math.cube on complex, imaginary part

Average Error: 7.2 → 0.2

Time: 10.5s

Precision: binary64

Cost: 1352

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x.re \leq -2.5 \cdot 10^{+129}:\\ \;\;\;\;\left(x.im \cdot \left(x.re \cdot 3\right)\right) \cdot x.re\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{+99}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot \left(x.im \cdot 3\right)\right) \cdot x.re\\ \end{array} \]

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)))

↓

(FPCore (x.re x.im)
 :precision binary64
 (if (<= x.re -2.5e+129)
   (* (* x.im (* x.re 3.0)) x.re)
   (if (<= x.re 3e+99)
     (+
      (* x.im (- (* x.re x.re) (* x.im x.im)))
      (* x.re (* (* x.re x.im) 2.0)))
     (* (* x.re (* x.im 3.0)) 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);
}

↓

double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= -2.5e+129) {
		tmp = (x_46_im * (x_46_re * 3.0)) * x_46_re;
	} else if (x_46_re <= 3e+99) {
		tmp = (x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + (x_46_re * ((x_46_re * x_46_im) * 2.0));
	} else {
		tmp = (x_46_re * (x_46_im * 3.0)) * x_46_re;
	}
	return tmp;
}

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

↓

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_46re <= (-2.5d+129)) then
        tmp = (x_46im * (x_46re * 3.0d0)) * x_46re
    else if (x_46re <= 3d+99) then
        tmp = (x_46im * ((x_46re * x_46re) - (x_46im * x_46im))) + (x_46re * ((x_46re * x_46im) * 2.0d0))
    else
        tmp = (x_46re * (x_46im * 3.0d0)) * x_46re
    end if
    code = tmp
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);
}

↓

public static double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= -2.5e+129) {
		tmp = (x_46_im * (x_46_re * 3.0)) * x_46_re;
	} else if (x_46_re <= 3e+99) {
		tmp = (x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + (x_46_re * ((x_46_re * x_46_im) * 2.0));
	} else {
		tmp = (x_46_re * (x_46_im * 3.0)) * x_46_re;
	}
	return tmp;
}

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)

↓

def code(x_46_re, x_46_im):
	tmp = 0
	if x_46_re <= -2.5e+129:
		tmp = (x_46_im * (x_46_re * 3.0)) * x_46_re
	elif x_46_re <= 3e+99:
		tmp = (x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + (x_46_re * ((x_46_re * x_46_im) * 2.0))
	else:
		tmp = (x_46_re * (x_46_im * 3.0)) * x_46_re
	return tmp

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

↓

function code(x_46_re, x_46_im)
	tmp = 0.0
	if (x_46_re <= -2.5e+129)
		tmp = Float64(Float64(x_46_im * Float64(x_46_re * 3.0)) * x_46_re);
	elseif (x_46_re <= 3e+99)
		tmp = Float64(Float64(x_46_im * Float64(Float64(x_46_re * x_46_re) - Float64(x_46_im * x_46_im))) + Float64(x_46_re * Float64(Float64(x_46_re * x_46_im) * 2.0)));
	else
		tmp = Float64(Float64(x_46_re * Float64(x_46_im * 3.0)) * x_46_re);
	end
	return tmp
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

↓

function tmp_2 = code(x_46_re, x_46_im)
	tmp = 0.0;
	if (x_46_re <= -2.5e+129)
		tmp = (x_46_im * (x_46_re * 3.0)) * x_46_re;
	elseif (x_46_re <= 3e+99)
		tmp = (x_46_im * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) + (x_46_re * ((x_46_re * x_46_im) * 2.0));
	else
		tmp = (x_46_re * (x_46_im * 3.0)) * x_46_re;
	end
	tmp_2 = tmp;
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]

↓

code[x$46$re_, x$46$im_] := If[LessEqual[x$46$re, -2.5e+129], N[(N[(x$46$im * N[(x$46$re * 3.0), $MachinePrecision]), $MachinePrecision] * x$46$re), $MachinePrecision], If[LessEqual[x$46$re, 3e+99], N[(N[(x$46$im * N[(N[(x$46$re * x$46$re), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(x$46$re * N[(N[(x$46$re * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re * N[(x$46$im * 3.0), $MachinePrecision]), $MachinePrecision] * x$46$re), $MachinePrecision]]]

Target

Original	7.2
Target	0.2
Herbie	0.2

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

Derivation

1. Split input into 3 regimes

2. if x.re < -2.5000000000000001e129

   1. Initial program 47.2

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

   2. Simplified 0.4

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

      [Start] 47.2	\[ \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 47.2	\[ \color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-111 [=>] 47.2	\[ x.im \cdot \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re - x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-50 [=>] 0.4	\[ \color{blue}{\left(x.re - x.im\right) \cdot \left(\left(x.im + x.re\right) \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-3 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\color{blue}{\left(x.re + x.im\right)} \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + \color{blue}{x.re \cdot \left(x.re \cdot x.im + x.im \cdot x.re\right)} \]
      rational_best-simplify-1 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + x.re \cdot \left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) \]
      rational_best-simplify-63 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + x.re \cdot \color{blue}{\left(x.re \cdot \left(x.im + x.im\right)\right)} \]

   3. Taylor expanded in x.re around inf 0.4

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

   4. Applied egg-rr 0.4

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

   5. Taylor expanded in x.im around 0 0.4

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

   6. Simplified 0.4

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

      [Start] 0.4	\[ \left(\left(x.re + 2 \cdot x.re\right) \cdot x.im\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 0.4	\[ \color{blue}{\left(x.im \cdot \left(x.re + 2 \cdot x.re\right)\right)} \cdot x.re \]
      rational_best-simplify-59 [=>] 0.4	\[ \left(x.im \cdot \color{blue}{\left(2 \cdot x.re - \left(-x.re\right)\right)}\right) \cdot x.re \]
      rational_best-simplify-11 [=>] 0.4	\[ \left(x.im \cdot \left(2 \cdot x.re - \color{blue}{x.re \cdot -1}\right)\right) \cdot x.re \]
      rational_best-simplify-62 [=>] 0.4	\[ \left(x.im \cdot \color{blue}{\left(x.re \cdot \left(2 - -1\right)\right)}\right) \cdot x.re \]
      metadata-eval [=>] 0.4	\[ \left(x.im \cdot \left(x.re \cdot \color{blue}{3}\right)\right) \cdot x.re \]

   if -2.5000000000000001e129 < x.re < 3.00000000000000014e99

   1. Initial program 0.2

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

   2. Simplified 0.2

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

      [Start] 0.2	\[ \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 0.2	\[ \color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-7 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \color{blue}{\left(x.re \cdot 1\right)} \]
      metadata-eval [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \left(x.re \cdot \color{blue}{\frac{-2}{-2}}\right) \]
      metadata-eval [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \left(x.re \cdot \frac{\color{blue}{-1 + -1}}{-2}\right) \]
      metadata-eval [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \left(x.re \cdot \frac{-1 + -1}{\color{blue}{-1 + -1}}\right) \]
      rational_best-simplify-1 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \color{blue}{\left(\frac{-1 + -1}{-1 + -1} \cdot x.re\right)} \]
      rational_best-simplify-50 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + \color{blue}{x.re \cdot \left(\frac{-1 + -1}{-1 + -1} \cdot \left(x.re \cdot x.im + x.im \cdot x.re\right)\right)} \]
      rational_best-simplify-1 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \color{blue}{\left(\left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot \frac{-1 + -1}{-1 + -1}\right)} \]
      rational_best-simplify-55 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \color{blue}{\left(\left(-1 + -1\right) \cdot \frac{x.re \cdot x.im + x.im \cdot x.re}{-1 + -1}\right)} \]
      rational_best-simplify-1 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(-1 + -1\right) \cdot \frac{x.re \cdot x.im + \color{blue}{x.re \cdot x.im}}{-1 + -1}\right) \]
      rational_best-simplify-108 [<=] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(-1 + -1\right) \cdot \color{blue}{\frac{x.re \cdot x.im}{-1}}\right) \]
      rational_best-simplify-55 [=>] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \color{blue}{\left(\left(x.re \cdot x.im\right) \cdot \frac{-1 + -1}{-1}\right)} \]
      metadata-eval [=>] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot \frac{\color{blue}{-2}}{-1}\right) \]
      metadata-eval [=>] 0.2	\[ x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot \color{blue}{2}\right) \]

   if 3.00000000000000014e99 < x.re

   1. Initial program 34.5

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

   2. Simplified 0.4

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

      [Start] 34.5	\[ \left(x.re \cdot x.re - x.im \cdot x.im\right) \cdot x.im + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 34.5	\[ \color{blue}{x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-111 [=>] 34.5	\[ x.im \cdot \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re - x.im\right)\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-50 [=>] 0.4	\[ \color{blue}{\left(x.re - x.im\right) \cdot \left(\left(x.im + x.re\right) \cdot x.im\right)} + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-3 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\color{blue}{\left(x.re + x.im\right)} \cdot x.im\right) + \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.re \]
      rational_best-simplify-1 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + \color{blue}{x.re \cdot \left(x.re \cdot x.im + x.im \cdot x.re\right)} \]
      rational_best-simplify-1 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + x.re \cdot \left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) \]
      rational_best-simplify-63 [=>] 0.4	\[ \left(x.re - x.im\right) \cdot \left(\left(x.re + x.im\right) \cdot x.im\right) + x.re \cdot \color{blue}{\left(x.re \cdot \left(x.im + x.im\right)\right)} \]

   3. Taylor expanded in x.re around inf 0.5

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

   4. Applied egg-rr 0.4

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

   5. Taylor expanded in x.re around inf 0.4

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

   6. Simplified 0.4

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

      [Start] 0.4	\[ \left(x.re \cdot \left(x.im + 2 \cdot x.im\right)\right) \cdot x.re \]
      rational_best-simplify-59 [=>] 0.4	\[ \left(x.re \cdot \color{blue}{\left(2 \cdot x.im - \left(-x.im\right)\right)}\right) \cdot x.re \]
      rational_best-simplify-11 [=>] 0.4	\[ \left(x.re \cdot \left(2 \cdot x.im - \color{blue}{x.im \cdot -1}\right)\right) \cdot x.re \]
      rational_best-simplify-62 [=>] 0.4	\[ \left(x.re \cdot \color{blue}{\left(x.im \cdot \left(2 - -1\right)\right)}\right) \cdot x.re \]
      metadata-eval [=>] 0.4	\[ \left(x.re \cdot \left(x.im \cdot \color{blue}{3}\right)\right) \cdot x.re \]

3. Recombined 3 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -2.5 \cdot 10^{+129}:\\ \;\;\;\;\left(x.im \cdot \left(x.re \cdot 3\right)\right) \cdot x.re\\ \mathbf{elif}\;x.re \leq 3 \cdot 10^{+99}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot \left(x.im \cdot 3\right)\right) \cdot x.re\\ \end{array} \]

Alternatives

Alternative 1
Error	0.2
Cost	1088

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

Alternative 2
Error	0.4
Cost	968

\[\begin{array}{l} \mathbf{if}\;x.re \leq -2 \cdot 10^{+78}:\\ \;\;\;\;\left(x.im \cdot \left(x.re \cdot 3\right)\right) \cdot x.re\\ \mathbf{elif}\;x.re \leq 3.8 \cdot 10^{+80}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot \left(x.re \cdot 3\right) - x.im \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot \left(x.im \cdot 3\right)\right) \cdot x.re\\ \end{array} \]

Alternative 3
Error	0.5
Cost	968

\[\begin{array}{l} \mathbf{if}\;x.re \leq -3.7 \cdot 10^{+56}:\\ \;\;\;\;\left(x.im \cdot \left(x.re \cdot 3\right)\right) \cdot x.re\\ \mathbf{elif}\;x.re \leq 6.1 \cdot 10^{+81}:\\ \;\;\;\;x.im \cdot \left(\left(x.re \cdot x.re\right) \cdot 3 - x.im \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot \left(x.im \cdot 3\right)\right) \cdot x.re\\ \end{array} \]

Alternative 4
Error	19.0
Cost	448

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

Alternative 5
Error	19.0
Cost	448

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

Alternative 6
Error	46.5
Cost	384

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

Reproduce

herbie shell --seed 2023100 
(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)))