math.cube on complex, real part

Percentage Accurate: 82.2% → 99.8%

Time: 8.9s

Alternatives: 9

Speedup: 0.9×

• 44.3% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (-
  (* (- (* x.re x.re) (* x.im x.im)) x.re)
  (* (+ (* x.re x.im) (* x.im 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (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_46re) - (x_46im * x_46im)) * x_46re) - (((x_46re * x_46im) + (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_re) - (x_46_im * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_im)

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_re) - Float64(Float64(Float64(x_46_re * x_46_im) + Float64(x_46_im * 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_im);
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$46$re), $MachinePrecision] - N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] * x$46$im), $MachinePrecision]), $MachinePrecision]

Initial Program: 82.2% accurate, 1.0× speedup

Math

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

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (-
  (* (- (* x.re x.re) (* x.im x.im)) x.re)
  (* (+ (* x.re x.im) (* x.im 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (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_46re) - (x_46im * x_46im)) * x_46re) - (((x_46re * x_46im) + (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_re) - (x_46_im * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_im)

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_re) - Float64(Float64(Float64(x_46_re * x_46_im) + Float64(x_46_im * 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 * x_46_im)) * x_46_re) - (((x_46_re * x_46_im) + (x_46_im * x_46_re)) * x_46_im);
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$46$re), $MachinePrecision] - N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$im * x$46$re), $MachinePrecision]), $MachinePrecision] * x$46$im), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.im \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\\ \mathbf{if}\;x.re \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) - t_0 \leq \infty:\\ \;\;\;\;\left(x.re \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right) - t_0\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (let* ((t_0 (* x.im (+ (* x.re x.im) (* x.re x.im)))))
   (if (<= (- (* x.re (- (* x.re x.re) (* x.im x.im))) t_0) INFINITY)
     (- (* (* x.re (- x.re x.im)) (+ x.re x.im)) t_0)
     (- (* x.re (* (- x.re x.im) (+ x.re x.im))) (* x.im -3.0)))))

C

double code(double x_46_re, double x_46_im) {
	double t_0 = x_46_im * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	double tmp;
	if (((x_46_re * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) - t_0) <= ((double) INFINITY)) {
		tmp = ((x_46_re * (x_46_re - x_46_im)) * (x_46_re + x_46_im)) - t_0;
	} else {
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	}
	return tmp;
}

Java

public static double code(double x_46_re, double x_46_im) {
	double t_0 = x_46_im * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	double tmp;
	if (((x_46_re * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) - t_0) <= Double.POSITIVE_INFINITY) {
		tmp = ((x_46_re * (x_46_re - x_46_im)) * (x_46_re + x_46_im)) - t_0;
	} else {
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	t_0 = x_46_im * ((x_46_re * x_46_im) + (x_46_re * x_46_im))
	tmp = 0
	if ((x_46_re * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) - t_0) <= math.inf:
		tmp = ((x_46_re * (x_46_re - x_46_im)) * (x_46_re + x_46_im)) - t_0
	else:
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0)
	return tmp

Julia

function code(x_46_re, x_46_im)
	t_0 = Float64(x_46_im * Float64(Float64(x_46_re * x_46_im) + Float64(x_46_re * x_46_im)))
	tmp = 0.0
	if (Float64(Float64(x_46_re * Float64(Float64(x_46_re * x_46_re) - Float64(x_46_im * x_46_im))) - t_0) <= Inf)
		tmp = Float64(Float64(Float64(x_46_re * Float64(x_46_re - x_46_im)) * Float64(x_46_re + x_46_im)) - t_0);
	else
		tmp = Float64(Float64(x_46_re * Float64(Float64(x_46_re - x_46_im) * Float64(x_46_re + x_46_im))) - Float64(x_46_im * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	t_0 = x_46_im * ((x_46_re * x_46_im) + (x_46_re * x_46_im));
	tmp = 0.0;
	if (((x_46_re * ((x_46_re * x_46_re) - (x_46_im * x_46_im))) - t_0) <= Inf)
		tmp = ((x_46_re * (x_46_re - x_46_im)) * (x_46_re + x_46_im)) - t_0;
	else
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := Block[{t$95$0 = N[(x$46$im * N[(N[(x$46$re * x$46$im), $MachinePrecision] + N[(x$46$re * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[N[(N[(x$46$re * N[(N[(x$46$re * x$46$re), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], Infinity], N[(N[(N[(x$46$re * N[(x$46$re - x$46$im), $MachinePrecision]), $MachinePrecision] * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision] - t$95$0), $MachinePrecision], N[(N[(x$46$re * N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * -3.0), $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.re) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.im)) < +inf.0

   1. Initial program 91.4%

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

      1. difference-of-squares 91.4%

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

      2. *-commutative 91.4%

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

   3. Applied egg-rr 91.4%

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

      1. *-commutative 91.4%

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

      2. distribute-rgt-in 90.5%

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

      3. distribute-rgt-in 84.1%

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

   5. Applied egg-rr 84.1%

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

      1. *-commutative 84.1%

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

      2. associate-*l* 88.8%

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

      3. *-commutative 88.8%

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

      4. distribute-rgt-out 99.7%

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

   7. Applied egg-rr 99.7%

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

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

   1. Initial program 0.0%

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

      1. difference-of-squares 25.0%

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

      2. *-commutative 25.0%

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

   3. Applied egg-rr 25.0%

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

      1. *-commutative 25.0%

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

      2. flip-+ 0.0%

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

      3. +-inverses 0.0%

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

      4. metadata-eval 0.0%

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

      5. +-inverses 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

      8. distribute-neg-frac 0.0%

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

      9. *-commutative 0.0%

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

      10. +-inverses 0.0%

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

      11. +-inverses 0.0%

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

      12. *-commutative 0.0%

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

      13. flip-+ 75.0%

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

      14. *-commutative 75.0%

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

      15. neg-sub0 75.0%

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

      16. *-commutative 75.0%

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

      17. flip-+ 0.0%

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

      18. +-inverses 0.0%

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

      19. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) - x.im \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right) \leq \infty:\\ \;\;\;\;\left(x.re \cdot \left(x.re - x.im\right)\right) \cdot \left(x.re + x.im\right) - x.im \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \end{array} \]

Alternative 2: 93.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right)\\ \mathbf{if}\;x.re \leq -1 \cdot 10^{+119} \lor \neg \left(x.re \leq 10^{+82}\right):\\ \;\;\;\;t_0 - x.im \cdot -3\\ \mathbf{else}:\\ \;\;\;\;t_0 - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (let* ((t_0 (* x.re (* (- x.re x.im) (+ x.re x.im)))))
   (if (or (<= x.re -1e+119) (not (<= x.re 1e+82)))
     (- t_0 (* x.im -3.0))
     (- t_0 (* x.im (* (* x.re x.im) 2.0))))))

C

double code(double x_46_re, double x_46_im) {
	double t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im));
	double tmp;
	if ((x_46_re <= -1e+119) || !(x_46_re <= 1e+82)) {
		tmp = t_0 - (x_46_im * -3.0);
	} else {
		tmp = t_0 - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	}
	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) :: t_0
    real(8) :: tmp
    t_0 = x_46re * ((x_46re - x_46im) * (x_46re + x_46im))
    if ((x_46re <= (-1d+119)) .or. (.not. (x_46re <= 1d+82))) then
        tmp = t_0 - (x_46im * (-3.0d0))
    else
        tmp = t_0 - (x_46im * ((x_46re * x_46im) * 2.0d0))
    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_re - x_46_im) * (x_46_re + x_46_im));
	double tmp;
	if ((x_46_re <= -1e+119) || !(x_46_re <= 1e+82)) {
		tmp = t_0 - (x_46_im * -3.0);
	} else {
		tmp = t_0 - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))
	tmp = 0
	if (x_46_re <= -1e+119) or not (x_46_re <= 1e+82):
		tmp = t_0 - (x_46_im * -3.0)
	else:
		tmp = t_0 - (x_46_im * ((x_46_re * x_46_im) * 2.0))
	return tmp

Julia

function code(x_46_re, x_46_im)
	t_0 = Float64(x_46_re * Float64(Float64(x_46_re - x_46_im) * Float64(x_46_re + x_46_im)))
	tmp = 0.0
	if ((x_46_re <= -1e+119) || !(x_46_re <= 1e+82))
		tmp = Float64(t_0 - Float64(x_46_im * -3.0));
	else
		tmp = Float64(t_0 - Float64(x_46_im * Float64(Float64(x_46_re * x_46_im) * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im));
	tmp = 0.0;
	if ((x_46_re <= -1e+119) || ~((x_46_re <= 1e+82)))
		tmp = t_0 - (x_46_im * -3.0);
	else
		tmp = t_0 - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := Block[{t$95$0 = N[(x$46$re * N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x$46$re, -1e+119], N[Not[LessEqual[x$46$re, 1e+82]], $MachinePrecision]], N[(t$95$0 - N[(x$46$im * -3.0), $MachinePrecision]), $MachinePrecision], N[(t$95$0 - N[(x$46$im * N[(N[(x$46$re * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x.re < -9.99999999999999944e118 or 9.9999999999999996e81 < x.re

   1. Initial program 59.1%

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

      1. difference-of-squares 69.3%

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

      2. *-commutative 69.3%

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

   3. Applied egg-rr 69.3%

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

      1. *-commutative 69.3%

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

      2. flip-+ 0.0%

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

      3. +-inverses 0.0%

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

      4. metadata-eval 0.0%

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

      5. +-inverses 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

      8. distribute-neg-frac 0.0%

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

      9. *-commutative 0.0%

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

      10. +-inverses 0.0%

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

      11. +-inverses 0.0%

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

      12. *-commutative 0.0%

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

      13. flip-+ 82.9%

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

      14. *-commutative 82.9%

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

      15. neg-sub0 82.9%

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

      16. *-commutative 82.9%

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

      17. flip-+ 0.0%

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

      18. +-inverses 0.0%

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

      19. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 100.0%

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

   if -9.99999999999999944e118 < x.re < 9.9999999999999996e81

   1. Initial program 88.7%

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

      1. difference-of-squares 88.7%

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

      2. *-commutative 88.7%

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

   3. Applied egg-rr 88.7%

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

      1. *-commutative 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) \cdot x.im \]

      2. *-un-lft-identity 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{1 \cdot \left(x.im \cdot x.re\right)} + x.im \cdot x.re\right) \cdot x.im \]

      3. *-un-lft-identity 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(1 \cdot \left(x.im \cdot x.re\right) + \color{blue}{1 \cdot \left(x.im \cdot x.re\right)}\right) \cdot x.im \]

      4. distribute-rgt-out 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \color{blue}{\left(\left(x.im \cdot x.re\right) \cdot \left(1 + 1\right)\right)} \cdot x.im \]

      5. *-commutative 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{\left(x.re \cdot x.im\right)} \cdot \left(1 + 1\right)\right) \cdot x.im \]

      6. metadata-eval 33.4%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\left(x.re \cdot x.im\right) \cdot \color{blue}{2}\right) \cdot x.im \]

   5. Applied egg-rr 88.7%

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

4. Final simplification 92.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -1 \cdot 10^{+119} \lor \neg \left(x.re \leq 10^{+82}\right):\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \end{array} \]

Alternative 3: 72.7% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.re \leq -1.8 \cdot 10^{-96} \lor \neg \left(x.re \leq 5.2 \cdot 10^{-78}\right):\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27 - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (if (or (<= x.re -1.8e-96) (not (<= x.re 5.2e-78)))
   (- (* x.re (* (- x.re x.im) (+ x.re x.im))) (* x.im -3.0))
   (- (* (* x.re x.im) -27.0) (* x.im (* (* x.re x.im) 2.0)))))

C

double code(double x_46_re, double x_46_im) {
	double tmp;
	if ((x_46_re <= -1.8e-96) || !(x_46_re <= 5.2e-78)) {
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	} else {
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	}
	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_46re <= (-1.8d-96)) .or. (.not. (x_46re <= 5.2d-78))) then
        tmp = (x_46re * ((x_46re - x_46im) * (x_46re + x_46im))) - (x_46im * (-3.0d0))
    else
        tmp = ((x_46re * x_46im) * (-27.0d0)) - (x_46im * ((x_46re * x_46im) * 2.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im) {
	double tmp;
	if ((x_46_re <= -1.8e-96) || !(x_46_re <= 5.2e-78)) {
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	} else {
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	tmp = 0
	if (x_46_re <= -1.8e-96) or not (x_46_re <= 5.2e-78):
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0)
	else:
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0))
	return tmp

Julia

function code(x_46_re, x_46_im)
	tmp = 0.0
	if ((x_46_re <= -1.8e-96) || !(x_46_re <= 5.2e-78))
		tmp = Float64(Float64(x_46_re * Float64(Float64(x_46_re - x_46_im) * Float64(x_46_re + x_46_im))) - Float64(x_46_im * -3.0));
	else
		tmp = Float64(Float64(Float64(x_46_re * x_46_im) * -27.0) - Float64(x_46_im * Float64(Float64(x_46_re * x_46_im) * 2.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	tmp = 0.0;
	if ((x_46_re <= -1.8e-96) || ~((x_46_re <= 5.2e-78)))
		tmp = (x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))) - (x_46_im * -3.0);
	else
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := If[Or[LessEqual[x$46$re, -1.8e-96], N[Not[LessEqual[x$46$re, 5.2e-78]], $MachinePrecision]], N[(N[(x$46$re * N[(N[(x$46$re - x$46$im), $MachinePrecision] * N[(x$46$re + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] * -27.0), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x.re < -1.80000000000000004e-96 or 5.2000000000000002e-78 < x.re

   1. Initial program 77.1%

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

      1. difference-of-squares 82.6%

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

      2. *-commutative 82.6%

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

   3. Applied egg-rr 82.6%

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

      1. *-commutative 82.6%

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

      2. flip-+ 0.0%

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

      3. +-inverses 0.0%

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

      4. metadata-eval 0.0%

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

      5. +-inverses 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

      8. distribute-neg-frac 0.0%

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

      9. *-commutative 0.0%

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

      10. +-inverses 0.0%

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

      11. +-inverses 0.0%

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

      12. *-commutative 0.0%

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

      13. flip-+ 71.2%

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

      14. *-commutative 71.2%

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

      15. neg-sub0 71.2%

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

      16. *-commutative 71.2%

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

      17. flip-+ 0.0%

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

      18. +-inverses 0.0%

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

      19. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 85.6%

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

   if -1.80000000000000004e-96 < x.re < 5.2000000000000002e-78

   1. Initial program 81.1%

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

      1. difference-of-squares 81.1%

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

   3. Applied egg-rr 81.1%

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

   5. Simplified 38.0%

      \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   6. Taylor expanded in x.re around 0 43.1%

      \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]
   7. Step-by-step derivation

      1. *-commutative 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) \cdot x.im \]

      2. *-un-lft-identity 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{1 \cdot \left(x.im \cdot x.re\right)} + x.im \cdot x.re\right) \cdot x.im \]

      3. *-un-lft-identity 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(1 \cdot \left(x.im \cdot x.re\right) + \color{blue}{1 \cdot \left(x.im \cdot x.re\right)}\right) \cdot x.im \]

      4. distribute-rgt-out 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \color{blue}{\left(\left(x.im \cdot x.re\right) \cdot \left(1 + 1\right)\right)} \cdot x.im \]

      5. *-commutative 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{\left(x.re \cdot x.im\right)} \cdot \left(1 + 1\right)\right) \cdot x.im \]

      6. metadata-eval 43.1%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\left(x.re \cdot x.im\right) \cdot \color{blue}{2}\right) \cdot x.im \]

   8. Applied egg-rr 43.1%

      \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \color{blue}{\left(\left(x.re \cdot x.im\right) \cdot 2\right)} \cdot x.im \]
3. Recombined 2 regimes into one program.

4. Final simplification 70.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq -1.8 \cdot 10^{-96} \lor \neg \left(x.re \leq 5.2 \cdot 10^{-78}\right):\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27 - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \end{array} \]

Alternative 4: 67.4% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right)\\ \mathbf{if}\;x.im \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;t_0 + x.im \cdot \left(x.re \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 - x.im \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (let* ((t_0 (* x.re (* (- x.re x.im) (+ x.re x.im)))))
   (if (<= x.im 6.4e+30)
     (+ t_0 (* x.im (* x.re x.im)))
     (- t_0 (* x.im -3.0)))))

C

double code(double x_46_re, double x_46_im) {
	double t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im));
	double tmp;
	if (x_46_im <= 6.4e+30) {
		tmp = t_0 + (x_46_im * (x_46_re * x_46_im));
	} else {
		tmp = t_0 - (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) :: t_0
    real(8) :: tmp
    t_0 = x_46re * ((x_46re - x_46im) * (x_46re + x_46im))
    if (x_46im <= 6.4d+30) then
        tmp = t_0 + (x_46im * (x_46re * x_46im))
    else
        tmp = t_0 - (x_46im * (-3.0d0))
    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_re - x_46_im) * (x_46_re + x_46_im));
	double tmp;
	if (x_46_im <= 6.4e+30) {
		tmp = t_0 + (x_46_im * (x_46_re * x_46_im));
	} else {
		tmp = t_0 - (x_46_im * -3.0);
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im))
	tmp = 0
	if x_46_im <= 6.4e+30:
		tmp = t_0 + (x_46_im * (x_46_re * x_46_im))
	else:
		tmp = t_0 - (x_46_im * -3.0)
	return tmp

Julia

function code(x_46_re, x_46_im)
	t_0 = Float64(x_46_re * Float64(Float64(x_46_re - x_46_im) * Float64(x_46_re + x_46_im)))
	tmp = 0.0
	if (x_46_im <= 6.4e+30)
		tmp = Float64(t_0 + Float64(x_46_im * Float64(x_46_re * x_46_im)));
	else
		tmp = Float64(t_0 - Float64(x_46_im * -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	t_0 = x_46_re * ((x_46_re - x_46_im) * (x_46_re + x_46_im));
	tmp = 0.0;
	if (x_46_im <= 6.4e+30)
		tmp = t_0 + (x_46_im * (x_46_re * x_46_im));
	else
		tmp = t_0 - (x_46_im * -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := Block[{t$95$0 = 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[x$46$im, 6.4e+30], N[(t$95$0 + N[(x$46$im * N[(x$46$re * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 - N[(x$46$im * -3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x.im < 6.39999999999999945e30

   1. Initial program 88.4%

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

      1. difference-of-squares 89.9%

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

      2. *-commutative 89.9%

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

   3. Applied egg-rr 89.9%

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

   4. Taylor expanded in x.re around 0 89.9%

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

   6. Simplified 71.2%

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

   if 6.39999999999999945e30 < x.im

   1. Initial program 45.0%

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

      1. difference-of-squares 55.3%

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

      2. *-commutative 55.3%

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

   3. Applied egg-rr 55.3%

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

      1. *-commutative 55.3%

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

      2. flip-+ 0.0%

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

      3. +-inverses 0.0%

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

      4. metadata-eval 0.0%

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

      5. +-inverses 0.0%

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

      6. *-commutative 0.0%

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

      7. *-commutative 0.0%

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

      8. distribute-neg-frac 0.0%

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

      9. *-commutative 0.0%

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

      10. +-inverses 0.0%

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

      11. +-inverses 0.0%

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

      12. *-commutative 0.0%

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

      13. flip-+ 24.7%

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

      14. *-commutative 24.7%

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

      15. neg-sub0 24.7%

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

      16. *-commutative 24.7%

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

      17. flip-+ 0.0%

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

      18. +-inverses 0.0%

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

      19. +-inverses 0.0%

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

   5. Applied egg-rr 0.0%

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

   7. Simplified 53.9%

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

4. Final simplification 67.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 6.4 \cdot 10^{+30}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) + x.im \cdot \left(x.re \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot -3\\ \end{array} \]

Alternative 5: 33.8% accurate, 1.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.re \leq 4.1 \cdot 10^{+186}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27 - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (if (<= x.re 4.1e+186)
   (- (* (* x.re x.im) -27.0) (* x.im (* (* x.re x.im) 2.0)))
   (* x.im (* x.re (- x.re 27.0)))))

C

double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= 4.1e+186) {
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	} else {
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	}
	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_46re <= 4.1d+186) then
        tmp = ((x_46re * x_46im) * (-27.0d0)) - (x_46im * ((x_46re * x_46im) * 2.0d0))
    else
        tmp = x_46im * (x_46re * (x_46re - 27.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= 4.1e+186) {
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	} else {
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	tmp = 0
	if x_46_re <= 4.1e+186:
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0))
	else:
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0))
	return tmp

Julia

function code(x_46_re, x_46_im)
	tmp = 0.0
	if (x_46_re <= 4.1e+186)
		tmp = Float64(Float64(Float64(x_46_re * x_46_im) * -27.0) - Float64(x_46_im * Float64(Float64(x_46_re * x_46_im) * 2.0)));
	else
		tmp = Float64(x_46_im * Float64(x_46_re * Float64(x_46_re - 27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	tmp = 0.0;
	if (x_46_re <= 4.1e+186)
		tmp = ((x_46_re * x_46_im) * -27.0) - (x_46_im * ((x_46_re * x_46_im) * 2.0));
	else
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := If[LessEqual[x$46$re, 4.1e+186], N[(N[(N[(x$46$re * x$46$im), $MachinePrecision] * -27.0), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$46$im * N[(x$46$re * N[(x$46$re - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x.re < 4.1e186

   1. Initial program 81.1%

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

      1. difference-of-squares 84.9%

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

   3. Applied egg-rr 84.9%

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

   5. Simplified 48.4%

      \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   6. Taylor expanded in x.re around 0 28.7%

      \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]
   7. Step-by-step derivation

      1. *-commutative 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{x.im \cdot x.re} + x.im \cdot x.re\right) \cdot x.im \]

      2. *-un-lft-identity 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{1 \cdot \left(x.im \cdot x.re\right)} + x.im \cdot x.re\right) \cdot x.im \]

      3. *-un-lft-identity 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(1 \cdot \left(x.im \cdot x.re\right) + \color{blue}{1 \cdot \left(x.im \cdot x.re\right)}\right) \cdot x.im \]

      4. distribute-rgt-out 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \color{blue}{\left(\left(x.im \cdot x.re\right) \cdot \left(1 + 1\right)\right)} \cdot x.im \]

      5. *-commutative 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\color{blue}{\left(x.re \cdot x.im\right)} \cdot \left(1 + 1\right)\right) \cdot x.im \]

      6. metadata-eval 28.7%

         \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \left(\left(x.re \cdot x.im\right) \cdot \color{blue}{2}\right) \cdot x.im \]

   8. Applied egg-rr 28.7%

      \[\leadsto -27 \cdot \left(x.im \cdot x.re\right) - \color{blue}{\left(\left(x.re \cdot x.im\right) \cdot 2\right)} \cdot x.im \]

   if 4.1e186 < x.re

   1. Initial program 54.2%

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

      1. difference-of-squares 54.2%

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

   3. Applied egg-rr 54.2%

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

   5. Simplified 54.2%

      \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   6. Taylor expanded in x.im around inf 20.8%

      \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   7. Taylor expanded in x.im around 0 45.8%

      \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 30.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 4.1 \cdot 10^{+186}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27 - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)\\ \end{array} \]

Alternative 6: 22.3% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x.re \leq 4.8 \cdot 10^{+189}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x.re x.im)
 :precision binary64
 (if (<= x.re 4.8e+189)
   (* (* x.re x.im) -27.0)
   (* x.im (* x.re (- x.re 27.0)))))

C

double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= 4.8e+189) {
		tmp = (x_46_re * x_46_im) * -27.0;
	} else {
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	}
	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_46re <= 4.8d+189) then
        tmp = (x_46re * x_46im) * (-27.0d0)
    else
        tmp = x_46im * (x_46re * (x_46re - 27.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x_46_re, double x_46_im) {
	double tmp;
	if (x_46_re <= 4.8e+189) {
		tmp = (x_46_re * x_46_im) * -27.0;
	} else {
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	}
	return tmp;
}

Python

def code(x_46_re, x_46_im):
	tmp = 0
	if x_46_re <= 4.8e+189:
		tmp = (x_46_re * x_46_im) * -27.0
	else:
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0))
	return tmp

Julia

function code(x_46_re, x_46_im)
	tmp = 0.0
	if (x_46_re <= 4.8e+189)
		tmp = Float64(Float64(x_46_re * x_46_im) * -27.0);
	else
		tmp = Float64(x_46_im * Float64(x_46_re * Float64(x_46_re - 27.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x_46_re, x_46_im)
	tmp = 0.0;
	if (x_46_re <= 4.8e+189)
		tmp = (x_46_re * x_46_im) * -27.0;
	else
		tmp = x_46_im * (x_46_re * (x_46_re - 27.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x$46$re_, x$46$im_] := If[LessEqual[x$46$re, 4.8e+189], N[(N[(x$46$re * x$46$im), $MachinePrecision] * -27.0), $MachinePrecision], N[(x$46$im * N[(x$46$re * N[(x$46$re - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x.re < 4.8000000000000001e189

   1. Initial program 81.1%

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

      1. difference-of-squares 84.9%

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

   3. Applied egg-rr 84.9%

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

   5. Simplified 48.4%

      \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   6. Taylor expanded in x.re around 0 28.7%

      \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   7. Taylor expanded in x.im around 0 21.1%

      \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} \]

   if 4.8000000000000001e189 < x.re

   1. Initial program 54.2%

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

      1. difference-of-squares 54.2%

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

   3. Applied egg-rr 54.2%

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

   5. Simplified 54.2%

      \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   6. Taylor expanded in x.im around inf 20.8%

      \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

   7. Taylor expanded in x.im around 0 45.8%

      \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 23.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 4.8 \cdot 10^{+189}:\\ \;\;\;\;\left(x.re \cdot x.im\right) \cdot -27\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)\\ \end{array} \]

Alternative 7: 19.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} \\ \left(x.re \cdot x.im\right) \cdot -27 \end{array} \]

FPCore

(FPCore (x.re x.im) :precision binary64 (* (* x.re x.im) -27.0))

C

double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_im) * -27.0;
}

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_46im) * (-27.0d0)
end function

Java

public static double code(double x_46_re, double x_46_im) {
	return (x_46_re * x_46_im) * -27.0;
}

Python

def code(x_46_re, x_46_im):
	return (x_46_re * x_46_im) * -27.0

Julia

function code(x_46_re, x_46_im)
	return Float64(Float64(x_46_re * x_46_im) * -27.0)
end

MATLAB

function tmp = code(x_46_re, x_46_im)
	tmp = (x_46_re * x_46_im) * -27.0;
end

Wolfram

code[x$46$re_, x$46$im_] := N[(N[(x$46$re * x$46$im), $MachinePrecision] * -27.0), $MachinePrecision]

Derivation

1. Initial program 78.5%

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

   1. difference-of-squares 82.1%

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

3. Applied egg-rr 82.1%

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

5. Simplified 49.0%

   \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

6. Taylor expanded in x.re around 0 26.1%

   \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

7. Taylor expanded in x.im around 0 20.8%

   \[\leadsto \color{blue}{-27 \cdot \left(x.im \cdot x.re\right)} \]

8. Final simplification 20.8%

   \[\leadsto \left(x.re \cdot x.im\right) \cdot -27 \]

Alternative 8: 3.6% accurate, 6.3× speedup

Math

\[\begin{array}{l} \\ x.im \cdot 3 \end{array} \]

FPCore

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

C

double code(double x_46_re, double x_46_im) {
	return 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_46im * 3.0d0
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 78.5%

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

   1. difference-of-squares 82.1%

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

3. Applied egg-rr 82.1%

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

5. Simplified 49.0%

   \[\leadsto \color{blue}{\left(\left(x.im + x.re\right) \cdot \left(x.re + -27\right)\right)} \cdot x.re - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]

6. Taylor expanded in x.im around inf 29.1%

   \[\leadsto \color{blue}{x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right)} - \left(x.re \cdot x.im + x.im \cdot x.re\right) \cdot x.im \]
7. Step-by-step derivation

   1. *-commutative 82.1%

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

   2. flip-+ 0.0%

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

   3. +-inverses 0.0%

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

   4. metadata-eval 0.0%

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

   5. +-inverses 0.0%

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

   6. *-commutative 0.0%

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

   7. *-commutative 0.0%

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

   8. distribute-neg-frac 0.0%

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

   9. *-commutative 0.0%

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

   10. +-inverses 0.0%

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

   11. +-inverses 0.0%

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

   12. *-commutative 0.0%

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

   13. flip-+ 60.4%

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

   14. *-commutative 60.4%

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

   15. neg-sub0 60.4%

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

   16. *-commutative 60.4%

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

   17. flip-+ 0.0%

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

   18. +-inverses 0.0%

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

   19. +-inverses 0.0%

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

8. Applied egg-rr 0.0%

   \[\leadsto x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right) - \color{blue}{\left(0 - \frac{0}{0}\right)} \cdot x.im \]

10. Simplified 16.7%

    \[\leadsto x.im \cdot \left(x.re \cdot \left(x.re - 27\right)\right) - \color{blue}{-3} \cdot x.im \]

11. Taylor expanded in x.re around 0 3.6%

    \[\leadsto \color{blue}{3 \cdot x.im} \]

13. Simplified 3.6%

    \[\leadsto \color{blue}{x.im \cdot 3} \]

14. Final simplification 3.6%

    \[\leadsto x.im \cdot 3 \]

Alternative 9: 3.0% accurate, 9.5× speedup

Math

\[\begin{array}{l} \\ -x.re \end{array} \]

FPCore

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

C

double code(double x_46_re, double x_46_im) {
	return -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
end function

Java

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

Python

def code(x_46_re, x_46_im):
	return -x_46_re

Julia

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

MATLAB

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

Wolfram

code[x$46$re_, x$46$im_] := (-x$46$re)

Derivation

1. Initial program 78.5%

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

3. Simplified 76.2%

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

4. Taylor expanded in x.re around 0 46.9%

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

6. Simplified 3.1%

   \[\leadsto \color{blue}{-x.re} \]

7. Final simplification 3.1%

   \[\leadsto -x.re \]

Developer target: 86.8% accurate, 1.1× speedup

Math

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

FPCore

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

C

double code(double x_46_re, double x_46_im) {
	return ((x_46_re * x_46_re) * (x_46_re - x_46_im)) + ((x_46_re * x_46_im) * (x_46_re - (3.0 * 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_46re - x_46im)) + ((x_46re * x_46im) * (x_46re - (3.0d0 * 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_re - x_46_im)) + ((x_46_re * x_46_im) * (x_46_re - (3.0 * x_46_im)));
}

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023320 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :herbie-target
  (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3.0 x.im))))

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