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

Percentage Accurate: 98.1% → 99.2%

Time: 11.9s

Alternatives: 9

Speedup: 1.7×

• 34.6% 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

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

   1. associate-+l+ N/A

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

   2. associate-+l+ N/A

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

   3. *-commutative N/A

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

   4. accelerator-lowering-fma.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, \color{blue}{x}, \left(\left(z \cdot z + z \cdot z\right) + z \cdot z\right)\right) \]

   5. count-2 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \left(2 \cdot \left(z \cdot z\right) + z \cdot z\right)\right) \]

   6. distribute-lft1-in N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \left(\left(2 + 1\right) \cdot \left(z \cdot z\right)\right)\right) \]

   7. metadata-eval N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \left(3 \cdot \left(z \cdot z\right)\right)\right) \]

   8. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{*.f64}\left(3, \left(z \cdot z\right)\right)\right) \]

   9. *-lowering-*.f64 99.1%

      \[\leadsto \mathsf{fma.f64}\left(y, x, \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(z, z\right)\right)\right) \]

4. Applied egg-rr 99.1%

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

Alternative 2: 85.8% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;z \cdot z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{3}{\frac{1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 1e-31) (+ (* z z) (* y x)) (* z (/ 3.0 (/ 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = (z * z) + (y * x);
	} else {
		tmp = z * (3.0 / (1.0 / 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) <= 1d-31) then
        tmp = (z * z) + (y * x)
    else
        tmp = z * (3.0d0 / (1.0d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = (z * z) + (y * x);
	} else {
		tmp = z * (3.0 / (1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 1e-31:
		tmp = (z * z) + (y * x)
	else:
		tmp = z * (3.0 / (1.0 / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 1e-31)
		tmp = Float64(Float64(z * z) + Float64(y * x));
	else
		tmp = Float64(z * Float64(3.0 / Float64(1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 1e-31)
		tmp = (z * z) + (y * x);
	else
		tmp = z * (3.0 / (1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e-31], N[(N[(z * z), $MachinePrecision] + N[(y * x), $MachinePrecision]), $MachinePrecision], N[(z * N[(3.0 / N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

      \[\leadsto \mathsf{+.f64}\left(\color{blue}{\left(x \cdot y\right)}, \mathsf{*.f64}\left(z, z\right)\right) \]
   4. Step-by-step derivation

      1. *-lowering-*.f64 91.5%

         \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\color{blue}{z}, z\right)\right) \]

   5. Simplified 91.5%

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

   if 1e-31 < (*.f64 z z)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right) \]

      6. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right) \]

   5. Simplified 83.4%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{\frac{1}{3}}} \]

      3. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{z}{\frac{1}{3}}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{z}{\frac{1}{3}}\right)}\right) \]

      5. /-lowering-/.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(z, \color{blue}{\frac{1}{3}}\right)\right) \]

   7. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{z \cdot \frac{z}{0.3333333333333333}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{1}{\color{blue}{\frac{\frac{1}{3}}{z}}}\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{1}{\frac{1}{3} \cdot \color{blue}{\frac{1}{z}}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{\frac{1}{\frac{1}{3}}}{\color{blue}{\frac{1}{z}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{3}{\frac{\color{blue}{1}}{z}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(3, \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(3, \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 83.4%

      \[\leadsto z \cdot \color{blue}{\frac{3}{\frac{1}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;z \cdot z + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{3}{\frac{1}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{3}{\frac{1}{z}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 1e-31) (* y x) (* z (/ 3.0 (/ 1.0 z)))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = y * x;
	} else {
		tmp = z * (3.0 / (1.0 / 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) <= 1d-31) then
        tmp = y * x
    else
        tmp = z * (3.0d0 / (1.0d0 / z))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = y * x;
	} else {
		tmp = z * (3.0 / (1.0 / z));
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 1e-31:
		tmp = y * x
	else:
		tmp = z * (3.0 / (1.0 / z))
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 1e-31)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * Float64(3.0 / Float64(1.0 / z)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 1e-31)
		tmp = y * x;
	else
		tmp = z * (3.0 / (1.0 / z));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e-31], N[(y * x), $MachinePrecision], N[(z * N[(3.0 / N[(1.0 / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 90.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 90.4%

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

   if 1e-31 < (*.f64 z z)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right) \]

      6. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right) \]

   5. Simplified 83.4%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{\frac{1}{3}}} \]

      3. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{z}{\frac{1}{3}}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{z}{\frac{1}{3}}\right)}\right) \]

      5. /-lowering-/.f64 83.3%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(z, \color{blue}{\frac{1}{3}}\right)\right) \]

   7. Applied egg-rr 83.3%

      \[\leadsto \color{blue}{z \cdot \frac{z}{0.3333333333333333}} \]
   8. Step-by-step derivation

      1. clear-num N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{1}{\color{blue}{\frac{\frac{1}{3}}{z}}}\right)\right) \]

      2. div-inv N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{1}{\frac{1}{3} \cdot \color{blue}{\frac{1}{z}}}\right)\right) \]

      3. associate-/r* N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{\frac{1}{\frac{1}{3}}}{\color{blue}{\frac{1}{z}}}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(z, \left(\frac{3}{\frac{\color{blue}{1}}{z}}\right)\right) \]

      5. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(3, \color{blue}{\left(\frac{1}{z}\right)}\right)\right) \]

      6. /-lowering-/.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(3, \mathsf{/.f64}\left(1, \color{blue}{z}\right)\right)\right) \]

   9. Applied egg-rr 83.4%

      \[\leadsto z \cdot \color{blue}{\frac{3}{\frac{1}{z}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{3}{\frac{1}{z}}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 85.0% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(z \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= (* z z) 1e-31) (* y x) (* 3.0 (* z z))))

C

double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = y * x;
	} else {
		tmp = 3.0 * (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) <= 1d-31) then
        tmp = y * x
    else
        tmp = 3.0d0 * (z * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if ((z * z) <= 1e-31) {
		tmp = y * x;
	} else {
		tmp = 3.0 * (z * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if (z * z) <= 1e-31:
		tmp = y * x
	else:
		tmp = 3.0 * (z * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (Float64(z * z) <= 1e-31)
		tmp = Float64(y * x);
	else
		tmp = Float64(3.0 * Float64(z * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if ((z * z) <= 1e-31)
		tmp = y * x;
	else
		tmp = 3.0 * (z * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[N[(z * z), $MachinePrecision], 1e-31], N[(y * x), $MachinePrecision], N[(3.0 * N[(z * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (*.f64 z z) < 1e-31

   1. Initial program 99.9%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 90.4%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 90.4%

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

   if 1e-31 < (*.f64 z z)

   1. Initial program 96.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right) \]

      6. *-lowering-*.f64 83.4%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right) \]

   5. Simplified 83.4%

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

4. Final simplification 86.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \cdot z \leq 10^{-31}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(z \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 67.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(3 \cdot z\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 1.05e-15) (* y x) (* z (* 3.0 z))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.05e-15) {
		tmp = y * x;
	} else {
		tmp = z * (3.0 * 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 <= 1.05d-15) then
        tmp = y * x
    else
        tmp = z * (3.0d0 * z)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 1.05e-15) {
		tmp = y * x;
	} else {
		tmp = z * (3.0 * z);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 1.05e-15:
		tmp = y * x
	else:
		tmp = z * (3.0 * z)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 1.05e-15)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * Float64(3.0 * z));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 1.05e-15)
		tmp = y * x;
	else
		tmp = z * (3.0 * z);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 1.05e-15], N[(y * x), $MachinePrecision], N[(z * N[(3.0 * z), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 1.0499999999999999e-15

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 64.3%

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

   if 1.0499999999999999e-15 < z

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right) \]

      6. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right) \]

   5. Simplified 80.7%

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

      1. associate-*l* N/A

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

      2. *-commutative N/A

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

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot 3\right), \color{blue}{z}\right) \]

      4. *-lowering-*.f64 80.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, 3\right), z\right) \]

   7. Applied egg-rr 80.6%

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

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 1.05 \cdot 10^{-15}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \left(3 \cdot z\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 67.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{z}{0.3333333333333333}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z)
 :precision binary64
 (if (<= z 6e-16) (* y x) (* z (/ z 0.3333333333333333))))

C

double code(double x, double y, double z) {
	double tmp;
	if (z <= 6e-16) {
		tmp = y * x;
	} else {
		tmp = z * (z / 0.3333333333333333);
	}
	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 <= 6d-16) then
        tmp = y * x
    else
        tmp = z * (z / 0.3333333333333333d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z) {
	double tmp;
	if (z <= 6e-16) {
		tmp = y * x;
	} else {
		tmp = z * (z / 0.3333333333333333);
	}
	return tmp;
}

Python

def code(x, y, z):
	tmp = 0
	if z <= 6e-16:
		tmp = y * x
	else:
		tmp = z * (z / 0.3333333333333333)
	return tmp

Julia

function code(x, y, z)
	tmp = 0.0
	if (z <= 6e-16)
		tmp = Float64(y * x);
	else
		tmp = Float64(z * Float64(z / 0.3333333333333333));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z)
	tmp = 0.0;
	if (z <= 6e-16)
		tmp = y * x;
	else
		tmp = z * (z / 0.3333333333333333);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_] := If[LessEqual[z, 6e-16], N[(y * x), $MachinePrecision], N[(z * N[(z / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < 5.99999999999999987e-16

   1. Initial program 99.3%

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

   3. Taylor expanded in x around inf

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

      1. *-lowering-*.f64 64.3%

         \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

   5. Simplified 64.3%

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

   if 5.99999999999999987e-16 < z

   1. Initial program 95.9%

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

   3. Taylor expanded in x around 0

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

      1. distribute-lft1-in N/A

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

      2. metadata-eval N/A

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

      3. *-commutative N/A

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

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right) \]

      5. unpow2 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right) \]

      6. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right) \]

   5. Simplified 80.7%

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

      1. metadata-eval N/A

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

      2. div-inv N/A

         \[\leadsto \frac{z \cdot z}{\color{blue}{\frac{1}{3}}} \]

      3. associate-/l* N/A

         \[\leadsto z \cdot \color{blue}{\frac{z}{\frac{1}{3}}} \]

      4. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(z, \color{blue}{\left(\frac{z}{\frac{1}{3}}\right)}\right) \]

      5. /-lowering-/.f64 80.7%

         \[\leadsto \mathsf{*.f64}\left(z, \mathsf{/.f64}\left(z, \color{blue}{\frac{1}{3}}\right)\right) \]

   7. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{z \cdot \frac{z}{0.3333333333333333}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq 6 \cdot 10^{-16}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;z \cdot \frac{z}{0.3333333333333333}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate-+r+ N/A

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

   3. +-commutative N/A

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

   4. *-rgt-identity N/A

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

   5. *-inverses N/A

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

   6. associate-/l* N/A

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

   7. associate-*l/ N/A

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

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{2 \cdot {z}^{2} + {z}^{2}}{y} \cdot y\right)}\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{2 \cdot {z}^{2} + {z}^{2}}{y}} \cdot y\right)\right) \]

   10. associate-*l/ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\frac{\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot y}{\color{blue}{y}}\right)\right) \]

   11. associate-/l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot \color{blue}{\frac{y}{y}}\right)\right) \]

   12. *-inverses N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot 1\right)\right) \]

   13. *-rgt-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(2 \cdot {z}^{2} + \color{blue}{{z}^{2}}\right)\right) \]

   14. *-lft-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(2 \cdot {z}^{2} + 1 \cdot \color{blue}{{z}^{2}}\right)\right) \]

   15. distribute-rgt-out N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left({z}^{2} \cdot \color{blue}{\left(2 + 1\right)}\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left({z}^{2} \cdot 3\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right)\right) \]

   18. unpow2 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right)\right) \]

   19. *-lowering-*.f64 98.3%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right)\right) \]

5. Simplified 98.3%

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

6. Final simplification 98.3%

   \[\leadsto y \cdot x + 3 \cdot \left(z \cdot z\right) \]
7. Add Preprocessing

Alternative 8: 98.1% accurate, 1.7× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around 0

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

   1. +-commutative N/A

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

   2. associate-+r+ N/A

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

   3. +-commutative N/A

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

   4. *-rgt-identity N/A

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

   5. *-inverses N/A

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

   6. associate-/l* N/A

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

   7. associate-*l/ N/A

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

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\left(x \cdot y\right), \color{blue}{\left(\frac{2 \cdot {z}^{2} + {z}^{2}}{y} \cdot y\right)}\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\color{blue}{\frac{2 \cdot {z}^{2} + {z}^{2}}{y}} \cdot y\right)\right) \]

   10. associate-*l/ N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\frac{\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot y}{\color{blue}{y}}\right)\right) \]

   11. associate-/l* N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot \color{blue}{\frac{y}{y}}\right)\right) \]

   12. *-inverses N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(2 \cdot {z}^{2} + {z}^{2}\right) \cdot 1\right)\right) \]

   13. *-rgt-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(2 \cdot {z}^{2} + \color{blue}{{z}^{2}}\right)\right) \]

   14. *-lft-identity N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(2 \cdot {z}^{2} + 1 \cdot \color{blue}{{z}^{2}}\right)\right) \]

   15. distribute-rgt-out N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left({z}^{2} \cdot \color{blue}{\left(2 + 1\right)}\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left({z}^{2} \cdot 3\right)\right) \]

   17. *-lowering-*.f64 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left({z}^{2}\right), \color{blue}{3}\right)\right) \]

   18. unpow2 N/A

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(z \cdot z\right), 3\right)\right) \]

   19. *-lowering-*.f64 98.3%

       \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(z, z\right), 3\right)\right) \]

5. Simplified 98.3%

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

   1. associate-*l* N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(z \cdot \color{blue}{\left(z \cdot 3\right)}\right)\right) \]

   2. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \left(\left(z \cdot 3\right) \cdot \color{blue}{z}\right)\right) \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(z \cdot 3\right), \color{blue}{z}\right)\right) \]

   4. *-commutative N/A

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\left(3 \cdot z\right), z\right)\right) \]

   5. *-lowering-*.f64 98.3%

      \[\leadsto \mathsf{+.f64}\left(\mathsf{*.f64}\left(x, y\right), \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, z\right), z\right)\right) \]

7. Applied egg-rr 98.3%

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

8. Final simplification 98.3%

   \[\leadsto y \cdot x + z \cdot \left(3 \cdot z\right) \]
9. Add Preprocessing

Alternative 9: 52.2% accurate, 5.0× speedup

Math

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

FPCore

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

C

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 98.3%

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

3. Taylor expanded in x around inf

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

   1. *-lowering-*.f64 51.0%

      \[\leadsto \mathsf{*.f64}\left(x, \color{blue}{y}\right) \]

5. Simplified 51.0%

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

6. Final simplification 51.0%

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

Developer Target 1: 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 2024191 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (* 3 z) z) (* y x)))

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