Linear.Quaternion:$c/ from linear-1.19.1.3, A

Percentage Accurate: 98.3% → 99.5%

Time: 9.0s

Alternatives: 8

Speedup: 0.7×

• 34.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((x * y) + (z * z)) + (z * z)) + (z * 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) + (z * z)) + (z * z)) + (z * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return (((x * y) + (z * z)) + (z * z)) + (z * 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) + (z * z)) + (z * z)) + (z * z)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(z, z, \mathsf{fma}\left(x, y, 2 \cdot \left(z \cdot z\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma z z (fma x y (* 2.0 (* z z)))))

C

double code(double x, double y, double z) {
	return fma(z, z, fma(x, y, (2.0 * (z * z))));
}

Julia

function code(x, y, z)
	return fma(z, z, fma(x, y, Float64(2.0 * Float64(z * z))))
end

Wolfram

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

Derivation

1. Initial program 97.9%

   \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]
2. Step-by-step derivation

   1. +-commutative 97.9%

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

   2. fma-define 98.0%

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

   3. associate-+l+ 98.0%

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

   4. fma-define 100.0%

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

   5. count-2 100.0%

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

3. Simplified 100.0%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, z, \mathsf{fma}\left(x, y, 2 \cdot \left(z \cdot z\right)\right)\right)} \]
4. Add Preprocessing

5. Final simplification 100.0%

   \[\leadsto \mathsf{fma}\left(z, z, \mathsf{fma}\left(x, y, 2 \cdot \left(z \cdot z\right)\right)\right) \]
6. Add Preprocessing

Alternative 2: 99.5% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right) \end{array} \]

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 97.9%

   \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]
2. Step-by-step derivation

   1. associate-+l+ 97.9%

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

   2. associate-+l+ 97.9%

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

   3. fma-define 99.9%

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

   4. distribute-lft-out 99.9%

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

   5. distribute-lft-out 99.9%

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

   6. count-2 99.9%

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

   7. distribute-rgt1-in 99.9%

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

   8. metadata-eval 99.9%

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

   9. *-commutative 99.9%

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

   10. metadata-eval 99.9%

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

   11. metadata-eval 99.9%

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

3. Simplified 99.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.9%

   \[\leadsto \mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right) \]
6. Add Preprocessing

Alternative 3: 98.9% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot z + \left(z \cdot z + \left(z \cdot z + x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \frac{z}{\frac{y}{z}}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= y 8e-57)
   (+ (* z z) (+ (* z z) (+ (* z z) (* x y))))
   (* y (+ x (* 3.0 (/ z (/ y z)))))))

C

double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e-57) {
		tmp = (z * z) + ((z * z) + ((z * z) + (x * y)));
	} else {
		tmp = y * (x + (3.0 * (z / (y / z))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8) :: tmp
    if (y <= 8d-57) then
        tmp = (z * z) + ((z * z) + ((z * z) + (x * y)))
    else
        tmp = y * (x + (3.0d0 * (z / (y / z))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (y <= 8e-57) {
		tmp = (z * z) + ((z * z) + ((z * z) + (x * y)));
	} else {
		tmp = y * (x + (3.0 * (z / (y / z))));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if y <= 8e-57:
		tmp = (z * z) + ((z * z) + ((z * z) + (x * y)))
	else:
		tmp = y * (x + (3.0 * (z / (y / z))))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (y <= 8e-57)
		tmp = Float64(Float64(z * z) + Float64(Float64(z * z) + Float64(Float64(z * z) + Float64(x * y))));
	else
		tmp = Float64(y * Float64(x + Float64(3.0 * Float64(z / Float64(y / z)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (y <= 8e-57)
		tmp = (z * z) + ((z * z) + ((z * z) + (x * y)));
	else
		tmp = y * (x + (3.0 * (z / (y / z))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[y, 8e-57], N[(N[(z * z), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] + N[(N[(z * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(x + N[(3.0 * N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < 7.99999999999999964e-57

   1. Initial program 99.3%

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

   if 7.99999999999999964e-57 < y

   1. Initial program 95.2%

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

   3. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(2 \cdot \frac{{z}^{2}}{y} + \frac{{z}^{2}}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 100.0%

         \[\leadsto y \cdot \left(x + \color{blue}{\left(2 + 1\right) \cdot \frac{{z}^{2}}{y}}\right) \]

      2. metadata-eval 100.0%

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

   5. Simplified 100.0%

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

      1. div-inv 100.0%

         \[\leadsto y \cdot \left(x + 3 \cdot \color{blue}{\left({z}^{2} \cdot \frac{1}{y}\right)}\right) \]

      2. pow2 100.0%

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

      3. associate-*l* 99.9%

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

   7. Applied egg-rr 99.9%

      \[\leadsto y \cdot \left(x + 3 \cdot \color{blue}{\left(z \cdot \left(z \cdot \frac{1}{y}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. div-inv 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   9. Applied egg-rr 99.9%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq 8 \cdot 10^{-57}:\\ \;\;\;\;z \cdot z + \left(z \cdot z + \left(z \cdot z + x \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \frac{z}{\frac{y}{z}}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 95.0% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+230}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \left(z \cdot \frac{z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 1e+230) (* y (+ x (* 3.0 (* z (/ z y))))) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e+230) {
		tmp = y * (x + (3.0 * (z * (z / y))));
	} else {
		tmp = z * (z * 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 ((z * z) <= 1d+230) then
        tmp = y * (x + (3.0d0 * (z * (z / y))))
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e+230) {
		tmp = y * (x + (3.0 * (z * (z / y))));
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 1e+230:
		tmp = y * (x + (3.0 * (z * (z / y))))
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 1e+230)
		tmp = Float64(y * Float64(x + Float64(3.0 * Float64(z * Float64(z / y)))));
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 1e+230)
		tmp = y * (x + (3.0 * (z * (z / y))));
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+230], N[(y * N[(x + N[(3.0 * N[(z * N[(z / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1.0000000000000001e230

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 95.7%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(2 \cdot \frac{{z}^{2}}{y} + \frac{{z}^{2}}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 95.7%

         \[\leadsto y \cdot \left(x + \color{blue}{\left(2 + 1\right) \cdot \frac{{z}^{2}}{y}}\right) \]

      2. metadata-eval 95.7%

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

   5. Simplified 95.7%

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

      1. pow2 95.7%

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

      2. associate-/l* 95.7%

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

   7. Applied egg-rr 95.7%

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

   if 1.0000000000000001e230 < (*.f64 z z)

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 98.5%

      \[\leadsto \color{blue}{2 \cdot {z}^{2} + {z}^{2}} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 98.5%

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot {z}^{2}} \]

      2. metadata-eval 98.5%

         \[\leadsto \color{blue}{3} \cdot {z}^{2} \]

      3. *-commutative 98.5%

         \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]
   6. Step-by-step derivation

      1. rem-square-sqrt 98.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \]

      2. pow2 98.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{{\left(\sqrt{3}\right)}^{2}} \]

      3. unpow-prod-down 98.4%

         \[\leadsto \color{blue}{{\left(z \cdot \sqrt{3}\right)}^{2}} \]

      4. add-cube-cbrt 98.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}} \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}} \]

      5. pow3 98.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right)}^{3}} \]

      6. *-commutative 98.3%

         \[\leadsto {\left(\sqrt[3]{{\color{blue}{\left(\sqrt{3} \cdot z\right)}}^{2}}\right)}^{3} \]

      7. unpow-prod-down 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt{3}\right)}^{2} \cdot {z}^{2}}}\right)}^{3} \]

      8. pow2 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \cdot {z}^{2}}\right)}^{3} \]

      9. rem-square-sqrt 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{3} \cdot {z}^{2}}\right)}^{3} \]

   7. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{3 \cdot {z}^{2}}\right)}^{3}} \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 98.5%

         \[\leadsto \color{blue}{3 \cdot {z}^{2}} \]

      2. unpow2 98.5%

         \[\leadsto 3 \cdot \color{blue}{\left(z \cdot z\right)} \]

      3. associate-*r* 98.6%

         \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   9. Applied egg-rr 98.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+230}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \left(z \cdot \frac{z}{y}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 94.9% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+230}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \frac{z}{\frac{y}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 1e+230) (* y (+ x (* 3.0 (/ z (/ y z))))) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e+230) {
		tmp = y * (x + (3.0 * (z / (y / z))));
	} else {
		tmp = z * (z * 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 ((z * z) <= 1d+230) then
        tmp = y * (x + (3.0d0 * (z / (y / z))))
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e+230) {
		tmp = y * (x + (3.0 * (z / (y / z))));
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 1e+230:
		tmp = y * (x + (3.0 * (z / (y / z))))
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 1e+230)
		tmp = Float64(y * Float64(x + Float64(3.0 * Float64(z / Float64(y / z)))));
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 1e+230)
		tmp = y * (x + (3.0 * (z / (y / z))));
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e+230], N[(y * N[(x + N[(3.0 * N[(z / N[(y / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1.0000000000000001e230

   1. Initial program 99.8%

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

   3. Taylor expanded in y around inf 95.7%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(2 \cdot \frac{{z}^{2}}{y} + \frac{{z}^{2}}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 95.7%

         \[\leadsto y \cdot \left(x + \color{blue}{\left(2 + 1\right) \cdot \frac{{z}^{2}}{y}}\right) \]

      2. metadata-eval 95.7%

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

   5. Simplified 95.7%

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

      1. div-inv 95.7%

         \[\leadsto y \cdot \left(x + 3 \cdot \color{blue}{\left({z}^{2} \cdot \frac{1}{y}\right)}\right) \]

      2. pow2 95.7%

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

      3. associate-*l* 95.7%

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

   7. Applied egg-rr 95.7%

      \[\leadsto y \cdot \left(x + 3 \cdot \color{blue}{\left(z \cdot \left(z \cdot \frac{1}{y}\right)\right)}\right) \]
   8. Step-by-step derivation

      1. div-inv 95.7%

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

      2. clear-num 95.7%

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

      3. un-div-inv 95.6%

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

   9. Applied egg-rr 95.6%

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

   if 1.0000000000000001e230 < (*.f64 z z)

   1. Initial program 93.0%

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

   3. Taylor expanded in x around 0 98.5%

      \[\leadsto \color{blue}{2 \cdot {z}^{2} + {z}^{2}} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 98.5%

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot {z}^{2}} \]

      2. metadata-eval 98.5%

         \[\leadsto \color{blue}{3} \cdot {z}^{2} \]

      3. *-commutative 98.5%

         \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]

   5. Simplified 98.5%

      \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]
   6. Step-by-step derivation

      1. rem-square-sqrt 98.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \]

      2. pow2 98.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{{\left(\sqrt{3}\right)}^{2}} \]

      3. unpow-prod-down 98.4%

         \[\leadsto \color{blue}{{\left(z \cdot \sqrt{3}\right)}^{2}} \]

      4. add-cube-cbrt 98.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}} \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}} \]

      5. pow3 98.3%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right)}^{3}} \]

      6. *-commutative 98.3%

         \[\leadsto {\left(\sqrt[3]{{\color{blue}{\left(\sqrt{3} \cdot z\right)}}^{2}}\right)}^{3} \]

      7. unpow-prod-down 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt{3}\right)}^{2} \cdot {z}^{2}}}\right)}^{3} \]

      8. pow2 98.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \cdot {z}^{2}}\right)}^{3} \]

      9. rem-square-sqrt 98.3%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{3} \cdot {z}^{2}}\right)}^{3} \]

   7. Applied egg-rr 98.3%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{3 \cdot {z}^{2}}\right)}^{3}} \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 98.5%

         \[\leadsto \color{blue}{3 \cdot {z}^{2}} \]

      2. unpow2 98.5%

         \[\leadsto 3 \cdot \color{blue}{\left(z \cdot z\right)} \]

      3. associate-*r* 98.6%

         \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   9. Applied egg-rr 98.6%

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

4. Final simplification 96.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{+230}:\\ \;\;\;\;y \cdot \left(x + 3 \cdot \frac{z}{\frac{y}{z}}\right)\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-85}:\\ \;\;\;\;z \cdot z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 5e-85) (+ (* z z) (* x y)) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e-85) {
		tmp = (z * z) + (x * y);
	} else {
		tmp = z * (z * 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 ((z * z) <= 5d-85) then
        tmp = (z * z) + (x * y)
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 5e-85) {
		tmp = (z * z) + (x * y);
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 5e-85:
		tmp = (z * z) + (x * y)
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 5e-85)
		tmp = Float64(Float64(z * z) + Float64(x * y));
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 5e-85)
		tmp = (z * z) + (x * y);
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 5e-85], N[(N[(z * z), $MachinePrecision] + N[(x * y), $MachinePrecision]), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 5.0000000000000002e-85

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf 93.1%

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

   4. Taylor expanded in x around inf 92.9%

      \[\leadsto \color{blue}{x \cdot y} + z \cdot z \]

   if 5.0000000000000002e-85 < (*.f64 z z)

   1. Initial program 96.2%

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

   3. Taylor expanded in x around 0 81.8%

      \[\leadsto \color{blue}{2 \cdot {z}^{2} + {z}^{2}} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 81.8%

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot {z}^{2}} \]

      2. metadata-eval 81.8%

         \[\leadsto \color{blue}{3} \cdot {z}^{2} \]

      3. *-commutative 81.8%

         \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]

   5. Simplified 81.8%

      \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]
   6. Step-by-step derivation

      1. rem-square-sqrt 81.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \]

      2. pow2 81.5%

         \[\leadsto {z}^{2} \cdot \color{blue}{{\left(\sqrt{3}\right)}^{2}} \]

      3. unpow-prod-down 81.6%

         \[\leadsto \color{blue}{{\left(z \cdot \sqrt{3}\right)}^{2}} \]

      4. add-cube-cbrt 81.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}} \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}} \]

      5. pow3 81.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right)}^{3}} \]

      6. *-commutative 81.1%

         \[\leadsto {\left(\sqrt[3]{{\color{blue}{\left(\sqrt{3} \cdot z\right)}}^{2}}\right)}^{3} \]

      7. unpow-prod-down 81.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt{3}\right)}^{2} \cdot {z}^{2}}}\right)}^{3} \]

      8. pow2 81.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \cdot {z}^{2}}\right)}^{3} \]

      9. rem-square-sqrt 81.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{3} \cdot {z}^{2}}\right)}^{3} \]

   7. Applied egg-rr 81.1%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{3 \cdot {z}^{2}}\right)}^{3}} \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 81.8%

         \[\leadsto \color{blue}{3 \cdot {z}^{2}} \]

      2. unpow2 81.8%

         \[\leadsto 3 \cdot \color{blue}{\left(z \cdot z\right)} \]

      3. associate-*r* 81.8%

         \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   9. Applied egg-rr 81.8%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 5 \cdot 10^{-85}:\\ \;\;\;\;z \cdot z + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 68.1% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 4.7 \cdot 10^{-42}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 4.7e-42) (* x y) (* z (* z 3.0))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.7e-42) {
		tmp = x * y;
	} else {
		tmp = z * (z * 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 (z <= 4.7d-42) then
        tmp = x * y
    else
        tmp = z * (z * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 4.7e-42) {
		tmp = x * y;
	} else {
		tmp = z * (z * 3.0);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 4.7e-42:
		tmp = x * y
	else:
		tmp = z * (z * 3.0)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 4.7e-42)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * Float64(z * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 4.7e-42)
		tmp = x * y;
	else
		tmp = z * (z * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 4.7e-42], N[(x * y), $MachinePrecision], N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 4.7000000000000001e-42

   1. Initial program 98.4%

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

   3. Taylor expanded in y around inf 96.1%

      \[\leadsto \color{blue}{y \cdot \left(x + \left(2 \cdot \frac{{z}^{2}}{y} + \frac{{z}^{2}}{y}\right)\right)} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 96.1%

         \[\leadsto y \cdot \left(x + \color{blue}{\left(2 + 1\right) \cdot \frac{{z}^{2}}{y}}\right) \]

      2. metadata-eval 96.1%

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

   5. Simplified 96.1%

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

   6. Taylor expanded in x around inf 62.4%

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

   if 4.7000000000000001e-42 < z

   1. Initial program 96.4%

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

   3. Taylor expanded in x around 0 82.5%

      \[\leadsto \color{blue}{2 \cdot {z}^{2} + {z}^{2}} \]
   4. Step-by-step derivation

      1. distribute-lft1-in 82.5%

         \[\leadsto \color{blue}{\left(2 + 1\right) \cdot {z}^{2}} \]

      2. metadata-eval 82.5%

         \[\leadsto \color{blue}{3} \cdot {z}^{2} \]

      3. *-commutative 82.5%

         \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]

   5. Simplified 82.5%

      \[\leadsto \color{blue}{{z}^{2} \cdot 3} \]
   6. Step-by-step derivation

      1. rem-square-sqrt 82.1%

         \[\leadsto {z}^{2} \cdot \color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \]

      2. pow2 82.1%

         \[\leadsto {z}^{2} \cdot \color{blue}{{\left(\sqrt{3}\right)}^{2}} \]

      3. unpow-prod-down 82.2%

         \[\leadsto \color{blue}{{\left(z \cdot \sqrt{3}\right)}^{2}} \]

      4. add-cube-cbrt 81.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}} \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right) \cdot \sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}} \]

      5. pow3 81.6%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{{\left(z \cdot \sqrt{3}\right)}^{2}}\right)}^{3}} \]

      6. *-commutative 81.6%

         \[\leadsto {\left(\sqrt[3]{{\color{blue}{\left(\sqrt{3} \cdot z\right)}}^{2}}\right)}^{3} \]

      7. unpow-prod-down 81.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{{\left(\sqrt{3}\right)}^{2} \cdot {z}^{2}}}\right)}^{3} \]

      8. pow2 81.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(\sqrt{3} \cdot \sqrt{3}\right)} \cdot {z}^{2}}\right)}^{3} \]

      9. rem-square-sqrt 81.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{3} \cdot {z}^{2}}\right)}^{3} \]

   7. Applied egg-rr 81.7%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{3 \cdot {z}^{2}}\right)}^{3}} \]
   8. Step-by-step derivation

      1. rem-cube-cbrt 82.5%

         \[\leadsto \color{blue}{3 \cdot {z}^{2}} \]

      2. unpow2 82.5%

         \[\leadsto 3 \cdot \color{blue}{\left(z \cdot z\right)} \]

      3. associate-*r* 82.5%

         \[\leadsto \color{blue}{\left(3 \cdot z\right) \cdot z} \]

   9. Applied egg-rr 82.5%

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

4. Final simplification 66.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 4.7 \cdot 10^{-42}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 52.6% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

3. Taylor expanded in y around inf 93.7%

   \[\leadsto \color{blue}{y \cdot \left(x + \left(2 \cdot \frac{{z}^{2}}{y} + \frac{{z}^{2}}{y}\right)\right)} \]
4. Step-by-step derivation

   1. distribute-lft1-in 93.7%

      \[\leadsto y \cdot \left(x + \color{blue}{\left(2 + 1\right) \cdot \frac{{z}^{2}}{y}}\right) \]

   2. metadata-eval 93.7%

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

5. Simplified 93.7%

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

6. Taylor expanded in x around inf 53.2%

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

7. Final simplification 53.2%

   \[\leadsto x \cdot y \]
8. Add Preprocessing

Developer target: 98.3% accurate, 1.7× speedup

Math

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

FPCore

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

C

double code(double x, double y, double z) {
	return ((3.0 * z) * z) + (y * 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 = ((3.0d0 * z) * z) + (y * x)
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024115 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (+ (* (* 3.0 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))