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

Percentage Accurate: 98.4% → 99.5%

Time: 6.4s

Alternatives: 6

Speedup: 1.0×

• 33.2% 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: 98.4% 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 99.4%

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

   1. +-commutative 99.4%

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

   2. fma-def 99.5%

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

   3. associate-+l+ 99.5%

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

   4. fma-def 99.5%

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

   5. count-2 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 2: 98.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \mathsf{fma}\left({z}^{2}, 3, x \cdot y\right) \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (fma (pow z 2.0) 3.0 (* x y)))

C

double code(double x, double y, double z) {
	return fma(pow(z, 2.0), 3.0, (x * y));
}

Julia

function code(x, y, z)
	return fma((z ^ 2.0), 3.0, Float64(x * y))
end

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]

2. Taylor expanded in x around 0 99.5%

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

   1. *-commutative 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+r+ 99.5%

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

   4. *-commutative 99.5%

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

   5. *-lft-identity 99.5%

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

   6. distribute-rgt-out 99.5%

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

   7. metadata-eval 99.5%

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

   8. fma-def 99.5%

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

4. Simplified 99.5%

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

5. Final simplification 99.5%

   \[\leadsto \mathsf{fma}\left({z}^{2}, 3, x \cdot y\right) \]

Alternative 3: 99.4% 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 99.4%

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

   1. associate-+l+ 99.5%

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

   2. associate-+l+ 99.5%

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

   3. fma-def 99.5%

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

   4. count-2 99.5%

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

   5. distribute-rgt1-in 99.5%

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

   6. metadata-eval 99.5%

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

   7. metadata-eval 99.5%

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

   8. metadata-eval 99.5%

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

   9. *-commutative 99.5%

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

   10. associate-*l* 99.5%

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

   11. metadata-eval 99.5%

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

   12. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 4: 98.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

   \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]

2. Final simplification 99.4%

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

Alternative 5: 73.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 3 \cdot 10^{+194}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot z\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z) :precision binary64 (if (<= (* z z) 3e+194) (* x y) (* z z)))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 3e+194) {
		tmp = x * y;
	} else {
		tmp = z * 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 ((z * z) <= 3d+194) then
        tmp = x * y
    else
        tmp = z * z
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 3e+194) {
		tmp = x * y;
	} else {
		tmp = z * z;
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 3e+194:
		tmp = x * y
	else:
		tmp = z * z
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 3e+194)
		tmp = Float64(x * y);
	else
		tmp = Float64(z * z);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 3e+194)
		tmp = x * y;
	else
		tmp = z * z;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 3e+194], N[(x * y), $MachinePrecision], N[(z * z), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 3.0000000000000003e194

   1. Initial program 99.8%

      \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]

   2. Taylor expanded in x around inf 72.6%

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

   if 3.0000000000000003e194 < (*.f64 z z)

   1. Initial program 98.8%

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

      1. associate-+l+ 98.8%

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

      2. associate-+l+ 98.8%

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

      3. fma-def 98.8%

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

      4. count-2 98.8%

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

      5. distribute-rgt1-in 98.8%

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

      6. metadata-eval 98.8%

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

      7. metadata-eval 98.8%

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

      8. metadata-eval 98.8%

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

      9. *-commutative 98.8%

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

      10. associate-*l* 98.8%

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

      11. metadata-eval 98.8%

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

      12. metadata-eval 98.8%

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

   3. Simplified 98.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, z \cdot \left(z \cdot 3\right)\right)} \]
   4. Step-by-step derivation

      1. fma-udef 98.8%

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

      2. flip-+ 1.9%

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

      3. pow2 1.9%

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

      4. associate-*r* 1.9%

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

      5. associate-*r* 1.9%

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

      6. swap-sqr 1.9%

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

      7. pow2 1.9%

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

      8. pow2 1.9%

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

      9. pow-prod-up 1.9%

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

      10. metadata-eval 1.9%

          \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - {z}^{\color{blue}{4}} \cdot \left(3 \cdot 3\right)}{x \cdot y - z \cdot \left(z \cdot 3\right)} \]

      11. metadata-eval 1.9%

          \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - {z}^{4} \cdot \color{blue}{9}}{x \cdot y - z \cdot \left(z \cdot 3\right)} \]

      12. associate-*r* 1.9%

          \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - {z}^{4} \cdot 9}{x \cdot y - \color{blue}{\left(z \cdot z\right) \cdot 3}} \]

      13. pow2 1.9%

          \[\leadsto \frac{{\left(x \cdot y\right)}^{2} - {z}^{4} \cdot 9}{x \cdot y - \color{blue}{{z}^{2}} \cdot 3} \]

   5. Applied egg-rr 1.9%

      \[\leadsto \color{blue}{\frac{{\left(x \cdot y\right)}^{2} - {z}^{4} \cdot 9}{x \cdot y - {z}^{2} \cdot 3}} \]

   6. Taylor expanded in x around 0 2.0%

      \[\leadsto \frac{\color{blue}{-9 \cdot {z}^{4}}}{x \cdot y - {z}^{2} \cdot 3} \]
   7. Step-by-step derivation

      1. *-commutative 2.0%

         \[\leadsto \frac{\color{blue}{{z}^{4} \cdot -9}}{x \cdot y - {z}^{2} \cdot 3} \]

   8. Simplified 2.0%

      \[\leadsto \frac{\color{blue}{{z}^{4} \cdot -9}}{x \cdot y - {z}^{2} \cdot 3} \]

   9. Taylor expanded in x around 0 3.2%

      \[\leadsto \frac{{z}^{4} \cdot -9}{\color{blue}{-3 \cdot {z}^{2}}} \]
   10. Step-by-step derivation

       1. *-commutative 3.2%

          \[\leadsto \frac{{z}^{4} \cdot -9}{\color{blue}{{z}^{2} \cdot -3}} \]

   11. Simplified 3.2%

       \[\leadsto \frac{{z}^{4} \cdot -9}{\color{blue}{{z}^{2} \cdot -3}} \]

   13. Applied egg-rr 75.9%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 3 \cdot 10^{+194}:\\ \;\;\;\;x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot z\\ \end{array} \]

Alternative 6: 52.1% 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 99.4%

   \[\left(\left(x \cdot y + z \cdot z\right) + z \cdot z\right) + z \cdot z \]

2. Taylor expanded in x around inf 50.7%

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

3. Final simplification 50.7%

   \[\leadsto x \cdot y \]

Developer target: 98.4% 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 2023322 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

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