6999999999999999e-81 or 7.6e-19 < z < 0.55000000000000004

   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. Add Preprocessing

   5. Taylor expanded in x around inf 61.1%

      \[\leadsto \color{blue}{x \cdot \left(1 + -6 \cdot \left(0.6666666666666666 - z\right)\right)} \]
   6. 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. metadata-eval 61.1%

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

      5. neg-mul-1 61.1%

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

      6. associate-*r* 61.1%

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

      7. *-commutative 61.1%

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

      8. distribute-lft-in 61.1%

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

      9. distribute-lft-in 61.1%

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

      10. metadata-eval 61.1%

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

      11. metadata-eval 61.1%

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

      12. associate-+r+ 61.1%

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

      13. metadata-eval 61.1%

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

      14. metadata-eval 61.1%

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

      15. associate-*r* 61.1%

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

      16. metadata-eval 61.1%

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

      17. *-commutative 61.1%

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

   7. Simplified 61.1%

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

   8. Taylor expanded in z around 0 59.1%

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

      1. *-commutative 59.1%

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

   10. Simplified 59.1%

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

   if -6.7999999999999998e-229 < z < 2.6e-271 or 2.6999999999999999e-81 < z < 7.6e-19

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.5%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 100.0%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 100.0%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 59.6%

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

   8. Taylor expanded in z around 0 59.8%

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

      1. *-commutative 59.8%

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

   10. Simplified 59.8%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -26:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -6.8 \cdot 10^{-229}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.6 \cdot 10^{-271}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{-81}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 7.6 \cdot 10^{-19}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.55:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-39} \lor \neg \left(x \leq 3.3 \cdot 10^{+24}\right) \land \left(x \leq 1.7 \cdot 10^{+45} \lor \neg \left(x \leq 1.15 \cdot 10^{+103}\right)\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -2.2e-39)
         (and (not (<= x 3.3e+24)) (or (<= x 1.7e+45) (not (<= x 1.15e+103)))))
   (* x (+ -3.0 (* z 6.0)))
   (* 6.0 (* y (- 0.6666666666666666 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-39) || (!(x <= 3.3e+24) && ((x <= 1.7e+45) || !(x <= 1.15e+103)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - 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 <= (-2.2d-39)) .or. (.not. (x <= 3.3d+24)) .and. (x <= 1.7d+45) .or. (.not. (x <= 1.15d+103))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -2.2e-39) || (!(x <= 3.3e+24) && ((x <= 1.7e+45) || !(x <= 1.15e+103)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -2.2e-39) or (not (x <= 3.3e+24) and ((x <= 1.7e+45) or not (x <= 1.15e+103))):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -2.2e-39) || (!(x <= 3.3e+24) && ((x <= 1.7e+45) || !(x <= 1.15e+103))))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -2.2e-39) || (~((x <= 3.3e+24)) && ((x <= 1.7e+45) || ~((x <= 1.15e+103)))))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -2.2e-39], And[N[Not[LessEqual[x, 3.3e+24]], $MachinePrecision], Or[LessEqual[x, 1.7e+45], N[Not[LessEqual[x, 1.15e+103]], $MachinePrecision]]]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -2.20000000000000001e-39 or 3.2999999999999999e24 < x < 1.7e45 or 1.15000000000000004e103 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. distribute-rgt-in 86.4%

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

      3. metadata-eval 86.4%

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

      4. metadata-eval 86.4%

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

      5. neg-mul-1 86.4%

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

      6. associate-*r* 86.4%

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

      7. *-commutative 86.4%

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

      8. distribute-lft-in 86.4%

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

      9. distribute-lft-in 86.4%

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

      10. metadata-eval 86.4%

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

      11. metadata-eval 86.4%

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

      12. associate-+r+ 86.4%

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

      13. metadata-eval 86.4%

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

      14. metadata-eval 86.4%

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

      15. associate-*r* 86.4%

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

      16. metadata-eval 86.4%

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

      17. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -2.20000000000000001e-39 < x < 3.2999999999999999e24 or 1.7e45 < x < 1.15000000000000004e103

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.6%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 79.0%

      \[\leadsto \color{blue}{6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.2 \cdot 10^{-39} \lor \neg \left(x \leq 3.3 \cdot 10^{+24}\right) \land \left(x \leq 1.7 \cdot 10^{+45} \lor \neg \left(x \leq 1.15 \cdot 10^{+103}\right)\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-45} \lor \neg \left(x \leq 10^{+24} \lor \neg \left(x \leq 1.6 \cdot 10^{+45}\right) \land x \leq 3.8 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.2e-45)
         (not (or (<= x 1e+24) (and (not (<= x 1.6e+45)) (<= x 3.8e+103)))))
   (* x (+ -3.0 (* z 6.0)))
   (* y (+ 4.0 (* z -6.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e-45) || !((x <= 1e+24) || (!(x <= 1.6e+45) && (x <= 3.8e+103)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((x <= (-4.2d-45)) .or. (.not. (x <= 1d+24) .or. (.not. (x <= 1.6d+45)) .and. (x <= 3.8d+103))) then
        tmp = x * ((-3.0d0) + (z * 6.0d0))
    else
        tmp = y * (4.0d0 + (z * (-6.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -4.2e-45) || !((x <= 1e+24) || (!(x <= 1.6e+45) && (x <= 3.8e+103)))) {
		tmp = x * (-3.0 + (z * 6.0));
	} else {
		tmp = y * (4.0 + (z * -6.0));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -4.2e-45) or not ((x <= 1e+24) or (not (x <= 1.6e+45) and (x <= 3.8e+103))):
		tmp = x * (-3.0 + (z * 6.0))
	else:
		tmp = y * (4.0 + (z * -6.0))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -4.2e-45) || !((x <= 1e+24) || (!(x <= 1.6e+45) && (x <= 3.8e+103))))
		tmp = Float64(x * Float64(-3.0 + Float64(z * 6.0)));
	else
		tmp = Float64(y * Float64(4.0 + Float64(z * -6.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -4.2e-45) || ~(((x <= 1e+24) || (~((x <= 1.6e+45)) && (x <= 3.8e+103)))))
		tmp = x * (-3.0 + (z * 6.0));
	else
		tmp = y * (4.0 + (z * -6.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -4.2e-45], N[Not[Or[LessEqual[x, 1e+24], And[N[Not[LessEqual[x, 1.6e+45]], $MachinePrecision], LessEqual[x, 3.8e+103]]]], $MachinePrecision]], N[(x * N[(-3.0 + N[(z * 6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(4.0 + N[(z * -6.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -4.1999999999999999e-45 or 9.9999999999999998e23 < x < 1.6000000000000001e45 or 3.7999999999999997e103 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 86.4%

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

      1. sub-neg 86.4%

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

      2. distribute-rgt-in 86.4%

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

      3. metadata-eval 86.4%

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

      4. metadata-eval 86.4%

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

      5. neg-mul-1 86.4%

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

      6. associate-*r* 86.4%

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

      7. *-commutative 86.4%

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

      8. distribute-lft-in 86.4%

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

      9. distribute-lft-in 86.4%

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

      10. metadata-eval 86.4%

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

      11. metadata-eval 86.4%

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

      12. associate-+r+ 86.4%

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

      13. metadata-eval 86.4%

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

      14. metadata-eval 86.4%

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

      15. associate-*r* 86.4%

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

      16. metadata-eval 86.4%

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

      17. *-commutative 86.4%

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

   7. Simplified 86.4%

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

   if -4.1999999999999999e-45 < x < 9.9999999999999998e23 or 1.6000000000000001e45 < x < 3.7999999999999997e103

   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. +-commutative 99.6%

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

      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-define 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. Add Preprocessing

   5. Taylor expanded in y around inf 79.1%

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

4. Final simplification 82.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.2 \cdot 10^{-45} \lor \neg \left(x \leq 10^{+24} \lor \neg \left(x \leq 1.6 \cdot 10^{+45}\right) \land x \leq 3.8 \cdot 10^{+103}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 97.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.58) (not (<= z 0.6)))
   (* (- y x) (* z -6.0))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.6)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if ((z <= (-0.58d0)) .or. (.not. (z <= 0.6d0))) then
        tmp = (y - x) * (z * (-6.0d0))
    else
        tmp = x + ((y - x) * 4.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.58) || !(z <= 0.6)) {
		tmp = (y - x) * (z * -6.0);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.58) or not (z <= 0.6):
		tmp = (y - x) * (z * -6.0)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.58) || !(z <= 0.6))
		tmp = Float64(Float64(y - x) * Float64(z * -6.0));
	else
		tmp = Float64(x + Float64(Float64(y - x) * 4.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z <= -0.58) || ~((z <= 0.6)))
		tmp = (y - x) * (z * -6.0);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.58], N[Not[LessEqual[z, 0.6]], $MachinePrecision]], N[(N[(y - x), $MachinePrecision] * N[(z * -6.0), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.57999999999999996 or 0.599999999999999978 < 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. Add Preprocessing
   5. Step-by-step derivation

      1. +-commutative 99.8%

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

      2. add-sqr-sqrt 52.8%

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

      3. fma-define 52.8%

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

      4. associate-*l* 52.9%

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

      5. associate-*l* 52.8%

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

   6. Applied egg-rr 52.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}, \sqrt{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}, x\right)} \]
   7. Step-by-step derivation

      1. fma-undefine 52.8%

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

      2. add-sqr-sqrt 99.7%

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

   8. Applied egg-rr 99.7%

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

   9. Taylor expanded in z around inf 97.8%

      \[\leadsto \color{blue}{-6 \cdot \left(z \cdot \left(y - x\right)\right)} \]
   10. 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%

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

   11. Simplified 97.8%

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

   if -0.57999999999999996 < z < 0.599999999999999978

   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. Add Preprocessing

   5. Taylor expanded in z around 0 98.2%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.58 \lor \neg \left(z \leq 0.6\right):\\ \;\;\;\;\left(y - x\right) \cdot \left(z \cdot -6\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return x + ((-6.0 * ((y - x) * z)) + ((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) * ((y - x) * z)) + ((y - x) * 4.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

5. Taylor expanded in z around 0 99.8%

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

6. Final simplification 99.8%

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

Alternative 13: 38.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+28} \lor \neg \left(x \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -6e+28) (not (<= x 1.5e+28))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+28) || !(x <= 1.5e+28)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	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 <= (-6d+28)) .or. (.not. (x <= 1.5d+28))) then
        tmp = x * (-3.0d0)
    else
        tmp = y * 4.0d0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((x <= -6e+28) || !(x <= 1.5e+28)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -6e+28) or not (x <= 1.5e+28):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -6e+28) || !(x <= 1.5e+28))
		tmp = Float64(x * -3.0);
	else
		tmp = Float64(y * 4.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((x <= -6e+28) || ~((x <= 1.5e+28)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -6e+28], N[Not[LessEqual[x, 1.5e+28]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -6.0000000000000002e28 or 1.5e28 < x

   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. Add Preprocessing

   5. Taylor expanded in x around inf 80.2%

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

      1. sub-neg 80.2%

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

      2. distribute-rgt-in 80.2%

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

      3. metadata-eval 80.2%

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

      4. metadata-eval 80.2%

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

      5. neg-mul-1 80.2%

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

      6. associate-*r* 80.2%

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

      7. *-commutative 80.2%

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

      8. distribute-lft-in 80.2%

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

      9. distribute-lft-in 80.2%

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

      10. metadata-eval 80.2%

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

      11. metadata-eval 80.2%

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

      12. associate-+r+ 80.2%

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

      13. metadata-eval 80.2%

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

      14. metadata-eval 80.2%

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

      15. associate-*r* 80.2%

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

      16. metadata-eval 80.2%

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

      17. *-commutative 80.2%

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

   7. Simplified 80.2%

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

   8. Taylor expanded in z around 0 48.1%

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

      1. *-commutative 48.1%

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

   10. Simplified 48.1%

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

   if -6.0000000000000002e28 < x < 1.5e28

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.6%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 76.6%

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

   8. Taylor expanded in z around 0 40.7%

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

      1. *-commutative 40.7%

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

   10. Simplified 40.7%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -6 \cdot 10^{+28} \lor \neg \left(x \leq 1.5 \cdot 10^{+28}\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 38.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{-0.3333333333333333}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+24}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -3e+28)
   (/ x -0.3333333333333333)
   (if (<= x 1.1e+24) (* y 4.0) (* x -3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -3e+28) {
		tmp = x / -0.3333333333333333;
	} else if (x <= 1.1e+24) {
		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 <= (-3d+28)) then
        tmp = x / (-0.3333333333333333d0)
    else if (x <= 1.1d+24) 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 <= -3e+28) {
		tmp = x / -0.3333333333333333;
	} else if (x <= 1.1e+24) {
		tmp = y * 4.0;
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -3e+28:
		tmp = x / -0.3333333333333333
	elif x <= 1.1e+24:
		tmp = y * 4.0
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -3e+28)
		tmp = Float64(x / -0.3333333333333333);
	elseif (x <= 1.1e+24)
		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 <= -3e+28)
		tmp = x / -0.3333333333333333;
	elseif (x <= 1.1e+24)
		tmp = y * 4.0;
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -3e+28], N[(x / -0.3333333333333333), $MachinePrecision], If[LessEqual[x, 1.1e+24], N[(y * 4.0), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < -3.0000000000000001e28

   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. Add Preprocessing

   5. Taylor expanded in x around inf 82.5%

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

      1. sub-neg 82.5%

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

      2. distribute-rgt-in 82.5%

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

      3. metadata-eval 82.5%

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

      4. metadata-eval 82.5%

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

      5. neg-mul-1 82.5%

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

      6. associate-*r* 82.5%

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

      7. *-commutative 82.5%

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

      8. distribute-lft-in 82.5%

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

      9. distribute-lft-in 82.5%

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

      10. metadata-eval 82.5%

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

      11. metadata-eval 82.5%

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

      12. associate-+r+ 82.5%

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

      13. metadata-eval 82.5%

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

      14. metadata-eval 82.5%

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

      15. associate-*r* 82.5%

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

      16. metadata-eval 82.5%

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

      17. *-commutative 82.5%

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

   7. Simplified 82.5%

      \[\leadsto \color{blue}{x \cdot \left(-3 + z \cdot 6\right)} \]
   8. Step-by-step derivation

      1. flip-+ 78.1%

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

      2. associate-*r/ 73.7%

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

      3. metadata-eval 73.7%

         \[\leadsto \frac{x \cdot \left(\color{blue}{9} - \left(z \cdot 6\right) \cdot \left(z \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      4. swap-sqr 73.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{\left(z \cdot z\right) \cdot \left(6 \cdot 6\right)}\right)}{-3 - z \cdot 6} \]

      5. pow2 73.6%

         \[\leadsto \frac{x \cdot \left(9 - \color{blue}{{z}^{2}} \cdot \left(6 \cdot 6\right)\right)}{-3 - z \cdot 6} \]

      6. metadata-eval 73.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot \color{blue}{36}\right)}{-3 - z \cdot 6} \]

      7. *-commutative 73.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 - \color{blue}{6 \cdot z}} \]

      8. cancel-sign-sub-inv 73.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{\color{blue}{-3 + \left(-6\right) \cdot z}} \]

      9. metadata-eval 73.6%

         \[\leadsto \frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + \color{blue}{-6} \cdot z} \]

   9. Applied egg-rr 73.6%

      \[\leadsto \color{blue}{\frac{x \cdot \left(9 - {z}^{2} \cdot 36\right)}{-3 + -6 \cdot z}} \]
   10. Step-by-step derivation

       1. associate-/l* 78.1%

          \[\leadsto \color{blue}{\frac{x}{\frac{-3 + -6 \cdot z}{9 - {z}^{2} \cdot 36}}} \]

       2. +-commutative 78.1%

          \[\leadsto \frac{x}{\frac{\color{blue}{-6 \cdot z + -3}}{9 - {z}^{2} \cdot 36}} \]

       3. *-commutative 78.1%

          \[\leadsto \frac{x}{\frac{\color{blue}{z \cdot -6} + -3}{9 - {z}^{2} \cdot 36}} \]

   11. Simplified 78.1%

       \[\leadsto \color{blue}{\frac{x}{\frac{z \cdot -6 + -3}{9 - {z}^{2} \cdot 36}}} \]

   12. Taylor expanded in z around 0 45.4%

       \[\leadsto \frac{x}{\color{blue}{-0.3333333333333333}} \]

   if -3.0000000000000001e28 < x < 1.10000000000000001e24

   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. Add Preprocessing
   5. Step-by-step derivation

      1. add0 99.6%

         \[\leadsto x + \color{blue}{\left(\left(\left(y - x\right) \cdot 6\right) \cdot \left(0.6666666666666666 - z\right) + 0\right)} \]

      2. associate-*l* 99.8%

         \[\leadsto x + \left(\color{blue}{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)} + 0\right) \]

   6. Applied egg-rr 99.8%

      \[\leadsto x + \color{blue}{\left(\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right) + 0\right)} \]

   7. Taylor expanded in x around 0 76.6%

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

   8. Taylor expanded in z around 0 40.7%

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

      1. *-commutative 40.7%

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

   10. Simplified 40.7%

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

   if 1.10000000000000001e24 < 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. Add Preprocessing

   5. Taylor expanded in x around inf 77.9%

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

      1. sub-neg 77.9%

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

      2. distribute-rgt-in 77.9%

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

      3. metadata-eval 77.9%

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

      4. metadata-eval 77.9%

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

      5. neg-mul-1 77.9%

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

      6. associate-*r* 77.9%

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

      7. *-commutative 77.9%

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

      8. distribute-lft-in 77.9%

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

      9. distribute-lft-in 77.9%

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

      10. metadata-eval 77.9%

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

      11. metadata-eval 77.9%

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

      12. associate-+r+ 77.9%

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

      13. metadata-eval 77.9%

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

      14. metadata-eval 77.9%

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

      15. associate-*r* 77.9%

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

      16. metadata-eval 77.9%

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

      17. *-commutative 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in z around 0 51.0%

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

      1. *-commutative 51.0%

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

   10. Simplified 51.0%

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

4. Final simplification 44.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3 \cdot 10^{+28}:\\ \;\;\;\;\frac{x}{-0.3333333333333333}\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+24}:\\ \;\;\;\;y \cdot 4\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 * (x - y)) * (z - 0.6666666666666666d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing

5. Final simplification 99.6%

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

Alternative 16: 99.8% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

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 + ((x - y) * (6.0d0 * (z - 0.6666666666666666d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. Add Preprocessing
5. Step-by-step derivation

   1. +-commutative 99.6%

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

   2. add-sqr-sqrt 46.5%

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

   3. fma-define 46.5%

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

   4. associate-*l* 46.6%

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

   5. associate-*l* 46.6%

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

6. Applied egg-rr 46.6%

   \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}, \sqrt{\left(y - x\right) \cdot \left(6 \cdot \left(0.6666666666666666 - z\right)\right)}, x\right)} \]
7. Step-by-step derivation

   1. fma-undefine 46.5%

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

   2. add-sqr-sqrt 99.8%

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

8. Applied egg-rr 99.8%

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

9. Final simplification 99.8%

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

Alternative 17: 26.3% 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 99.6%

   \[x + \left(\left(y - x\right) \cdot 6\right) \cdot \left(\frac{2}{3} - z\right) \]
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. Add Preprocessing

5. Taylor expanded in x around inf 52.1%

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

   1. sub-neg 52.1%

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

   2. distribute-rgt-in 52.1%

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

   3. metadata-eval 52.1%

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

   4. metadata-eval 52.1%

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

   5. neg-mul-1 52.1%

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

   6. associate-*r* 52.1%

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

   7. *-commutative 52.1%

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

   8. distribute-lft-in 52.1%

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

   9. distribute-lft-in 52.1%

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

   10. metadata-eval 52.1%

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

   11. metadata-eval 52.1%

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

   12. associate-+r+ 52.1%

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

   13. metadata-eval 52.1%

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

   14. metadata-eval 52.1%

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

   15. associate-*r* 52.1%

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

   16. metadata-eval 52.1%

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

   17. *-commutative 52.1%

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

7. Simplified 52.1%

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

8. Taylor expanded in z around 0 31.3%

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

   1. *-commutative 31.3%

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

10. Simplified 31.3%

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

11. Final simplification 31.3%

    \[\leadsto x \cdot -3 \]
12. Add Preprocessing

Reproduce

herbie shell --seed 2024034 
(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))))