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

Percentage Accurate: 99.5% → 99.8%

Time: 15.3s

Alternatives: 14

Speedup: 1.2×

• 21.5% 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 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.7%

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

   3. fma-define 99.7%

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

   4. sub-neg 99.7%

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

   5. distribute-rgt-in 99.7%

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

   6. metadata-eval 99.7%

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

   7. metadata-eval 99.7%

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

   8. distribute-lft-neg-out 99.7%

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

   9. distribute-rgt-neg-in 99.7%

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

   10. metadata-eval 99.7%

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

3. Simplified 99.7%

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

Alternative 2: 99.7% accurate, 0.1× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.7%

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

   3. fma-define 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

Alternative 3: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(y \cdot -6\right)\\ \mathbf{if}\;z \leq -3.4 \cdot 10^{+167}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -17:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* y -6.0))))
   (if (<= z -3.4e+167)
     (* -6.0 (* y z))
     (if (<= z -4.5e+36)
       (* 6.0 (* x z))
       (if (<= z -17.0)
         t_0
         (if (<= z -4e-185)
           (* x -3.0)
           (if (<= z 1.15e-215)
             (* y 4.0)
             (if (<= z 0.5)
               (* x -3.0)
               (if (<= z 2.7e+118) (* x (* z 6.0)) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double tmp;
	if (z <= -3.4e+167) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.5e+36) {
		tmp = 6.0 * (x * z);
	} else if (z <= -17.0) {
		tmp = t_0;
	} else if (z <= -4e-185) {
		tmp = x * -3.0;
	} else if (z <= 1.15e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.7e+118) {
		tmp = x * (z * 6.0);
	} 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 = z * (y * (-6.0d0))
    if (z <= (-3.4d+167)) then
        tmp = (-6.0d0) * (y * z)
    else if (z <= (-4.5d+36)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-17.0d0)) then
        tmp = t_0
    else if (z <= (-4d-185)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.15d-215) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.7d+118) then
        tmp = x * (z * 6.0d0)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = z * (y * -6.0);
	double tmp;
	if (z <= -3.4e+167) {
		tmp = -6.0 * (y * z);
	} else if (z <= -4.5e+36) {
		tmp = 6.0 * (x * z);
	} else if (z <= -17.0) {
		tmp = t_0;
	} else if (z <= -4e-185) {
		tmp = x * -3.0;
	} else if (z <= 1.15e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.7e+118) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (y * -6.0)
	tmp = 0
	if z <= -3.4e+167:
		tmp = -6.0 * (y * z)
	elif z <= -4.5e+36:
		tmp = 6.0 * (x * z)
	elif z <= -17.0:
		tmp = t_0
	elif z <= -4e-185:
		tmp = x * -3.0
	elif z <= 1.15e-215:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 2.7e+118:
		tmp = x * (z * 6.0)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(y * -6.0))
	tmp = 0.0
	if (z <= -3.4e+167)
		tmp = Float64(-6.0 * Float64(y * z));
	elseif (z <= -4.5e+36)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -17.0)
		tmp = t_0;
	elseif (z <= -4e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.15e-215)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.7e+118)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (y * -6.0);
	tmp = 0.0;
	if (z <= -3.4e+167)
		tmp = -6.0 * (y * z);
	elseif (z <= -4.5e+36)
		tmp = 6.0 * (x * z);
	elseif (z <= -17.0)
		tmp = t_0;
	elseif (z <= -4e-185)
		tmp = x * -3.0;
	elseif (z <= 1.15e-215)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 2.7e+118)
		tmp = x * (z * 6.0);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(y * -6.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -3.4e+167], N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -4.5e+36], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -17.0], t$95$0, If[LessEqual[z, -4e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.15e-215], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.7e+118], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if z < -3.4e167

   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 y around inf 63.3%

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

   6. Taylor expanded in z around inf 63.3%

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

   7. Taylor expanded in x around 0 63.4%

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

   if -3.4e167 < z < -4.49999999999999997e36

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.5%

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

      3. fma-define 99.5%

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

      4. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r* 75.2%

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

      3. *-lft-identity 75.2%

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

      4. sub-neg 75.2%

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

      5. distribute-rgt-in 75.2%

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

      6. metadata-eval 75.2%

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

      7. neg-mul-1 75.2%

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

      8. associate-*r* 75.2%

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

      9. *-commutative 75.2%

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

      10. metadata-eval 75.2%

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

      11. distribute-lft-in 75.2%

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

      12. distribute-rgt-in 75.2%

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

      13. distribute-lft-in 75.2%

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

      14. metadata-eval 75.2%

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

      15. associate-+r+ 75.2%

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

      16. metadata-eval 75.2%

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

      17. associate-*r* 75.2%

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

      18. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in z around inf 75.3%

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

   if -4.49999999999999997e36 < z < -17 or 2.7e118 < z

   1. Initial program 99.7%

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

      1. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 68.0%

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

   6. Taylor expanded in z around inf 66.2%

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

   7. Taylor expanded in x around 0 65.7%

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

      1. associate-*r* 65.7%

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

      2. *-commutative 65.7%

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

      3. *-commutative 65.7%

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

   9. Simplified 65.7%

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

   if -17 < z < -4e-185 or 1.15e-215 < 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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.2%

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

      3. *-lft-identity 63.2%

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

      4. sub-neg 63.2%

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

      5. distribute-rgt-in 63.3%

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

      6. metadata-eval 63.3%

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

      7. neg-mul-1 63.3%

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

      8. associate-*r* 63.3%

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

      9. *-commutative 63.3%

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

      10. metadata-eval 63.3%

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

      11. distribute-lft-in 63.3%

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

      12. distribute-rgt-in 63.3%

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

      13. distribute-lft-in 63.3%

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

      14. metadata-eval 63.3%

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

      15. associate-+r+ 63.3%

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

      16. metadata-eval 63.3%

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

      17. associate-*r* 63.3%

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

      18. metadata-eval 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in z around 0 59.4%

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

      1. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -4e-185 < z < 1.15e-215

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. add-sqr-sqrt 43.8%

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

      2. pow2 43.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 43.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 97.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 97.9%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.6%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.6%

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

      8. rem-square-sqrt 100.0%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-*r* 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 66.2%

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

   11. Taylor expanded in z around 0 66.5%

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

       1. *-commutative 66.5%

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

   13. Simplified 66.5%

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

   if 0.5 < z < 2.7e118

   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. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*r* 63.5%

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

      3. *-lft-identity 63.5%

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

      4. sub-neg 63.5%

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

      5. distribute-rgt-in 63.5%

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

      6. metadata-eval 63.5%

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

      7. neg-mul-1 63.5%

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

      8. associate-*r* 63.5%

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

      9. *-commutative 63.5%

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

      10. metadata-eval 63.5%

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

      11. distribute-lft-in 63.5%

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

      12. distribute-rgt-in 63.4%

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

      13. distribute-lft-in 63.4%

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

      14. metadata-eval 63.4%

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

      15. associate-+r+ 63.4%

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

      16. metadata-eval 63.4%

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

      17. associate-*r* 63.4%

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

      18. metadata-eval 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around inf 57.2%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. associate-*r* 57.2%

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

   10. Simplified 57.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -3.4 \cdot 10^{+167}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -4.5 \cdot 10^{+36}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -17:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \mathbf{elif}\;z \leq -4 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.15 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(y \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -31:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -2.5e+162)
     t_0
     (if (<= z -2.1e+35)
       (* 6.0 (* x z))
       (if (<= z -31.0)
         t_0
         (if (<= z -1.8e-186)
           (* x -3.0)
           (if (<= z 1.7e-215)
             (* y 4.0)
             (if (<= z 0.5)
               (* x -3.0)
               (if (<= z 2.55e+118) (* x (* z 6.0)) t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double tmp;
	if (z <= -2.5e+162) {
		tmp = t_0;
	} else if (z <= -2.1e+35) {
		tmp = 6.0 * (x * z);
	} else if (z <= -31.0) {
		tmp = t_0;
	} else if (z <= -1.8e-186) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.55e+118) {
		tmp = x * (z * 6.0);
	} 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 <= (-2.5d+162)) then
        tmp = t_0
    else if (z <= (-2.1d+35)) then
        tmp = 6.0d0 * (x * z)
    else if (z <= (-31.0d0)) then
        tmp = t_0
    else if (z <= (-1.8d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= 1.7d-215) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.55d+118) then
        tmp = x * (z * 6.0d0)
    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 <= -2.5e+162) {
		tmp = t_0;
	} else if (z <= -2.1e+35) {
		tmp = 6.0 * (x * z);
	} else if (z <= -31.0) {
		tmp = t_0;
	} else if (z <= -1.8e-186) {
		tmp = x * -3.0;
	} else if (z <= 1.7e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.55e+118) {
		tmp = x * (z * 6.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	tmp = 0
	if z <= -2.5e+162:
		tmp = t_0
	elif z <= -2.1e+35:
		tmp = 6.0 * (x * z)
	elif z <= -31.0:
		tmp = t_0
	elif z <= -1.8e-186:
		tmp = x * -3.0
	elif z <= 1.7e-215:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 2.55e+118:
		tmp = x * (z * 6.0)
	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 <= -2.5e+162)
		tmp = t_0;
	elseif (z <= -2.1e+35)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (z <= -31.0)
		tmp = t_0;
	elseif (z <= -1.8e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 1.7e-215)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.55e+118)
		tmp = Float64(x * Float64(z * 6.0));
	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 <= -2.5e+162)
		tmp = t_0;
	elseif (z <= -2.1e+35)
		tmp = 6.0 * (x * z);
	elseif (z <= -31.0)
		tmp = t_0;
	elseif (z <= -1.8e-186)
		tmp = x * -3.0;
	elseif (z <= 1.7e-215)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 2.55e+118)
		tmp = x * (z * 6.0);
	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, -2.5e+162], t$95$0, If[LessEqual[z, -2.1e+35], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[z, -31.0], t$95$0, If[LessEqual[z, -1.8e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 1.7e-215], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.55e+118], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if z < -2.4999999999999998e162 or -2.0999999999999999e35 < z < -31 or 2.55000000000000001e118 < 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 y around inf 65.9%

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

   6. Taylor expanded in z around inf 64.9%

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

   7. Taylor expanded in x around 0 64.7%

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

   if -2.4999999999999998e162 < z < -2.0999999999999999e35

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.5%

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

      3. fma-define 99.5%

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

      4. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 75.3%

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

      1. *-commutative 75.3%

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

      2. associate-*r* 75.2%

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

      3. *-lft-identity 75.2%

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

      4. sub-neg 75.2%

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

      5. distribute-rgt-in 75.2%

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

      6. metadata-eval 75.2%

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

      7. neg-mul-1 75.2%

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

      8. associate-*r* 75.2%

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

      9. *-commutative 75.2%

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

      10. metadata-eval 75.2%

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

      11. distribute-lft-in 75.2%

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

      12. distribute-rgt-in 75.2%

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

      13. distribute-lft-in 75.2%

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

      14. metadata-eval 75.2%

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

      15. associate-+r+ 75.2%

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

      16. metadata-eval 75.2%

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

      17. associate-*r* 75.2%

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

      18. metadata-eval 75.2%

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

   7. Simplified 75.2%

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

   8. Taylor expanded in z around inf 75.3%

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

   if -31 < z < -1.7999999999999999e-186 or 1.70000000000000001e-215 < 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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.2%

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

      3. *-lft-identity 63.2%

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

      4. sub-neg 63.2%

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

      5. distribute-rgt-in 63.3%

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

      6. metadata-eval 63.3%

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

      7. neg-mul-1 63.3%

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

      8. associate-*r* 63.3%

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

      9. *-commutative 63.3%

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

      10. metadata-eval 63.3%

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

      11. distribute-lft-in 63.3%

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

      12. distribute-rgt-in 63.3%

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

      13. distribute-lft-in 63.3%

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

      14. metadata-eval 63.3%

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

      15. associate-+r+ 63.3%

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

      16. metadata-eval 63.3%

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

      17. associate-*r* 63.3%

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

      18. metadata-eval 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in z around 0 59.4%

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

      1. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -1.7999999999999999e-186 < z < 1.70000000000000001e-215

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. add-sqr-sqrt 43.8%

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

      2. pow2 43.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 43.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 97.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 97.9%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.6%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.6%

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

      8. rem-square-sqrt 100.0%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-*r* 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 66.2%

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

   11. Taylor expanded in z around 0 66.5%

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

       1. *-commutative 66.5%

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

   13. Simplified 66.5%

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

   if 0.5 < z < 2.55000000000000001e118

   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. +-commutative 99.4%

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

      2. associate-*l* 99.6%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 63.3%

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

      1. *-commutative 63.3%

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

      2. associate-*r* 63.5%

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

      3. *-lft-identity 63.5%

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

      4. sub-neg 63.5%

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

      5. distribute-rgt-in 63.5%

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

      6. metadata-eval 63.5%

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

      7. neg-mul-1 63.5%

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

      8. associate-*r* 63.5%

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

      9. *-commutative 63.5%

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

      10. metadata-eval 63.5%

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

      11. distribute-lft-in 63.5%

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

      12. distribute-rgt-in 63.4%

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

      13. distribute-lft-in 63.4%

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

      14. metadata-eval 63.4%

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

      15. associate-+r+ 63.4%

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

      16. metadata-eval 63.4%

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

      17. associate-*r* 63.4%

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

      18. metadata-eval 63.4%

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

   7. Simplified 63.4%

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

   8. Taylor expanded in z around inf 57.2%

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

      1. associate-*r* 57.1%

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

      2. *-commutative 57.1%

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

      3. associate-*r* 57.2%

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

   10. Simplified 57.2%

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

4. Final simplification 63.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -2.5 \cdot 10^{+162}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -2.1 \cdot 10^{+35}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;z \leq -31:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \mathbf{elif}\;z \leq -1.8 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 1.7 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.55 \cdot 10^{+118}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;-6 \cdot \left(y \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 50.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ t_1 := 6 \cdot \left(x \cdot z\right)\\ \mathbf{if}\;z \leq -5.2 \cdot 10^{+161}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.05 \cdot 10^{+34}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;z \leq -21:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -1.16 \cdot 10^{-186}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 8.8 \cdot 10^{-215}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.5:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 2.7 \cdot 10^{+118}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))) (t_1 (* 6.0 (* x z))))
   (if (<= z -5.2e+161)
     t_0
     (if (<= z -1.05e+34)
       t_1
       (if (<= z -21.0)
         t_0
         (if (<= z -1.16e-186)
           (* x -3.0)
           (if (<= z 8.8e-215)
             (* y 4.0)
             (if (<= z 0.5) (* x -3.0) (if (<= z 2.7e+118) t_1 t_0)))))))))

C

double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.2e+161) {
		tmp = t_0;
	} else if (z <= -1.05e+34) {
		tmp = t_1;
	} else if (z <= -21.0) {
		tmp = t_0;
	} else if (z <= -1.16e-186) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.7e+118) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = (-6.0d0) * (y * z)
    t_1 = 6.0d0 * (x * z)
    if (z <= (-5.2d+161)) then
        tmp = t_0
    else if (z <= (-1.05d+34)) then
        tmp = t_1
    else if (z <= (-21.0d0)) then
        tmp = t_0
    else if (z <= (-1.16d-186)) then
        tmp = x * (-3.0d0)
    else if (z <= 8.8d-215) then
        tmp = y * 4.0d0
    else if (z <= 0.5d0) then
        tmp = x * (-3.0d0)
    else if (z <= 2.7d+118) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double t_0 = -6.0 * (y * z);
	double t_1 = 6.0 * (x * z);
	double tmp;
	if (z <= -5.2e+161) {
		tmp = t_0;
	} else if (z <= -1.05e+34) {
		tmp = t_1;
	} else if (z <= -21.0) {
		tmp = t_0;
	} else if (z <= -1.16e-186) {
		tmp = x * -3.0;
	} else if (z <= 8.8e-215) {
		tmp = y * 4.0;
	} else if (z <= 0.5) {
		tmp = x * -3.0;
	} else if (z <= 2.7e+118) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = -6.0 * (y * z)
	t_1 = 6.0 * (x * z)
	tmp = 0
	if z <= -5.2e+161:
		tmp = t_0
	elif z <= -1.05e+34:
		tmp = t_1
	elif z <= -21.0:
		tmp = t_0
	elif z <= -1.16e-186:
		tmp = x * -3.0
	elif z <= 8.8e-215:
		tmp = y * 4.0
	elif z <= 0.5:
		tmp = x * -3.0
	elif z <= 2.7e+118:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(-6.0 * Float64(y * z))
	t_1 = Float64(6.0 * Float64(x * z))
	tmp = 0.0
	if (z <= -5.2e+161)
		tmp = t_0;
	elseif (z <= -1.05e+34)
		tmp = t_1;
	elseif (z <= -21.0)
		tmp = t_0;
	elseif (z <= -1.16e-186)
		tmp = Float64(x * -3.0);
	elseif (z <= 8.8e-215)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.5)
		tmp = Float64(x * -3.0);
	elseif (z <= 2.7e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = -6.0 * (y * z);
	t_1 = 6.0 * (x * z);
	tmp = 0.0;
	if (z <= -5.2e+161)
		tmp = t_0;
	elseif (z <= -1.05e+34)
		tmp = t_1;
	elseif (z <= -21.0)
		tmp = t_0;
	elseif (z <= -1.16e-186)
		tmp = x * -3.0;
	elseif (z <= 8.8e-215)
		tmp = y * 4.0;
	elseif (z <= 0.5)
		tmp = x * -3.0;
	elseif (z <= 2.7e+118)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(-6.0 * N[(y * z), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[z, -5.2e+161], t$95$0, If[LessEqual[z, -1.05e+34], t$95$1, If[LessEqual[z, -21.0], t$95$0, If[LessEqual[z, -1.16e-186], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 8.8e-215], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.5], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 2.7e+118], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if z < -5.1999999999999996e161 or -1.05000000000000009e34 < z < -21 or 2.7e118 < 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 y around inf 65.9%

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

   6. Taylor expanded in z around inf 64.9%

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

   7. Taylor expanded in x around 0 64.7%

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

   if -5.1999999999999996e161 < z < -1.05000000000000009e34 or 0.5 < z < 2.7e118

   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. +-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. fma-define 99.6%

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

      4. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.0%

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

      1. *-commutative 68.0%

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

      2. associate-*r* 68.0%

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

      3. *-lft-identity 68.0%

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

      4. sub-neg 68.0%

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

      5. distribute-rgt-in 68.0%

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

      6. metadata-eval 68.0%

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

      7. neg-mul-1 68.0%

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

      8. associate-*r* 68.0%

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

      9. *-commutative 68.0%

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

      10. metadata-eval 68.0%

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

      11. distribute-lft-in 68.0%

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

      12. distribute-rgt-in 67.9%

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

      13. distribute-lft-in 67.9%

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

      14. metadata-eval 67.9%

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

      15. associate-+r+ 67.9%

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

      16. metadata-eval 67.9%

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

      17. associate-*r* 67.9%

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

      18. metadata-eval 67.9%

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

   7. Simplified 67.9%

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

   8. Taylor expanded in z around inf 64.2%

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

   if -21 < z < -1.15999999999999995e-186 or 8.79999999999999985e-215 < 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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.2%

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

      3. *-lft-identity 63.2%

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

      4. sub-neg 63.2%

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

      5. distribute-rgt-in 63.3%

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

      6. metadata-eval 63.3%

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

      7. neg-mul-1 63.3%

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

      8. associate-*r* 63.3%

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

      9. *-commutative 63.3%

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

      10. metadata-eval 63.3%

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

      11. distribute-lft-in 63.3%

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

      12. distribute-rgt-in 63.3%

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

      13. distribute-lft-in 63.3%

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

      14. metadata-eval 63.3%

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

      15. associate-+r+ 63.3%

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

      16. metadata-eval 63.3%

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

      17. associate-*r* 63.3%

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

      18. metadata-eval 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in z around 0 59.4%

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

      1. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -1.15999999999999995e-186 < z < 8.79999999999999985e-215

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. add-sqr-sqrt 43.8%

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

      2. pow2 43.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 43.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 97.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 97.9%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.6%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.6%

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

      8. rem-square-sqrt 100.0%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-*r* 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 66.2%

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

   11. Taylor expanded in z around 0 66.5%

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

       1. *-commutative 66.5%

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

   13. Simplified 66.5%

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

Alternative 6: 50.6% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := -6 \cdot \left(y \cdot z\right)\\ \mathbf{if}\;z \leq -19:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;z \leq -2.7 \cdot 10^{-185}:\\ \;\;\;\;x \cdot -3\\ \mathbf{elif}\;z \leq 3 \cdot 10^{-214}:\\ \;\;\;\;y \cdot 4\\ \mathbf{elif}\;z \leq 0.54:\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* -6.0 (* y z))))
   (if (<= z -19.0)
     t_0
     (if (<= z -2.7e-185)
       (* x -3.0)
       (if (<= z 3e-214) (* y 4.0) (if (<= z 0.54) (* 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 <= -19.0) {
		tmp = t_0;
	} else if (z <= -2.7e-185) {
		tmp = x * -3.0;
	} else if (z <= 3e-214) {
		tmp = y * 4.0;
	} else if (z <= 0.54) {
		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 <= (-19.0d0)) then
        tmp = t_0
    else if (z <= (-2.7d-185)) then
        tmp = x * (-3.0d0)
    else if (z <= 3d-214) then
        tmp = y * 4.0d0
    else if (z <= 0.54d0) 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 <= -19.0) {
		tmp = t_0;
	} else if (z <= -2.7e-185) {
		tmp = x * -3.0;
	} else if (z <= 3e-214) {
		tmp = y * 4.0;
	} else if (z <= 0.54) {
		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 <= -19.0:
		tmp = t_0
	elif z <= -2.7e-185:
		tmp = x * -3.0
	elif z <= 3e-214:
		tmp = y * 4.0
	elif z <= 0.54:
		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 <= -19.0)
		tmp = t_0;
	elseif (z <= -2.7e-185)
		tmp = Float64(x * -3.0);
	elseif (z <= 3e-214)
		tmp = Float64(y * 4.0);
	elseif (z <= 0.54)
		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 <= -19.0)
		tmp = t_0;
	elseif (z <= -2.7e-185)
		tmp = x * -3.0;
	elseif (z <= 3e-214)
		tmp = y * 4.0;
	elseif (z <= 0.54)
		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, -19.0], t$95$0, If[LessEqual[z, -2.7e-185], N[(x * -3.0), $MachinePrecision], If[LessEqual[z, 3e-214], N[(y * 4.0), $MachinePrecision], If[LessEqual[z, 0.54], N[(x * -3.0), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 3 regimes

2. if z < -19 or 0.54000000000000004 < z

   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 y around inf 53.8%

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

   6. Taylor expanded in z around inf 52.3%

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

   7. Taylor expanded in x around 0 51.6%

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

   if -19 < z < -2.69999999999999988e-185 or 2.99999999999999994e-214 < z < 0.54000000000000004

   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. +-commutative 99.4%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 63.1%

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

      1. *-commutative 63.1%

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

      2. associate-*r* 63.2%

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

      3. *-lft-identity 63.2%

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

      4. sub-neg 63.2%

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

      5. distribute-rgt-in 63.3%

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

      6. metadata-eval 63.3%

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

      7. neg-mul-1 63.3%

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

      8. associate-*r* 63.3%

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

      9. *-commutative 63.3%

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

      10. metadata-eval 63.3%

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

      11. distribute-lft-in 63.3%

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

      12. distribute-rgt-in 63.3%

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

      13. distribute-lft-in 63.3%

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

      14. metadata-eval 63.3%

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

      15. associate-+r+ 63.3%

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

      16. metadata-eval 63.3%

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

      17. associate-*r* 63.3%

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

      18. metadata-eval 63.3%

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

   7. Simplified 63.3%

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

   8. Taylor expanded in z around 0 59.4%

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

      1. *-commutative 59.4%

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

   10. Simplified 59.4%

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

   if -2.69999999999999988e-185 < z < 2.99999999999999994e-214

   1. Initial program 99.2%

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

      1. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. add-sqr-sqrt 43.8%

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

      2. pow2 43.8%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 43.8%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 97.9%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 97.9%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 97.9%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 97.9%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.6%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.6%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.6%

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

      8. rem-square-sqrt 100.0%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-*r* 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 66.2%

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

   11. Taylor expanded in z around 0 66.5%

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

       1. *-commutative 66.5%

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

   13. Simplified 66.5%

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

Alternative 7: 55.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-11}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= x -5.8e-11)
   (* 6.0 (* x z))
   (if (<= x 6.8e-36)
     (* 6.0 (* y (- 0.6666666666666666 z)))
     (if (<= x 1.1e+83) (* x (* z 6.0)) (* x -3.0)))))

C

double code(double x, double y, double z) {
	double tmp;
	if (x <= -5.8e-11) {
		tmp = 6.0 * (x * z);
	} else if (x <= 6.8e-36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (x <= 1.1e+83) {
		tmp = x * (z * 6.0);
	} 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 <= (-5.8d-11)) then
        tmp = 6.0d0 * (x * z)
    else if (x <= 6.8d-36) then
        tmp = 6.0d0 * (y * (0.6666666666666666d0 - z))
    else if (x <= 1.1d+83) then
        tmp = x * (z * 6.0d0)
    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 <= -5.8e-11) {
		tmp = 6.0 * (x * z);
	} else if (x <= 6.8e-36) {
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	} else if (x <= 1.1e+83) {
		tmp = x * (z * 6.0);
	} else {
		tmp = x * -3.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if x <= -5.8e-11:
		tmp = 6.0 * (x * z)
	elif x <= 6.8e-36:
		tmp = 6.0 * (y * (0.6666666666666666 - z))
	elif x <= 1.1e+83:
		tmp = x * (z * 6.0)
	else:
		tmp = x * -3.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (x <= -5.8e-11)
		tmp = Float64(6.0 * Float64(x * z));
	elseif (x <= 6.8e-36)
		tmp = Float64(6.0 * Float64(y * Float64(0.6666666666666666 - z)));
	elseif (x <= 1.1e+83)
		tmp = Float64(x * Float64(z * 6.0));
	else
		tmp = Float64(x * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (x <= -5.8e-11)
		tmp = 6.0 * (x * z);
	elseif (x <= 6.8e-36)
		tmp = 6.0 * (y * (0.6666666666666666 - z));
	elseif (x <= 1.1e+83)
		tmp = x * (z * 6.0);
	else
		tmp = x * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[x, -5.8e-11], N[(6.0 * N[(x * z), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6.8e-36], N[(6.0 * N[(y * N[(0.6666666666666666 - z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.1e+83], N[(x * N[(z * 6.0), $MachinePrecision]), $MachinePrecision], N[(x * -3.0), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < -5.8e-11

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.8%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 74.2%

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

      1. *-commutative 74.2%

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

      2. associate-*r* 74.3%

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

      3. *-lft-identity 74.3%

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

      4. sub-neg 74.3%

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

      5. distribute-rgt-in 74.3%

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

      6. metadata-eval 74.3%

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

      7. neg-mul-1 74.3%

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

      8. associate-*r* 74.3%

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

      9. *-commutative 74.3%

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

      10. metadata-eval 74.3%

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

      11. distribute-lft-in 74.3%

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

      12. distribute-rgt-in 74.3%

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

      13. distribute-lft-in 74.3%

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

      14. metadata-eval 74.3%

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

      15. associate-+r+ 74.3%

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

      16. metadata-eval 74.3%

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

      17. associate-*r* 74.3%

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

      18. metadata-eval 74.3%

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

   7. Simplified 74.3%

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

   8. Taylor expanded in z around inf 46.8%

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

   if -5.8e-11 < x < 6.8000000000000005e-36

   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. add-sqr-sqrt 47.5%

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

      2. pow2 47.5%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 47.5%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 98.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 98.4%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 98.4%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.7%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.7%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.7%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.7%

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

      8. rem-square-sqrt 99.7%

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

      9. associate-*r* 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-*r* 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 75.8%

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

   if 6.8000000000000005e-36 < x < 1.09999999999999999e83

   1. Initial program 99.2%

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

      1. +-commutative 99.2%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 78.6%

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

      1. *-commutative 78.6%

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

      2. associate-*r* 78.7%

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

      3. *-lft-identity 78.7%

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

      4. sub-neg 78.7%

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

      5. distribute-rgt-in 78.6%

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

      6. metadata-eval 78.6%

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

      7. neg-mul-1 78.6%

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

      8. associate-*r* 78.6%

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

      9. *-commutative 78.6%

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

      10. metadata-eval 78.6%

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

      11. distribute-lft-in 78.6%

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

      12. distribute-rgt-in 78.6%

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

      13. distribute-lft-in 78.6%

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

      14. metadata-eval 78.6%

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

      15. associate-+r+ 78.6%

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

      16. metadata-eval 78.6%

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

      17. associate-*r* 78.6%

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

      18. metadata-eval 78.6%

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

   7. Simplified 78.6%

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

   8. Taylor expanded in z around inf 53.8%

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

      1. associate-*r* 53.7%

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

      2. *-commutative 53.7%

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

      3. associate-*r* 53.8%

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

   10. Simplified 53.8%

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

   if 1.09999999999999999e83 < 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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*r* 88.4%

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

      3. *-lft-identity 88.4%

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

      4. sub-neg 88.4%

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

      5. distribute-rgt-in 88.4%

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

      6. metadata-eval 88.4%

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

      7. neg-mul-1 88.4%

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

      8. associate-*r* 88.4%

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

      9. *-commutative 88.4%

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

      10. metadata-eval 88.4%

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

      11. distribute-lft-in 88.4%

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

      12. distribute-rgt-in 88.5%

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

      13. distribute-lft-in 88.5%

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

      14. metadata-eval 88.5%

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

      15. associate-+r+ 88.5%

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

      16. metadata-eval 88.5%

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

      17. associate-*r* 88.5%

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

      18. metadata-eval 88.5%

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

   7. Simplified 88.5%

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

   8. Taylor expanded in z around 0 51.1%

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

      1. *-commutative 51.1%

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

   10. Simplified 51.1%

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

4. Final simplification 62.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -5.8 \cdot 10^{-11}:\\ \;\;\;\;6 \cdot \left(x \cdot z\right)\\ \mathbf{elif}\;x \leq 6.8 \cdot 10^{-36}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \mathbf{elif}\;x \leq 1.1 \cdot 10^{+83}:\\ \;\;\;\;x \cdot \left(z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;x \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 97.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= z -0.56) (not (<= z 0.65)))
   (* -6.0 (* (- y x) z))
   (+ x (* (- y x) 4.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z <= -0.56) || !(z <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} 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 <= (-0.56d0)) .or. (.not. (z <= 0.65d0))) then
        tmp = (-6.0d0) * ((y - x) * z)
    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 <= -0.56) || !(z <= 0.65)) {
		tmp = -6.0 * ((y - x) * z);
	} else {
		tmp = x + ((y - x) * 4.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z <= -0.56) or not (z <= 0.65):
		tmp = -6.0 * ((y - x) * z)
	else:
		tmp = x + ((y - x) * 4.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((z <= -0.56) || !(z <= 0.65))
		tmp = Float64(-6.0 * Float64(Float64(y - x) * z));
	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 <= -0.56) || ~((z <= 0.65)))
		tmp = -6.0 * ((y - x) * z);
	else
		tmp = x + ((y - x) * 4.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[z, -0.56], N[Not[LessEqual[z, 0.65]], $MachinePrecision]], N[(-6.0 * N[(N[(y - x), $MachinePrecision] * z), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(y - x), $MachinePrecision] * 4.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -0.56000000000000005 or 0.650000000000000022 < z

   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* 99.6%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 83.1%

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

   6. Taylor expanded in z around inf 86.8%

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

      1. associate-*r* 92.5%

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

      2. sub-neg 92.5%

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

      3. *-commutative 92.5%

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

      4. metadata-eval 92.5%

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

      5. associate-*l* 92.5%

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

      6. *-commutative 92.5%

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

      7. mul-1-neg 92.5%

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

      8. metadata-eval 92.5%

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

      9. distribute-rgt-out 80.1%

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

      10. associate-*r* 80.2%

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

      11. *-commutative 80.2%

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

      12. associate-*l* 80.2%

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

      13. *-commutative 80.2%

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

      14. distribute-frac-neg2 80.2%

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

      15. distribute-lft-out 80.2%

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

      16. distribute-frac-neg2 80.2%

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

      17. associate-*r* 88.7%

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

      18. distribute-rgt-out 92.6%

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

   8. Simplified 96.1%

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

   if -0.56000000000000005 < z < 0.650000000000000022

   1. Initial program 99.3%

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

      1. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in z around 0 97.4%

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

4. Final simplification 96.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -0.56 \lor \neg \left(z \leq 0.65\right):\\ \;\;\;\;-6 \cdot \left(\left(y - x\right) \cdot z\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(y - x\right) \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 75.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-41} \lor \neg \left(x \leq 4.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -4.6e-41) (not (<= x 4.5e-38)))
   (* 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 <= -4.6e-41) || !(x <= 4.5e-38)) {
		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 <= (-4.6d-41)) .or. (.not. (x <= 4.5d-38))) 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 <= -4.6e-41) || !(x <= 4.5e-38)) {
		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 <= -4.6e-41) or not (x <= 4.5e-38):
		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 <= -4.6e-41) || !(x <= 4.5e-38))
		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 <= -4.6e-41) || ~((x <= 4.5e-38)))
		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, -4.6e-41], N[Not[LessEqual[x, 4.5e-38]], $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 < -4.6000000000000002e-41 or 4.50000000000000009e-38 < 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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*r* 79.1%

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

      3. *-lft-identity 79.1%

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

      4. sub-neg 79.1%

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

      5. distribute-rgt-in 79.1%

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

      6. metadata-eval 79.1%

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

      7. neg-mul-1 79.1%

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

      8. associate-*r* 79.1%

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

      9. *-commutative 79.1%

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

      10. metadata-eval 79.1%

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

      11. distribute-lft-in 79.1%

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

      12. distribute-rgt-in 79.1%

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

      13. distribute-lft-in 79.1%

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

      14. metadata-eval 79.1%

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

      15. associate-+r+ 79.1%

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

      16. metadata-eval 79.1%

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

      17. associate-*r* 79.1%

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

      18. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   if -4.6000000000000002e-41 < x < 4.50000000000000009e-38

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. sub-neg 99.7%

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

      5. distribute-rgt-in 99.7%

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

      6. metadata-eval 99.7%

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

      7. metadata-eval 99.7%

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

      8. distribute-lft-neg-out 99.7%

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

      9. distribute-rgt-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around inf 78.1%

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

4. Final simplification 78.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -4.6 \cdot 10^{-41} \lor \neg \left(x \leq 4.5 \cdot 10^{-38}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(4 + z \cdot -6\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 75.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-40} \lor \neg \left(x \leq 2.6 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -1.35e-40) (not (<= x 2.6e-33)))
   (* 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 <= -1.35e-40) || !(x <= 2.6e-33)) {
		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 <= (-1.35d-40)) .or. (.not. (x <= 2.6d-33))) 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 <= -1.35e-40) || !(x <= 2.6e-33)) {
		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 <= -1.35e-40) or not (x <= 2.6e-33):
		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 <= -1.35e-40) || !(x <= 2.6e-33))
		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 <= -1.35e-40) || ~((x <= 2.6e-33)))
		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, -1.35e-40], N[Not[LessEqual[x, 2.6e-33]], $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 < -1.35e-40 or 2.59999999999999994e-33 < 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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.7%

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

      4. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 78.9%

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

      1. *-commutative 78.9%

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

      2. associate-*r* 79.1%

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

      3. *-lft-identity 79.1%

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

      4. sub-neg 79.1%

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

      5. distribute-rgt-in 79.1%

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

      6. metadata-eval 79.1%

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

      7. neg-mul-1 79.1%

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

      8. associate-*r* 79.1%

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

      9. *-commutative 79.1%

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

      10. metadata-eval 79.1%

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

      11. distribute-lft-in 79.1%

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

      12. distribute-rgt-in 79.1%

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

      13. distribute-lft-in 79.1%

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

      14. metadata-eval 79.1%

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

      15. associate-+r+ 79.1%

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

      16. metadata-eval 79.1%

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

      17. associate-*r* 79.1%

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

      18. metadata-eval 79.1%

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

   7. Simplified 79.1%

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

   if -1.35e-40 < x < 2.59999999999999994e-33

   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. add-sqr-sqrt 45.2%

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

      2. pow2 45.2%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 45.2%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 98.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 98.4%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 98.4%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.7%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.7%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.7%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.7%

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

      8. rem-square-sqrt 99.7%

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

      9. associate-*r* 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-*r* 99.7%

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

   9. Simplified 99.7%

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

   10. Taylor expanded in x around 0 78.1%

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

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -1.35 \cdot 10^{-40} \lor \neg \left(x \leq 2.6 \cdot 10^{-33}\right):\\ \;\;\;\;x \cdot \left(-3 + z \cdot 6\right)\\ \mathbf{else}:\\ \;\;\;\;6 \cdot \left(y \cdot \left(0.6666666666666666 - z\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 36.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+52} \lor \neg \left(x \leq 32000000000\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (or (<= x -3.1e+52) (not (<= x 32000000000.0))) (* x -3.0) (* y 4.0)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((x <= -3.1e+52) || !(x <= 32000000000.0)) {
		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 <= (-3.1d+52)) .or. (.not. (x <= 32000000000.0d0))) 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 <= -3.1e+52) || !(x <= 32000000000.0)) {
		tmp = x * -3.0;
	} else {
		tmp = y * 4.0;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (x <= -3.1e+52) or not (x <= 32000000000.0):
		tmp = x * -3.0
	else:
		tmp = y * 4.0
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if ((x <= -3.1e+52) || !(x <= 32000000000.0))
		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 <= -3.1e+52) || ~((x <= 32000000000.0)))
		tmp = x * -3.0;
	else
		tmp = y * 4.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[Or[LessEqual[x, -3.1e+52], N[Not[LessEqual[x, 32000000000.0]], $MachinePrecision]], N[(x * -3.0), $MachinePrecision], N[(y * 4.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < -3.1e52 or 3.2e10 < 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. +-commutative 99.5%

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

      2. associate-*l* 99.7%

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

      3. fma-define 99.8%

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

      4. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   5. Taylor expanded in y around 0 81.2%

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

      1. *-commutative 81.2%

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

      2. associate-*r* 81.3%

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

      3. *-lft-identity 81.3%

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

      4. sub-neg 81.3%

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

      5. distribute-rgt-in 81.3%

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

      6. metadata-eval 81.3%

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

      7. neg-mul-1 81.3%

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

      8. associate-*r* 81.3%

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

      9. *-commutative 81.3%

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

      10. metadata-eval 81.3%

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

      11. distribute-lft-in 81.3%

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

      12. distribute-rgt-in 81.3%

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

      13. distribute-lft-in 81.3%

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

      14. metadata-eval 81.3%

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

      15. associate-+r+ 81.3%

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

      16. metadata-eval 81.3%

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

      17. associate-*r* 81.3%

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

      18. metadata-eval 81.3%

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

   7. Simplified 81.3%

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

   8. Taylor expanded in z around 0 41.3%

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

      1. *-commutative 41.3%

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

   10. Simplified 41.3%

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

   if -3.1e52 < x < 3.2e10

   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. add-sqr-sqrt 47.7%

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

      2. pow2 47.7%

         \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   6. Applied egg-rr 47.7%

      \[\leadsto x + \color{blue}{{\left(\sqrt{\left(y - x\right) \cdot 6}\right)}^{2}} \cdot \left(0.6666666666666666 - z\right) \]

   7. Taylor expanded in x around 0 98.4%

      \[\leadsto \color{blue}{x \cdot \left(1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) + y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)} \]
   8. Step-by-step derivation

      1. fma-define 98.4%

         \[\leadsto \color{blue}{\mathsf{fma}\left(x, 1 + -1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right), y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right)} \]

      2. +-commutative 98.4%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-1 \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right) + 1}, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      3. unpow2 98.4%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{\left(\sqrt{6} \cdot \sqrt{6}\right)} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      4. rem-square-sqrt 98.8%

         \[\leadsto \mathsf{fma}\left(x, -1 \cdot \left(\color{blue}{6} \cdot \left(0.6666666666666666 - z\right)\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      5. associate-*r* 98.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{\left(-1 \cdot 6\right) \cdot \left(0.6666666666666666 - z\right)} + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      6. metadata-eval 98.8%

         \[\leadsto \mathsf{fma}\left(x, \color{blue}{-6} \cdot \left(0.6666666666666666 - z\right) + 1, y \cdot \left({\left(\sqrt{6}\right)}^{2} \cdot \left(0.6666666666666666 - z\right)\right)\right) \]

      7. unpow2 98.8%

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

      8. rem-square-sqrt 99.7%

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

      9. associate-*r* 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-*r* 99.6%

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

   9. Simplified 99.6%

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

   10. Taylor expanded in x around 0 70.2%

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

   11. Taylor expanded in z around 0 34.0%

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

       1. *-commutative 34.0%

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

   13. Simplified 34.0%

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

4. Final simplification 37.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -3.1 \cdot 10^{+52} \lor \neg \left(x \leq 32000000000\right):\\ \;\;\;\;x \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot 4\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.5% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x + ((0.6666666666666666d0 - z) * ((y - x) * 6.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Final simplification 99.5%

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

Alternative 13: 25.8% accurate, 4.3× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = x * (-3.0d0)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. +-commutative 99.5%

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

   2. associate-*l* 99.7%

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

   3. fma-define 99.7%

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

   4. metadata-eval 99.7%

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

3. Simplified 99.7%

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

5. Taylor expanded in y around 0 53.9%

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

   1. *-commutative 53.9%

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

   2. associate-*r* 53.9%

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

   3. *-lft-identity 53.9%

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

   4. sub-neg 53.9%

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

   5. distribute-rgt-in 53.9%

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

   6. metadata-eval 53.9%

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

   7. neg-mul-1 53.9%

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

   8. associate-*r* 53.9%

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

   9. *-commutative 53.9%

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

   10. metadata-eval 53.9%

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

   11. distribute-lft-in 53.9%

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

   12. distribute-rgt-in 53.9%

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

   13. distribute-lft-in 53.9%

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

   14. metadata-eval 53.9%

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

   15. associate-+r+ 54.0%

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

   16. metadata-eval 54.0%

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

   17. associate-*r* 54.0%

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

   18. metadata-eval 54.0%

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

7. Simplified 54.0%

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

8. Taylor expanded in z around 0 27.3%

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

   1. *-commutative 27.3%

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

10. Simplified 27.3%

    \[\leadsto \color{blue}{x \cdot -3} \]
11. Add Preprocessing

Alternative 14: 2.7% accurate, 13.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := x

Derivation

1. Initial program 99.5%

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

   1. metadata-eval 99.5%

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

3. Simplified 99.5%

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

5. Taylor expanded in y around inf 49.2%

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

6. Taylor expanded in x around inf 2.8%

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

Reproduce

herbie shell --seed 2024139 
(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))))