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

Percentage Accurate: 98.1% → 99.2%

Time: 5.4s

Alternatives: 5

Speedup: 1.1×

• 33.3% 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: 98.1% 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: 99.2% 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-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. *-commutative 99.5%

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

   7. associate-*l* 99.5%

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

   8. 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 2: 99.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := z \cdot \left(z \cdot 3\right)\\ \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+289}:\\ \;\;\;\;t_0 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (let* ((t_0 (* z (* z 3.0)))) (if (<= (* z z) 4e+289) (+ t_0 (* x y)) t_0)))

C

double code(double x, double y, double z) {
	double t_0 = z * (z * 3.0);
	double tmp;
	if ((z * z) <= 4e+289) {
		tmp = t_0 + (x * y);
	} 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 * (z * 3.0d0)
    if ((z * z) <= 4d+289) then
        tmp = t_0 + (x * y)
    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 * (z * 3.0);
	double tmp;
	if ((z * z) <= 4e+289) {
		tmp = t_0 + (x * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y, z):
	t_0 = z * (z * 3.0)
	tmp = 0
	if (z * z) <= 4e+289:
		tmp = t_0 + (x * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y, z)
	t_0 = Float64(z * Float64(z * 3.0))
	tmp = 0.0
	if (Float64(z * z) <= 4e+289)
		tmp = Float64(t_0 + Float64(x * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	t_0 = z * (z * 3.0);
	tmp = 0.0;
	if ((z * z) <= 4e+289)
		tmp = t_0 + (x * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := Block[{t$95$0 = N[(z * N[(z * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(z * z), $MachinePrecision], 4e+289], N[(t$95$0 + N[(x * y), $MachinePrecision]), $MachinePrecision], t$95$0]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 4.0000000000000002e289

   1. Initial program 99.8%

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

      1. associate-+l+ 99.8%

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

      2. associate-+l+ 99.8%

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

      3. fma-def 99.9%

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

      4. count-2 99.9%

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

      5. distribute-rgt1-in 99.9%

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

      6. *-commutative 99.9%

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

      7. associate-*l* 99.9%

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

      8. 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. Step-by-step derivation

      1. fma-udef 99.9%

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

      2. +-commutative 99.9%

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

   5. Applied egg-rr 99.9%

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

   if 4.0000000000000002e289 < (*.f64 z z)

   1. Initial program 93.9%

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

   2. Taylor expanded in x around 0 98.8%

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

      1. unpow2 98.8%

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

      2. unpow2 98.8%

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

      3. distribute-rgt1-in 98.8%

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

      4. metadata-eval 98.8%

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

      5. *-commutative 98.8%

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

      6. associate-*r* 98.8%

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

   4. Simplified 98.8%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 4 \cdot 10^{+289}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right) + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(z \cdot 3\right)\\ \end{array} \]

Alternative 3: 52.5% accurate, 3.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_, z_] := N[(z * N[(z * 3.0), $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. Taylor expanded in x around 0 56.7%

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

   1. unpow2 56.7%

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

   2. unpow2 56.7%

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

   3. distribute-rgt1-in 56.7%

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

   4. metadata-eval 56.7%

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

   5. *-commutative 56.7%

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

   6. associate-*r* 56.7%

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

4. Simplified 56.7%

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

5. Final simplification 56.7%

   \[\leadsto z \cdot \left(z \cdot 3\right) \]

Alternative 4: 3.7% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ z \cdot 2 \end{array} \]

FPCore

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

C

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

Fortran

real(8) function code(x, y, z)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    code = z * 2.0d0
end function

Java

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

Python

def code(x, y, z):
	return z * 2.0

Julia

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

MATLAB

function tmp = code(x, y, z)
	tmp = z * 2.0;
end

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in x around 0 56.7%

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

   1. unpow2 56.7%

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

   2. *-commutative 56.7%

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

   3. associate-*l* 56.7%

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

   4. *-commutative 56.7%

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

   5. count-2 56.7%

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

4. Simplified 56.7%

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

   1. +-commutative 56.7%

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

   2. fma-def 56.7%

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

   3. flip-+ 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \color{blue}{\frac{z \cdot z - z \cdot z}{z - z}}\right) \]

   4. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \frac{z \cdot z - z \cdot z}{\color{blue}{0}}\right) \]

   5. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \frac{z \cdot z - z \cdot z}{\color{blue}{z \cdot z - z \cdot z}}\right) \]

   6. associate-*r/ 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \color{blue}{\frac{z \cdot \left(z \cdot z - z \cdot z\right)}{z \cdot z - z \cdot z}}\right) \]

   7. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot \color{blue}{0}}{z \cdot z - z \cdot z}\right) \]

   8. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot \color{blue}{\left(z - z\right)}}{z \cdot z - z \cdot z}\right) \]

   9. distribute-lft-out-- 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{\color{blue}{z \cdot z - z \cdot z}}{z \cdot z - z \cdot z}\right) \]

   10. +-inverses 0.0%

       \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot z - z \cdot z}{\color{blue}{0}}\right) \]

   11. +-inverses 0.0%

       \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot z - z \cdot z}{\color{blue}{z - z}}\right) \]

   12. flip-+ 33.7%

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

6. Applied egg-rr 33.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, z, z + z\right)} \]
7. Step-by-step derivation

   1. fma-udef 33.7%

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

   2. +-commutative 33.7%

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

   3. count-2 33.7%

      \[\leadsto \color{blue}{2 \cdot z} + z \cdot z \]

   4. distribute-rgt-out 34.1%

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

8. Simplified 34.1%

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

9. Taylor expanded in z around 0 3.4%

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

11. Simplified 3.4%

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

12. Final simplification 3.4%

    \[\leadsto z \cdot 2 \]

Alternative 5: 32.5% accurate, 5.0× speedup

Math

\[\begin{array}{l} \\ z \cdot z \end{array} \]

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 97.9%

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

2. Taylor expanded in x around 0 56.7%

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

   1. unpow2 56.7%

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

   2. *-commutative 56.7%

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

   3. associate-*l* 56.7%

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

   4. *-commutative 56.7%

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

   5. count-2 56.7%

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

4. Simplified 56.7%

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

   1. +-commutative 56.7%

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

   2. fma-def 56.7%

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

   3. flip-+ 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \color{blue}{\frac{z \cdot z - z \cdot z}{z - z}}\right) \]

   4. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \frac{z \cdot z - z \cdot z}{\color{blue}{0}}\right) \]

   5. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, z \cdot \frac{z \cdot z - z \cdot z}{\color{blue}{z \cdot z - z \cdot z}}\right) \]

   6. associate-*r/ 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \color{blue}{\frac{z \cdot \left(z \cdot z - z \cdot z\right)}{z \cdot z - z \cdot z}}\right) \]

   7. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot \color{blue}{0}}{z \cdot z - z \cdot z}\right) \]

   8. +-inverses 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot \color{blue}{\left(z - z\right)}}{z \cdot z - z \cdot z}\right) \]

   9. distribute-lft-out-- 0.0%

      \[\leadsto \mathsf{fma}\left(z, z, \frac{\color{blue}{z \cdot z - z \cdot z}}{z \cdot z - z \cdot z}\right) \]

   10. +-inverses 0.0%

       \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot z - z \cdot z}{\color{blue}{0}}\right) \]

   11. +-inverses 0.0%

       \[\leadsto \mathsf{fma}\left(z, z, \frac{z \cdot z - z \cdot z}{\color{blue}{z - z}}\right) \]

   12. flip-+ 33.7%

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

6. Applied egg-rr 33.7%

   \[\leadsto \color{blue}{\mathsf{fma}\left(z, z, z + z\right)} \]
7. Step-by-step derivation

   1. fma-udef 33.7%

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

   2. +-commutative 33.7%

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

   3. count-2 33.7%

      \[\leadsto \color{blue}{2 \cdot z} + z \cdot z \]

   4. distribute-rgt-out 34.1%

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

8. Simplified 34.1%

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

9. Taylor expanded in z around inf 38.2%

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

11. Simplified 38.2%

    \[\leadsto \color{blue}{z \cdot z} \]

12. Final simplification 38.2%

    \[\leadsto z \cdot z \]

Developer target: 98.1% 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 2023224 
(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)))