math.cube on complex, imaginary part

Percentage Accurate: 82.4% → 99.8%

Time: 6.6s

Alternatives: 9

Speedup: 1.1×

• 43.5% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (+
  (* (- (* x.re x.re) (* x.im x.im)) x.im)
  (* (+ (* x.re x.im) (* x.im x.re)) x.re)))

C

double code(double x_46_re, double x_46_im) {
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = (((x_46re * x_46re) - (x_46im * x_46im)) * x_46im) + (((x_46re * x_46im) + (x_46im * x_46re)) * x_46re)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
}

Python

def code(x_46_re, x_46_im):
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re)

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(Float64(Float64(x_46_re * x_46_re) - Float64(x_46_im * x_46_im)) * x_46_im) + Float64(Float64(Float64(x_46_re * x_46_im) + Float64(x_46_im * x_46_re)) * x_46_re))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(N[(N[(x$46$re * x$46$re), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision] * x$46$im), $MachinePrecision] + N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] * x$46$re), $MachinePrecision]), $MachinePrecision]

Initial Program: 82.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (+
  (* (- (* x.re x.re) (* x.im x.im)) x.im)
  (* (+ (* x.re x.im) (* x.im x.re)) x.re)))

C

double code(double x_46_re, double x_46_im) {
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = (((x_46re * x_46re) - (x_46im * x_46im)) * x_46im) + (((x_46re * x_46im) + (x_46im * x_46re)) * x_46re)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
}

Python

def code(x_46_re, x_46_im):
	return (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re)

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(Float64(Float64(x_46_re * x_46_re) - Float64(x_46_im * x_46_im)) * x_46_im) + Float64(Float64(Float64(x_46_re * x_46_im) + Float64(x_46_im * x_46_re)) * x_46_re))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = (((x_46_re * x_46_re) - (x_46_im * x_46_im)) * x_46_im) + (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_re);
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(N[(N[(x$46$re * x$46$re), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision] * x$46$im), $MachinePrecision] + N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] * x$46$re), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)\\ t_1 := x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\\ \mathbf{if}\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + t_1 \leq \infty:\\ \;\;\;\;t_1 + t_0\\ \mathbf{else}:\\ \;\;\;\;t_0 + x.re \cdot 0\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (let* ((t_0 (* (- x.re x.im) (* x.im (+ x.re x.im))))
        (t_1 (* x.re (+ (* x.re x.im) (* x.re x.im)))))
   (if (<= (+ (* x.im (- (* x.re x.re) (* x.im x.im))) t_1) INFINITY)
     (+ t_1 t_0)
     (+ t_0 (* x.re 0.0)))))

C

double code(double x_46_re, double x_46_im) {
	double t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	double t_1 = x_46_re * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	double tmp;
	if (((x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + t_1) <= ((double) INFINITY)) {
		tmp = t_1 + t_0;
	} else {
		tmp = t_0 + (x_46_re * 0.0);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im) {
	double t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	double t_1 = x_46_re * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	double tmp;
	if (((x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + t_1) <= Double.POSITIVE_INFINITY) {
		tmp = t_1 + t_0;
	} else {
		tmp = t_0 + (x_46_re * 0.0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))
	t_1 = x_46_re * ((x_46_re * x_46_im) + (x_46_re * x_46_im))
	tmp = 0
	if ((x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + t_1) <= math.inf:
		tmp = t_1 + t_0
	else:
		tmp = t_0 + (x_46_re * 0.0)
	return tmp

Julia

function code(x_46_re, x_46_im)
	t_0 = Float64(Float64(x_46_re - x_46_im) * Float64(x_46_im * Float64(x_46_re + x_46_im)))
	t_1 = Float64(x_46_re * Float64(Float64(x_46_re * x_46_im) + Float64(x_46_re * x_46_im)))
	tmp = 0.0
	if (Float64(Float64(x_46_im * Float64(Float64(x_46_re * x_46_re) - Float64(x_46_im * x_46_im))) + t_1) <= Inf)
		tmp = Float64(t_1 + t_0);
	else
		tmp = Float64(t_0 + Float64(x_46_re * 0.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	t_1 = x_46_re * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	tmp = 0.0;
	if (((x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + t_1) <= Inf)
		tmp = t_1 + t_0;
	else
		tmp = t_0 + (x_46_re * 0.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := Block[{t$95$0 = N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$im * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(x$46$re * N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$re * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x$46$im * N[(N[(x$46$re * x$46$re), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision], Infinity], N[(t$95$1 + t$95$0), $MachinePrecision], N[(t$95$0 + N[(x$46$re * 0.0), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)) < +inf.0

   1. Initial program 93.4%

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

      1. add-cube-cbrt 93.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. pow3 93.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 93.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. difference-of-squares 93.0%

         \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      5. associate-*r* 99.4%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
   4. Step-by-step derivation

      1. unpow3 99.4%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right) \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. add-cube-cbrt 99.7%

         \[\leadsto \color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 99.7%

         \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. +-commutative 99.7%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \color{blue}{\left(x.im + x.re\right)}\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   if +inf.0 < (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re))

   1. Initial program 0.0%

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

      1. add-cube-cbrt 0.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. pow3 0.0%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 0.0%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. difference-of-squares 28.9%

         \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      5. associate-*r* 28.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. Applied egg-rr 28.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
   4. Step-by-step derivation

      1. unpow3 28.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right) \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. add-cube-cbrt 28.9%

         \[\leadsto \color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 28.9%

         \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. +-commutative 28.9%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \color{blue}{\left(x.im + x.re\right)}\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Applied egg-rr 28.9%

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

      1. *-commutative 28.9%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \cdot x.re \]

      2. flip-+ 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \cdot x.re \]

      3. div-sub 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\left(\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right)} \cdot x.re \]

      4. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      5. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      6. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      7. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      8. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      9. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      10. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}}\right) \cdot x.re \]

      11. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re}\right) \cdot x.re \]

   7. Applied egg-rr 0.0%

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

      1. +-inverses 100.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]

   9. Simplified 100.0%

      \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right) \leq \infty:\\ \;\;\;\;x.re \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right) + \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right) + x.re \cdot 0\\ \end{array} \]

Alternative 2: 99.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)\\ \mathbf{if}\;x.im \leq -1 \cdot 10^{+130} \lor \neg \left(x.im \leq 1.95 \cdot 10^{+44}\right):\\ \;\;\;\;t_0 + x.re \cdot 0\\ \mathbf{else}:\\ \;\;\;\;t_0 + x.re \cdot \left(x.re \cdot \left(x.im + x.im\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (let* ((t_0 (* (- x.re x.im) (* x.im (+ x.re x.im)))))
   (if (or (<= x.im -1e+130) (not (<= x.im 1.95e+44)))
     (+ t_0 (* x.re 0.0))
     (+ t_0 (* x.re (* x.re (+ x.im x.im)))))))

C

double code(double x_46_re, double x_46_im) {
	double t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	double tmp;
	if ((x_46_im <= -1e+130) || !(x_46_im <= 1.95e+44)) {
		tmp = t_0 + (x_46_re * 0.0);
	} else {
		tmp = t_0 + (x_46_re * (x_46_re * (x_46_im + x_46_im)));
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x_46re - x_46im) * (x_46im * (x_46re + x_46im))
    if ((x_46im <= (-1d+130)) .or. (.not. (x_46im <= 1.95d+44))) then
        tmp = t_0 + (x_46re * 0.0d0)
    else
        tmp = t_0 + (x_46re * (x_46re * (x_46im + x_46im)))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im) {
	double t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	double tmp;
	if ((x_46_im <= -1e+130) || !(x_46_im <= 1.95e+44)) {
		tmp = t_0 + (x_46_re * 0.0);
	} else {
		tmp = t_0 + (x_46_re * (x_46_re * (x_46_im + x_46_im)));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))
	tmp = 0
	if (x_46_im <= -1e+130) or not (x_46_im <= 1.95e+44):
		tmp = t_0 + (x_46_re * 0.0)
	else:
		tmp = t_0 + (x_46_re * (x_46_re * (x_46_im + x_46_im)))
	return tmp

Julia

function code(x_46_re, x_46_im)
	t_0 = Float64(Float64(x_46_re - x_46_im) * Float64(x_46_im * Float64(x_46_re + x_46_im)))
	tmp = 0.0
	if ((x_46_im <= -1e+130) || !(x_46_im <= 1.95e+44))
		tmp = Float64(t_0 + Float64(x_46_re * 0.0));
	else
		tmp = Float64(t_0 + Float64(x_46_re * Float64(x_46_re * Float64(x_46_im + x_46_im))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	t_0 = (x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im));
	tmp = 0.0;
	if ((x_46_im <= -1e+130) || ~((x_46_im <= 1.95e+44)))
		tmp = t_0 + (x_46_re * 0.0);
	else
		tmp = t_0 + (x_46_re * (x_46_re * (x_46_im + x_46_im)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := Block[{t$95$0 = N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$im * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x$46$im, -1e+130], N[Not[LessEqual[x$46$im, 1.95e+44]], $MachinePrecision]], N[(t$95$0 + N[(x$46$re * 0.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + N[(x$46$re * N[(x$46$re * N[(x$46$im + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x.im < -1.0000000000000001e130 or 1.9500000000000001e44 < x.im

   1. Initial program 64.8%

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

      1. add-cube-cbrt 64.7%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. pow3 64.7%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 64.7%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. difference-of-squares 74.9%

         \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      5. associate-*r* 74.9%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. Applied egg-rr 74.9%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
   4. Step-by-step derivation

      1. unpow3 74.9%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right) \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. add-cube-cbrt 75.0%

         \[\leadsto \color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 75.0%

         \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. +-commutative 75.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \color{blue}{\left(x.im + x.re\right)}\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Applied egg-rr 75.0%

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

      1. *-commutative 75.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \cdot x.re \]

      2. flip-+ 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \cdot x.re \]

      3. div-sub 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\left(\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right)} \cdot x.re \]

      4. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      5. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      6. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      7. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      8. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      9. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      10. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}}\right) \cdot x.re \]

      11. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re}\right) \cdot x.re \]

   7. Applied egg-rr 0.0%

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

      1. +-inverses 100.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]

   9. Simplified 100.0%

      \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]

   if -1.0000000000000001e130 < x.im < 1.9500000000000001e44

   1. Initial program 90.2%

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

      1. add-cube-cbrt 89.8%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. pow3 89.8%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 89.8%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. difference-of-squares 89.8%

         \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      5. associate-*r* 99.2%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. Applied egg-rr 99.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
   4. Step-by-step derivation

      1. unpow3 99.1%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right) \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. add-cube-cbrt 99.6%

         \[\leadsto \color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 99.6%

         \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. +-commutative 99.6%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \color{blue}{\left(x.im + x.re\right)}\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Applied egg-rr 99.6%

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

      1. *-commutative 99.6%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \cdot x.re \]

      2. distribute-lft-out 99.6%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\left(x.re \cdot \left(x.im + x.im\right)\right)} \cdot x.re \]

   7. Applied egg-rr 99.6%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq -1 \cdot 10^{+130} \lor \neg \left(x.im \leq 1.95 \cdot 10^{+44}\right):\\ \;\;\;\;\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right) + x.re \cdot 0\\ \mathbf{else}:\\ \;\;\;\;\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right) + x.re \cdot \left(x.re \cdot \left(x.im + x.im\right)\right)\\ \end{array} \]

Alternative 3: 85.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.im \leq -1.9 \cdot 10^{-101} \lor \neg \left(x.im \leq 1.4 \cdot 10^{-29}\right):\\ \;\;\;\;\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right) + x.re \cdot 0\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot x.re\right) \cdot \left(x.im \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (if (or (<= x.im -1.9e-101) (not (<= x.im 1.4e-29)))
   (+ (* (- x.re x.im) (* x.im (+ x.re x.im))) (* x.re 0.0))
   (* (* x.re x.re) (* x.im 3.0))))

C

double code(double x_46_re, double x_46_im) {
	double tmp;
	if ((x_46_im <= -1.9e-101) || !(x_46_im <= 1.4e-29)) {
		tmp = ((x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))) + (x_46_re * 0.0);
	} else {
		tmp = (x_46_re * x_46_re) * (x_46_im * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    real(8) :: tmp
    if ((x_46im <= (-1.9d-101)) .or. (.not. (x_46im <= 1.4d-29))) then
        tmp = ((x_46re - x_46im) * (x_46im * (x_46re + x_46im))) + (x_46re * 0.0d0)
    else
        tmp = (x_46re * x_46re) * (x_46im * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im) {
	double tmp;
	if ((x_46_im <= -1.9e-101) || !(x_46_im <= 1.4e-29)) {
		tmp = ((x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))) + (x_46_re * 0.0);
	} else {
		tmp = (x_46_re * x_46_re) * (x_46_im * 3.0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	tmp = 0
	if (x_46_im <= -1.9e-101) or not (x_46_im <= 1.4e-29):
		tmp = ((x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))) + (x_46_re * 0.0)
	else:
		tmp = (x_46_re * x_46_re) * (x_46_im * 3.0)
	return tmp

Julia

function code(x_46_re, x_46_im)
	tmp = 0.0
	if ((x_46_im <= -1.9e-101) || !(x_46_im <= 1.4e-29))
		tmp = Float64(Float64(Float64(x_46_re - x_46_im) * Float64(x_46_im * Float64(x_46_re + x_46_im))) + Float64(x_46_re * 0.0));
	else
		tmp = Float64(Float64(x_46_re * x_46_re) * Float64(x_46_im * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	tmp = 0.0;
	if ((x_46_im <= -1.9e-101) || ~((x_46_im <= 1.4e-29)))
		tmp = ((x_46_re - x_46_im) * (x_46_im * (x_46_re + x_46_im))) + (x_46_re * 0.0);
	else
		tmp = (x_46_re * x_46_re) * (x_46_im * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := If[Or[LessEqual[x$46$im, -1.9e-101], N[Not[LessEqual[x$46$im, 1.4e-29]], $MachinePrecision]], N[(N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$im * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x$46$re * 0.0), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re * x$46$re), $MachinePrecision] * N[(x$46$im * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x.im < -1.90000000000000005e-101 or 1.4000000000000001e-29 < x.im

   1. Initial program 75.4%

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

      1. add-cube-cbrt 75.0%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. pow3 75.1%

         \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 75.1%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. difference-of-squares 82.0%

         \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      5. associate-*r* 82.6%

         \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. Applied egg-rr 82.6%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
   4. Step-by-step derivation

      1. unpow3 82.5%

         \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right) \cdot \sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      2. add-cube-cbrt 82.9%

         \[\leadsto \color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      3. *-commutative 82.9%

         \[\leadsto \color{blue}{\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

      4. +-commutative 82.9%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \color{blue}{\left(x.im + x.re\right)}\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Applied egg-rr 82.9%

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

      1. *-commutative 82.9%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \cdot x.re \]

      2. flip-+ 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \cdot x.re \]

      3. div-sub 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{\left(\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right)} \cdot x.re \]

      4. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      5. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      6. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      7. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re} - \frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      8. pow2 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{\color{blue}{{\left(x.re \cdot x.im\right)}^{2}}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      9. *-commutative 0.0%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\color{blue}{\left(x.im \cdot x.re\right)}}^{2}}{x.re \cdot x.im - x.re \cdot x.im}\right) \cdot x.re \]

      10. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{x.re \cdot x.im - \color{blue}{x.im \cdot x.re}}\right) \cdot x.re \]

      11. *-commutative 0.0%

          \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \left(\frac{{\left(x.im \cdot x.re\right)}^{2}}{x.im \cdot x.re - x.im \cdot x.re} - \frac{{\left(x.im \cdot x.re\right)}^{2}}{\color{blue}{x.im \cdot x.re} - x.im \cdot x.re}\right) \cdot x.re \]

   7. Applied egg-rr 0.0%

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

      1. +-inverses 93.8%

         \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]

   9. Simplified 93.8%

      \[\leadsto \left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.im + x.re\right)\right) + \color{blue}{0} \cdot x.re \]

   if -1.90000000000000005e-101 < x.im < 1.4000000000000001e-29

   1. Initial program 86.2%

      \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   2. Taylor expanded in x.re around inf 82.1%

      \[\leadsto \color{blue}{{x.re}^{2}} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   4. Simplified 82.1%

      \[\leadsto \color{blue}{\left(x.re \cdot x.re\right)} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. Taylor expanded in x.re around 0 82.2%

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

      1. unpow2 82.2%

         \[\leadsto \color{blue}{\left(x.re \cdot x.re\right)} \cdot \left(x.im + 2 \cdot x.im\right) \]

      2. distribute-rgt1-in 82.2%

         \[\leadsto \left(x.re \cdot x.re\right) \cdot \color{blue}{\left(\left(2 + 1\right) \cdot x.im\right)} \]

      3. metadata-eval 82.2%

         \[\leadsto \left(x.re \cdot x.re\right) \cdot \left(\color{blue}{3} \cdot x.im\right) \]

   7. Simplified 82.2%

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

4. Final simplification 89.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq -1.9 \cdot 10^{-101} \lor \neg \left(x.im \leq 1.4 \cdot 10^{-29}\right):\\ \;\;\;\;\left(x.re - x.im\right) \cdot \left(x.im \cdot \left(x.re + x.im\right)\right) + x.re \cdot 0\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot x.re\right) \cdot \left(x.im \cdot 3\right)\\ \end{array} \]

Alternative 4: 34.8% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ 2 \cdot \left(x.re \cdot \left(x.re \cdot x.im\right)\right) \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* 2.0 (* x.re (* x.re x.im))))

C

double code(double x_46_re, double x_46_im) {
	return 2.0 * (x_46_re * (x_46_re * x_46_im));
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = 2.0d0 * (x_46re * (x_46re * x_46im))
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return 2.0 * (x_46_re * (x_46_re * x_46_im));
}

Python

def code(x_46_re, x_46_im):
	return 2.0 * (x_46_re * (x_46_re * x_46_im))

Julia

function code(x_46_re, x_46_im)
	return Float64(2.0 * Float64(x_46_re * Float64(x_46_re * x_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = 2.0 * (x_46_re * (x_46_re * x_46_im));
end

Wolfram

code[x$46$re_, x$46$im_] := N[(2.0 * N[(x$46$re * N[(x$46$re * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

   1. add-cube-cbrt 79.2%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right) \cdot \sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   2. pow3 79.2%

      \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   3. *-commutative 79.2%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   4. difference-of-squares 83.5%

      \[\leadsto {\left(\sqrt[3]{x.im \cdot \color{blue}{\left(\left(x.re + x.im\right) \cdot \left(x.re - x.im\right)\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

   5. associate-*r* 88.9%

      \[\leadsto {\left(\sqrt[3]{\color{blue}{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}}\right)}^{3} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

3. Applied egg-rr 88.9%

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\left(x.im \cdot \left(x.re + x.im\right)\right) \cdot \left(x.re - x.im\right)}\right)}^{3}} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

4. Taylor expanded in x.im around 0 31.0%

   \[\leadsto \color{blue}{2 \cdot \left({x.re}^{2} \cdot x.im\right)} \]
5. Step-by-step derivation

   1. *-commutative 31.0%

      \[\leadsto 2 \cdot \color{blue}{\left(x.im \cdot {x.re}^{2}\right)} \]

   2. unpow2 31.0%

      \[\leadsto 2 \cdot \left(x.im \cdot \color{blue}{\left(x.re \cdot x.re\right)}\right) \]

   3. associate-*r* 31.8%

      \[\leadsto 2 \cdot \color{blue}{\left(\left(x.im \cdot x.re\right) \cdot x.re\right)} \]

6. Simplified 31.8%

   \[\leadsto \color{blue}{2 \cdot \left(\left(x.im \cdot x.re\right) \cdot x.re\right)} \]

7. Final simplification 31.8%

   \[\leadsto 2 \cdot \left(x.re \cdot \left(x.re \cdot x.im\right)\right) \]

Alternative 5: 49.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ x.im \cdot \left(\left(x.re \cdot x.re\right) \cdot 3\right) \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* x.im (* (* x.re x.re) 3.0)))

C

double code(double x_46_re, double x_46_im) {
	return x_46_im * ((x_46_re * x_46_re) * 3.0);
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = x_46im * ((x_46re * x_46re) * 3.0d0)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return x_46_im * ((x_46_re * x_46_re) * 3.0);
}

Python

def code(x_46_re, x_46_im):
	return x_46_im * ((x_46_re * x_46_re) * 3.0)

Julia

function code(x_46_re, x_46_im)
	return Float64(x_46_im * Float64(Float64(x_46_re * x_46_re) * 3.0))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = x_46_im * ((x_46_re * x_46_re) * 3.0);
end

Wolfram

code[x$46$re_, x$46$im_] := N[(x$46$im * N[(N[(x$46$re * x$46$re), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

   \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

2. Taylor expanded in x.re around inf 48.1%

   \[\leadsto \color{blue}{{x.re}^{2}} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

4. Simplified 48.1%

   \[\leadsto \color{blue}{\left(x.re \cdot x.re\right)} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

5. Taylor expanded in x.im around 0 48.1%

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

   1. *-commutative 48.1%

      \[\leadsto \color{blue}{x.im \cdot \left(2 \cdot {x.re}^{2} + {x.re}^{2}\right)} \]

   2. distribute-lft1-in 48.1%

      \[\leadsto x.im \cdot \color{blue}{\left(\left(2 + 1\right) \cdot {x.re}^{2}\right)} \]

   3. metadata-eval 48.1%

      \[\leadsto x.im \cdot \left(\color{blue}{3} \cdot {x.re}^{2}\right) \]

   4. unpow2 48.1%

      \[\leadsto x.im \cdot \left(3 \cdot \color{blue}{\left(x.re \cdot x.re\right)}\right) \]

7. Simplified 48.1%

   \[\leadsto \color{blue}{x.im \cdot \left(3 \cdot \left(x.re \cdot x.re\right)\right)} \]

8. Final simplification 48.1%

   \[\leadsto x.im \cdot \left(\left(x.re \cdot x.re\right) \cdot 3\right) \]

Alternative 6: 49.1% accurate, 2.7× speedup

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.re\right) \cdot \left(x.im \cdot 3\right) \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* (* x.re x.re) (* x.im 3.0)))

C

double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_re) * (x_46_im * 3.0);
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = (x_46re * x_46re) * (x_46im * 3.0d0)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_re) * (x_46_im * 3.0);
}

Python

def code(x_46_re, x_46_im):
	return (x_46_re * x_46_re) * (x_46_im * 3.0)

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(x_46_re * x_46_re) * Float64(x_46_im * 3.0))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = (x_46_re * x_46_re) * (x_46_im * 3.0);
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(x$46$re * x$46$re), $MachinePrecision] * N[(x$46$im * 3.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

   \[\left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

2. Taylor expanded in x.re around inf 48.1%

   \[\leadsto \color{blue}{{x.re}^{2}} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

4. Simplified 48.1%

   \[\leadsto \color{blue}{\left(x.re \cdot x.re\right)} \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]

5. Taylor expanded in x.re around 0 48.1%

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

   1. unpow2 48.1%

      \[\leadsto \color{blue}{\left(x.re \cdot x.re\right)} \cdot \left(x.im + 2 \cdot x.im\right) \]

   2. distribute-rgt1-in 48.1%

      \[\leadsto \left(x.re \cdot x.re\right) \cdot \color{blue}{\left(\left(2 + 1\right) \cdot x.im\right)} \]

   3. metadata-eval 48.1%

      \[\leadsto \left(x.re \cdot x.re\right) \cdot \left(\color{blue}{3} \cdot x.im\right) \]

7. Simplified 48.1%

   \[\leadsto \color{blue}{\left(x.re \cdot x.re\right) \cdot \left(3 \cdot x.im\right)} \]

8. Final simplification 48.1%

   \[\leadsto \left(x.re \cdot x.re\right) \cdot \left(x.im \cdot 3\right) \]

Alternative 7: 33.5% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.re\right) \cdot x.im \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* (* x.re x.re) x.im))

C

double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_re) * x_46_im;
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = (x_46re * x_46re) * x_46im
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_re) * x_46_im;
}

Python

def code(x_46_re, x_46_im):
	return (x_46_re * x_46_re) * x_46_im

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(x_46_re * x_46_re) * x_46_im)
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = (x_46_re * x_46_re) * x_46_im;
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(x$46$re * x$46$re), $MachinePrecision] * x$46$im), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

   1. *-commutative 79.5%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{x.re \cdot \left(x.re \cdot x.im + x.im \cdot x.re\right)} \]

   2. *-commutative 79.5%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \]

   3. flip-+ 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \]

   4. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{\color{blue}{0}}{x.re \cdot x.im - x.re \cdot x.im} \]

   5. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{\color{blue}{x.im \cdot x.im - x.im \cdot x.im}}{x.re \cdot x.im - x.re \cdot x.im} \]

   6. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{0}} \]

   7. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{x.im - x.im}} \]

   8. flip-+ 60.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \color{blue}{\left(x.im + x.im\right)} \]

   9. distribute-lft-in 60.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.re \cdot x.im + x.re \cdot x.im\right)} \]

   10. flip-+ 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \]

   11. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{\color{blue}{0}}{x.re \cdot x.im - x.re \cdot x.im} \]

   12. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{\color{blue}{x.im \cdot x.im - x.im \cdot x.im}}{x.re \cdot x.im - x.re \cdot x.im} \]

   13. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{0}} \]

   14. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{x.im - x.im}} \]

   15. flip-+ 53.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.im + x.im\right)} \]

3. Applied egg-rr 53.0%

   \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.im + x.im\right)} \]

4. Taylor expanded in x.re around inf 30.5%

   \[\leadsto \color{blue}{{x.re}^{2} \cdot x.im} \]
5. Step-by-step derivation

   1. *-commutative 30.5%

      \[\leadsto \color{blue}{x.im \cdot {x.re}^{2}} \]

   2. unpow2 30.5%

      \[\leadsto x.im \cdot \color{blue}{\left(x.re \cdot x.re\right)} \]

6. Simplified 30.5%

   \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot x.re\right)} \]

7. Final simplification 30.5%

   \[\leadsto \left(x.re \cdot x.re\right) \cdot x.im \]

Alternative 8: 34.2% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ x.re \cdot \left(x.re \cdot x.im\right) \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* x.re (* x.re x.im)))

C

double code(double x_46_re, double x_46_im) {
	return x_46_re * (x_46_re * x_46_im);
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = x_46re * (x_46re * x_46im)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return x_46_re * (x_46_re * x_46_im);
}

Python

def code(x_46_re, x_46_im):
	return x_46_re * (x_46_re * x_46_im)

Julia

function code(x_46_re, x_46_im)
	return Float64(x_46_re * Float64(x_46_re * x_46_im))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = x_46_re * (x_46_re * x_46_im);
end

Wolfram

code[x$46$re_, x$46$im_] := N[(x$46$re * N[(x$46$re * x$46$im), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 79.5%

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

   1. *-commutative 79.5%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{x.re \cdot \left(x.re \cdot x.im + x.im \cdot x.re\right)} \]

   2. *-commutative 79.5%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \left(x.re \cdot x.im + \color{blue}{x.re \cdot x.im}\right) \]

   3. flip-+ 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \]

   4. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{\color{blue}{0}}{x.re \cdot x.im - x.re \cdot x.im} \]

   5. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{\color{blue}{x.im \cdot x.im - x.im \cdot x.im}}{x.re \cdot x.im - x.re \cdot x.im} \]

   6. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{0}} \]

   7. +-inverses 0.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{x.im - x.im}} \]

   8. flip-+ 60.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + x.re \cdot \color{blue}{\left(x.im + x.im\right)} \]

   9. distribute-lft-in 60.0%

      \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.re \cdot x.im + x.re \cdot x.im\right)} \]

   10. flip-+ 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\frac{\left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right) - \left(x.re \cdot x.im\right) \cdot \left(x.re \cdot x.im\right)}{x.re \cdot x.im - x.re \cdot x.im}} \]

   11. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{\color{blue}{0}}{x.re \cdot x.im - x.re \cdot x.im} \]

   12. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{\color{blue}{x.im \cdot x.im - x.im \cdot x.im}}{x.re \cdot x.im - x.re \cdot x.im} \]

   13. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{0}} \]

   14. +-inverses 0.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \frac{x.im \cdot x.im - x.im \cdot x.im}{\color{blue}{x.im - x.im}} \]

   15. flip-+ 53.0%

       \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.im + x.im\right)} \]

3. Applied egg-rr 53.0%

   \[\leadsto \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \color{blue}{\left(x.im + x.im\right)} \]

4. Taylor expanded in x.re around inf 30.5%

   \[\leadsto \color{blue}{{x.re}^{2} \cdot x.im} \]
5. Step-by-step derivation

   1. *-commutative 30.5%

      \[\leadsto \color{blue}{x.im \cdot {x.re}^{2}} \]

   2. unpow2 30.5%

      \[\leadsto x.im \cdot \color{blue}{\left(x.re \cdot x.re\right)} \]

   3. associate-*r* 31.2%

      \[\leadsto \color{blue}{\left(x.im \cdot x.re\right) \cdot x.re} \]

6. Simplified 31.2%

   \[\leadsto \color{blue}{\left(x.im \cdot x.re\right) \cdot x.re} \]

7. Final simplification 31.2%

   \[\leadsto x.re \cdot \left(x.re \cdot x.im\right) \]

Alternative 9: 2.7% accurate, 19.0× speedup

Math

\[\begin{array}{l} \\ -10 \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 -10.0)

C

double code(double x_46_re, double x_46_im) {
	return -10.0;
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = -10.0d0
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return -10.0;
}

Python

def code(x_46_re, x_46_im):
	return -10.0

Julia

function code(x_46_re, x_46_im)
	return -10.0
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = -10.0;
end

Wolfram

code[x$46$re_, x$46$im_] := -10.0

Derivation

1. Initial program 79.5%

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

   1. +-commutative 79.5%

      \[\leadsto \color{blue}{\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im} \]

   2. *-commutative 79.5%

      \[\leadsto \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + \color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)} \]

   3. sub-neg 79.5%

      \[\leadsto \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + x.im \cdot \color{blue}{\left(x.re \cdot x.re + \left(-x.im \cdot x.im\right)\right)} \]

   4. distribute-lft-in 76.8%

      \[\leadsto \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + \color{blue}{\left(x.im \cdot \left(x.re \cdot x.re\right) + x.im \cdot \left(-x.im \cdot x.im\right)\right)} \]

   5. associate-+r+ 76.8%

      \[\leadsto \color{blue}{\left(\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + x.im \cdot \left(x.re \cdot x.re\right)\right) + x.im \cdot \left(-x.im \cdot x.im\right)} \]

   6. distribute-rgt-neg-out 76.8%

      \[\leadsto \left(\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + x.im \cdot \left(x.re \cdot x.re\right)\right) + \color{blue}{\left(-x.im \cdot \left(x.im \cdot x.im\right)\right)} \]

   7. unsub-neg 76.8%

      \[\leadsto \color{blue}{\left(\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + x.im \cdot \left(x.re \cdot x.re\right)\right) - x.im \cdot \left(x.im \cdot x.im\right)} \]

   8. associate-*r* 82.2%

      \[\leadsto \left(\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re + \color{blue}{\left(x.im \cdot x.re\right) \cdot x.re}\right) - x.im \cdot \left(x.im \cdot x.im\right) \]

   9. distribute-rgt-out 82.2%

      \[\leadsto \color{blue}{x.re \cdot \left(\left(x.re \cdot x.im + x.im \cdot x.re\right) + x.im \cdot x.re\right)} - x.im \cdot \left(x.im \cdot x.im\right) \]

   10. *-commutative 82.2%

       \[\leadsto x.re \cdot \left(\left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) + x.im \cdot x.re\right) - x.im \cdot \left(x.im \cdot x.im\right) \]

   11. count-2 82.2%

       \[\leadsto x.re \cdot \left(\color{blue}{2 \cdot \left(x.im \cdot x.re\right)} + x.im \cdot x.re\right) - x.im \cdot \left(x.im \cdot x.im\right) \]

   12. distribute-lft1-in 82.2%

       \[\leadsto x.re \cdot \color{blue}{\left(\left(2 + 1\right) \cdot \left(x.im \cdot x.re\right)\right)} - x.im \cdot \left(x.im \cdot x.im\right) \]

   13. metadata-eval 82.2%

       \[\leadsto x.re \cdot \left(\color{blue}{3} \cdot \left(x.im \cdot x.re\right)\right) - x.im \cdot \left(x.im \cdot x.im\right) \]

   14. *-commutative 82.2%

       \[\leadsto x.re \cdot \color{blue}{\left(\left(x.im \cdot x.re\right) \cdot 3\right)} - x.im \cdot \left(x.im \cdot x.im\right) \]

   15. *-commutative 82.2%

       \[\leadsto x.re \cdot \left(\color{blue}{\left(x.re \cdot x.im\right)} \cdot 3\right) - x.im \cdot \left(x.im \cdot x.im\right) \]

   16. associate-*r* 81.8%

       \[\leadsto x.re \cdot \color{blue}{\left(x.re \cdot \left(x.im \cdot 3\right)\right)} - x.im \cdot \left(x.im \cdot x.im\right) \]

   17. cube-unmult 81.8%

       \[\leadsto x.re \cdot \left(x.re \cdot \left(x.im \cdot 3\right)\right) - \color{blue}{{x.im}^{3}} \]

3. Simplified 81.8%

   \[\leadsto \color{blue}{x.re \cdot \left(x.re \cdot \left(x.im \cdot 3\right)\right) - {x.im}^{3}} \]
4. Step-by-step derivation

   1. associate-*r* 82.3%

      \[\leadsto x.re \cdot \color{blue}{\left(\left(x.re \cdot x.im\right) \cdot 3\right)} - {x.im}^{3} \]

   2. associate-*l* 82.2%

      \[\leadsto \color{blue}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3} - {x.im}^{3} \]

   3. flip-- 19.6%

      \[\leadsto \color{blue}{\frac{\left(\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3\right) \cdot \left(\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3\right) - {x.im}^{3} \cdot {x.im}^{3}}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}}} \]

   4. div-inv 18.3%

      \[\leadsto \color{blue}{\left(\left(\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3\right) \cdot \left(\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3\right) - {x.im}^{3} \cdot {x.im}^{3}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}}} \]

   5. swap-sqr 18.2%

      \[\leadsto \left(\color{blue}{\left(\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot \left(x.re \cdot \left(x.re \cdot x.im\right)\right)\right) \cdot \left(3 \cdot 3\right)} - {x.im}^{3} \cdot {x.im}^{3}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}} \]

   6. pow2 18.2%

      \[\leadsto \left(\color{blue}{{\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2}} \cdot \left(3 \cdot 3\right) - {x.im}^{3} \cdot {x.im}^{3}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}} \]

   7. metadata-eval 18.2%

      \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot \color{blue}{9} - {x.im}^{3} \cdot {x.im}^{3}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}} \]

   8. pow-prod-up 18.2%

      \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - \color{blue}{{x.im}^{\left(3 + 3\right)}}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}} \]

   9. metadata-eval 18.2%

      \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - {x.im}^{\color{blue}{6}}\right) \cdot \frac{1}{\left(x.re \cdot \left(x.re \cdot x.im\right)\right) \cdot 3 + {x.im}^{3}} \]

   10. associate-*l* 18.2%

       \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - {x.im}^{6}\right) \cdot \frac{1}{\color{blue}{x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 3\right)} + {x.im}^{3}} \]

   11. associate-*r* 18.2%

       \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - {x.im}^{6}\right) \cdot \frac{1}{x.re \cdot \color{blue}{\left(x.re \cdot \left(x.im \cdot 3\right)\right)} + {x.im}^{3}} \]

   12. fma-def 18.2%

       \[\leadsto \left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - {x.im}^{6}\right) \cdot \frac{1}{\color{blue}{\mathsf{fma}\left(x.re, x.re \cdot \left(x.im \cdot 3\right), {x.im}^{3}\right)}} \]

5. Applied egg-rr 18.2%

   \[\leadsto \color{blue}{\left({\left(x.re \cdot \left(x.re \cdot x.im\right)\right)}^{2} \cdot 9 - {x.im}^{6}\right) \cdot \frac{1}{\mathsf{fma}\left(x.re, x.re \cdot \left(x.im \cdot 3\right), {x.im}^{3}\right)}} \]

7. Simplified 2.7%

   \[\leadsto \color{blue}{-10} \]

8. Final simplification 2.7%

   \[\leadsto -10 \]

Developer target: 91.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.im\right) \cdot \left(2 \cdot x.re\right) + \left(x.im \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right) \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (+ (* (* x.re x.im) (* 2.0 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im))))

C

double code(double x_46_re, double x_46_im) {
	return ((x_46_re * x_46_im) * (2.0 * x_46_re)) + ((x_46_im * (x_46_re - x_46_im)) * (x_46_re + x_46_im));
}

Fortran

real(8) function code(x_46re, x_46im)
    real(8), intent (in) :: x_46re
    real(8), intent (in) :: x_46im
    code = ((x_46re * x_46im) * (2.0d0 * x_46re)) + ((x_46im * (x_46re - x_46im)) * (x_46re + x_46im))
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return ((x_46_re * x_46_im) * (2.0 * x_46_re)) + ((x_46_im * (x_46_re - x_46_im)) * (x_46_re + x_46_im));
}

Python

def code(x_46_re, x_46_im):
	return ((x_46_re * x_46_im) * (2.0 * x_46_re)) + ((x_46_im * (x_46_re - x_46_im)) * (x_46_re + x_46_im))

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(Float64(x_46_re * x_46_im) * Float64(2.0 * x_46_re)) + Float64(Float64(x_46_im * Float64(x_46_re - x_46_im)) * Float64(x_46_re + x_46_im)))
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = ((x_46_re * x_46_im) * (2.0 * x_46_re)) + ((x_46_im * (x_46_re - x_46_im)) * (x_46_re + x_46_im));
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] * N[(2.0 * x$46$re), $MachinePrecision]), $MachinePrecision] + N[(N[(x$46$im * N[(x$46$re - x$46$im), $MachinePrecision]), $MachinePrecision] * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023196 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.im) (* 2.0 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im)))

  (+ (* (- (* x.re x.re) (* x.im x.im)) x.im) (* (+ (* x.re x.im) (* x.im x.re)) x.re)))