math.cube on complex, real part

Percentage Accurate: 82.6% → 97.7%

Time: 9.0s

Alternatives: 10

Speedup: 0.9×

• 43.8% 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: 82.6% 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: 97.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \begin{array}{l} \mathbf{if}\;x.re\_m \leq 2 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(x.re\_m \cdot x.im, x.im \cdot -3, {x.re\_m}^{3}\right)\\ \mathbf{elif}\;x.re\_m \leq 6 \cdot 10^{+171}:\\ \;\;\;\;x.re\_m \cdot \left(\left(x.re\_m - x.im\right) \cdot \left(x.re\_m + x.im\right)\right) - x.im \cdot \left(x.re\_m \cdot x.im + x.re\_m \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re\_m \cdot \left(x.im \cdot \left(x.re\_m + \left(x.re\_m \cdot \frac{x.re\_m + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (*
  x.re_s
  (if (<= x.re_m 2e+96)
    (fma (* x.re_m x.im) (* x.im -3.0) (pow x.re_m 3.0))
    (if (<= x.re_m 6e+171)
      (-
       (* x.re_m (* (- x.re_m x.im) (+ x.re_m x.im)))
       (* x.im (+ (* x.re_m x.im) (* x.re_m x.im))))
      (-
       (*
        x.re_m
        (* x.im (+ x.re_m (- (* x.re_m (/ (+ x.re_m -27.0) x.im)) 27.0))))
       (* x.im -27.0))))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 2e+96) {
		tmp = fma((x_46_re_m * x_46_im), (x_46_im * -3.0), pow(x_46_re_m, 3.0));
	} else if (x_46_re_m <= 6e+171) {
		tmp = (x_46_re_m * ((x_46_re_m - x_46_im) * (x_46_re_m + x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) + (x_46_re_m * x_46_im)));
	} else {
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	}
	return x_46_re_s * tmp;
}

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0
	if (x_46_re_m <= 2e+96)
		tmp = fma(Float64(x_46_re_m * x_46_im), Float64(x_46_im * -3.0), (x_46_re_m ^ 3.0));
	elseif (x_46_re_m <= 6e+171)
		tmp = Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m - x_46_im) * Float64(x_46_re_m + x_46_im))) - Float64(x_46_im * Float64(Float64(x_46_re_m * x_46_im) + Float64(x_46_re_m * x_46_im))));
	else
		tmp = Float64(Float64(x_46_re_m * Float64(x_46_im * Float64(x_46_re_m + Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - Float64(x_46_im * -27.0));
	end
	return Float64(x_46_re_s * tmp)
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * If[LessEqual[x$46$re$95$m, 2e+96], N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] * N[(x$46$im * -3.0), $MachinePrecision] + N[Power[x$46$re$95$m, 3.0], $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$re$95$m, 6e+171], N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m - x$46$im), $MachinePrecision] * N[(x$46$re$95$m + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] + N[(x$46$re$95$m * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re$95$m * N[(x$46$im * N[(x$46$re$95$m + N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m + -27.0), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision] - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * -27.0), $MachinePrecision]), $MachinePrecision]]]), $MachinePrecision]

Derivation

1. Split input into 3 regimes

2. if x.re < 2.0000000000000001e96

   1. Initial program 89.3%

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

   3. Simplified 87.5%

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

      1. +-commutative 87.5%

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

      2. associate-*r* 93.1%

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

      3. fma-define 93.6%

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

   6. Applied egg-rr 93.6%

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

   if 2.0000000000000001e96 < x.re < 6.0000000000000002e171

   1. Initial program 93.3%

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

      1. difference-of-squares 100.0%

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

      2. *-commutative 100.0%

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

   4. Applied egg-rr 100.0%

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

   if 6.0000000000000002e171 < x.re

   1. Initial program 61.3%

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

      1. difference-of-squares 64.5%

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

   4. Applied egg-rr 64.5%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in x.im around inf 61.3%

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

   9. Simplified 61.3%

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

       1. *-un-lft-identity 61.3%

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

       2. *-commutative 61.3%

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

       3. fma-define 61.3%

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

   11. Applied egg-rr 61.3%

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

   13. Simplified 61.3%

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

   14. Taylor expanded in x.im around 0 96.8%

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

       1. *-commutative 96.8%

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

   16. Simplified 96.8%

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

4. Final simplification 94.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 2 \cdot 10^{+96}:\\ \;\;\;\;\mathsf{fma}\left(x.re \cdot x.im, x.im \cdot -3, {x.re}^{3}\right)\\ \mathbf{elif}\;x.re \leq 6 \cdot 10^{+171}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(x.im \cdot \left(x.re + \left(x.re \cdot \frac{x.re + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 91.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \begin{array}{l} \mathbf{if}\;x.re\_m \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x.re\_m \cdot \left(\left(x.re\_m - x.im\right) \cdot \left(x.re\_m + x.im\right)\right) - x.im \cdot \left(x.re\_m \cdot x.im + x.re\_m \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re\_m \cdot \left(x.im \cdot \left(x.re\_m + \left(x.re\_m \cdot \frac{x.re\_m + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (*
  x.re_s
  (if (<= x.re_m 3.3e+170)
    (-
     (* x.re_m (* (- x.re_m x.im) (+ x.re_m x.im)))
     (* x.im (+ (* x.re_m x.im) (* x.re_m x.im))))
    (-
     (*
      x.re_m
      (* x.im (+ x.re_m (- (* x.re_m (/ (+ x.re_m -27.0) x.im)) 27.0))))
     (* x.im -27.0)))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 3.3e+170) {
		tmp = (x_46_re_m * ((x_46_re_m - x_46_im) * (x_46_re_m + x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) + (x_46_re_m * x_46_im)));
	} else {
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	}
	return x_46_re_s * tmp;
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    real(8) :: tmp
    if (x_46re_m <= 3.3d+170) then
        tmp = (x_46re_m * ((x_46re_m - x_46im) * (x_46re_m + x_46im))) - (x_46im * ((x_46re_m * x_46im) + (x_46re_m * x_46im)))
    else
        tmp = (x_46re_m * (x_46im * (x_46re_m + ((x_46re_m * ((x_46re_m + (-27.0d0)) / x_46im)) - 27.0d0)))) - (x_46im * (-27.0d0))
    end if
    code = x_46re_s * tmp
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 3.3e+170) {
		tmp = (x_46_re_m * ((x_46_re_m - x_46_im) * (x_46_re_m + x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) + (x_46_re_m * x_46_im)));
	} else {
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	}
	return x_46_re_s * tmp;
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	tmp = 0
	if x_46_re_m <= 3.3e+170:
		tmp = (x_46_re_m * ((x_46_re_m - x_46_im) * (x_46_re_m + x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) + (x_46_re_m * x_46_im)))
	else:
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0)
	return x_46_re_s * tmp

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0
	if (x_46_re_m <= 3.3e+170)
		tmp = Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m - x_46_im) * Float64(x_46_re_m + x_46_im))) - Float64(x_46_im * Float64(Float64(x_46_re_m * x_46_im) + Float64(x_46_re_m * x_46_im))));
	else
		tmp = Float64(Float64(x_46_re_m * Float64(x_46_im * Float64(x_46_re_m + Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - Float64(x_46_im * -27.0));
	end
	return Float64(x_46_re_s * tmp)
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp_2 = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0;
	if (x_46_re_m <= 3.3e+170)
		tmp = (x_46_re_m * ((x_46_re_m - x_46_im) * (x_46_re_m + x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) + (x_46_re_m * x_46_im)));
	else
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	end
	tmp_2 = x_46_re_s * tmp;
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * If[LessEqual[x$46$re$95$m, 3.3e+170], N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m - x$46$im), $MachinePrecision] * N[(x$46$re$95$m + x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] + N[(x$46$re$95$m * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re$95$m * N[(x$46$im * N[(x$46$re$95$m + N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m + -27.0), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision] - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * -27.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.re < 3.30000000000000023e170

   1. Initial program 89.6%

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

      1. difference-of-squares 91.3%

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

      2. *-commutative 91.3%

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

   4. Applied egg-rr 91.3%

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

   if 3.30000000000000023e170 < x.re

   1. Initial program 61.3%

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

      1. difference-of-squares 64.5%

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

   4. Applied egg-rr 64.5%

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

   6. Simplified 61.3%

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

   7. Taylor expanded in x.im around inf 61.3%

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

   9. Simplified 61.3%

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

       1. *-un-lft-identity 61.3%

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

       2. *-commutative 61.3%

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

       3. fma-define 61.3%

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

   11. Applied egg-rr 61.3%

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

   13. Simplified 61.3%

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

   14. Taylor expanded in x.im around 0 96.8%

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

       1. *-commutative 96.8%

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

   16. Simplified 96.8%

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

4. Final simplification 92.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 3.3 \cdot 10^{+170}:\\ \;\;\;\;x.re \cdot \left(\left(x.re - x.im\right) \cdot \left(x.re + x.im\right)\right) - x.im \cdot \left(x.re \cdot x.im + x.re \cdot x.im\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(x.im \cdot \left(x.re + \left(x.re \cdot \frac{x.re + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 91.8% accurate, 0.8× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \begin{array}{l} \mathbf{if}\;x.re\_m \leq 2.7 \cdot 10^{+153}:\\ \;\;\;\;x.re\_m \cdot \left(x.re\_m \cdot x.re\_m - x.im \cdot x.im\right) - x.im \cdot \left(\left(x.re\_m \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.re\_m \cdot \left(x.im \cdot \left(x.re\_m + \left(x.re\_m \cdot \frac{x.re\_m + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (*
  x.re_s
  (if (<= x.re_m 2.7e+153)
    (-
     (* x.re_m (- (* x.re_m x.re_m) (* x.im x.im)))
     (* x.im (* (* x.re_m x.im) 2.0)))
    (-
     (*
      x.re_m
      (* x.im (+ x.re_m (- (* x.re_m (/ (+ x.re_m -27.0) x.im)) 27.0))))
     (* x.im -27.0)))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 2.7e+153) {
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	} else {
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	}
	return x_46_re_s * tmp;
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    real(8) :: tmp
    if (x_46re_m <= 2.7d+153) then
        tmp = (x_46re_m * ((x_46re_m * x_46re_m) - (x_46im * x_46im))) - (x_46im * ((x_46re_m * x_46im) * 2.0d0))
    else
        tmp = (x_46re_m * (x_46im * (x_46re_m + ((x_46re_m * ((x_46re_m + (-27.0d0)) / x_46im)) - 27.0d0)))) - (x_46im * (-27.0d0))
    end if
    code = x_46re_s * tmp
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 2.7e+153) {
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	} else {
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	}
	return x_46_re_s * tmp;
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	tmp = 0
	if x_46_re_m <= 2.7e+153:
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0))
	else:
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0)
	return x_46_re_s * tmp

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0
	if (x_46_re_m <= 2.7e+153)
		tmp = Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m * x_46_re_m) - Float64(x_46_im * x_46_im))) - Float64(x_46_im * Float64(Float64(x_46_re_m * x_46_im) * 2.0)));
	else
		tmp = Float64(Float64(x_46_re_m * Float64(x_46_im * Float64(x_46_re_m + Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - Float64(x_46_im * -27.0));
	end
	return Float64(x_46_re_s * tmp)
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp_2 = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0;
	if (x_46_re_m <= 2.7e+153)
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	else
		tmp = (x_46_re_m * (x_46_im * (x_46_re_m + ((x_46_re_m * ((x_46_re_m + -27.0) / x_46_im)) - 27.0)))) - (x_46_im * -27.0);
	end
	tmp_2 = x_46_re_s * tmp;
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * If[LessEqual[x$46$re$95$m, 2.7e+153], N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re$95$m * N[(x$46$im * N[(x$46$re$95$m + N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m + -27.0), $MachinePrecision] / x$46$im), $MachinePrecision]), $MachinePrecision] - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * -27.0), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.re < 2.7000000000000001e153

   1. Initial program 90.0%

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

      1. *-commutative 90.0%

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

      2. *-un-lft-identity 90.0%

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

      3. distribute-lft-in 90.0%

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

      4. distribute-rgt-out 90.0%

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

      5. metadata-eval 90.0%

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

   4. Applied egg-rr 90.0%

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

   if 2.7000000000000001e153 < x.re

   1. Initial program 59.4%

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

      1. difference-of-squares 65.6%

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

   4. Applied egg-rr 65.6%

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

   6. Simplified 62.5%

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

   7. Taylor expanded in x.im around inf 59.4%

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

   9. Simplified 62.5%

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

       1. *-un-lft-identity 62.5%

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

       2. *-commutative 62.5%

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

       3. fma-define 62.5%

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

   11. Applied egg-rr 62.5%

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

   13. Simplified 62.5%

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

   14. Taylor expanded in x.im around 0 96.9%

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

       1. *-commutative 96.9%

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

   16. Simplified 96.9%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 2.7 \cdot 10^{+153}:\\ \;\;\;\;x.re \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(x.im \cdot \left(x.re + \left(x.re \cdot \frac{x.re + -27}{x.im} - 27\right)\right)\right) - x.im \cdot -27\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 84.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \begin{array}{l} \mathbf{if}\;x.im \leq 6.6 \cdot 10^{+150}:\\ \;\;\;\;x.re\_m \cdot \left(x.re\_m \cdot x.re\_m - x.im \cdot x.im\right) - x.im \cdot \left(\left(x.re\_m \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re\_m \cdot -27 + \left(x.re\_m \cdot x.im\right) \cdot -2\right)\\ \end{array} \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (*
  x.re_s
  (if (<= x.im 6.6e+150)
    (-
     (* x.re_m (- (* x.re_m x.re_m) (* x.im x.im)))
     (* x.im (* (* x.re_m x.im) 2.0)))
    (* x.im (+ (* x.re_m -27.0) (* (* x.re_m x.im) -2.0))))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_im <= 6.6e+150) {
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	} else {
		tmp = x_46_im * ((x_46_re_m * -27.0) + ((x_46_re_m * x_46_im) * -2.0));
	}
	return x_46_re_s * tmp;
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    real(8) :: tmp
    if (x_46im <= 6.6d+150) then
        tmp = (x_46re_m * ((x_46re_m * x_46re_m) - (x_46im * x_46im))) - (x_46im * ((x_46re_m * x_46im) * 2.0d0))
    else
        tmp = x_46im * ((x_46re_m * (-27.0d0)) + ((x_46re_m * x_46im) * (-2.0d0)))
    end if
    code = x_46re_s * tmp
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_im <= 6.6e+150) {
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	} else {
		tmp = x_46_im * ((x_46_re_m * -27.0) + ((x_46_re_m * x_46_im) * -2.0));
	}
	return x_46_re_s * tmp;
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	tmp = 0
	if x_46_im <= 6.6e+150:
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0))
	else:
		tmp = x_46_im * ((x_46_re_m * -27.0) + ((x_46_re_m * x_46_im) * -2.0))
	return x_46_re_s * tmp

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0
	if (x_46_im <= 6.6e+150)
		tmp = Float64(Float64(x_46_re_m * Float64(Float64(x_46_re_m * x_46_re_m) - Float64(x_46_im * x_46_im))) - Float64(x_46_im * Float64(Float64(x_46_re_m * x_46_im) * 2.0)));
	else
		tmp = Float64(x_46_im * Float64(Float64(x_46_re_m * -27.0) + Float64(Float64(x_46_re_m * x_46_im) * -2.0)));
	end
	return Float64(x_46_re_s * tmp)
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp_2 = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0;
	if (x_46_im <= 6.6e+150)
		tmp = (x_46_re_m * ((x_46_re_m * x_46_re_m) - (x_46_im * x_46_im))) - (x_46_im * ((x_46_re_m * x_46_im) * 2.0));
	else
		tmp = x_46_im * ((x_46_re_m * -27.0) + ((x_46_re_m * x_46_im) * -2.0));
	end
	tmp_2 = x_46_re_s * tmp;
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * If[LessEqual[x$46$im, 6.6e+150], N[(N[(x$46$re$95$m * N[(N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision] - N[(x$46$im * x$46$im), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x$46$im * N[(N[(x$46$re$95$m * -27.0), $MachinePrecision] + N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.im < 6.59999999999999962e150

   1. Initial program 89.3%

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

      1. *-commutative 89.3%

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

      2. *-un-lft-identity 89.3%

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

      3. distribute-lft-in 89.3%

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

      4. distribute-rgt-out 89.3%

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

      5. metadata-eval 89.3%

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

   4. Applied egg-rr 89.3%

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

   if 6.59999999999999962e150 < x.im

   1. Initial program 64.3%

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

      1. difference-of-squares 67.4%

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

   4. Applied egg-rr 67.4%

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

   6. Simplified 55.0%

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

   7. Taylor expanded in x.re around 0 70.6%

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

   8. Taylor expanded in x.im around 0 70.6%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 6.6 \cdot 10^{+150}:\\ \;\;\;\;x.re \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) - x.im \cdot \left(\left(x.re \cdot x.im\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot -27 + \left(x.re \cdot x.im\right) \cdot -2\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 70.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \begin{array}{l} \mathbf{if}\;x.re\_m \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;\left(x.im \cdot x.im\right) \cdot \left(x.re\_m \cdot -3\right)\\ \mathbf{else}:\\ \;\;\;\;x.re\_m \cdot \left(x.re\_m \cdot \left(x.re\_m - 27\right)\right) - x.im \cdot \left(x.re\_m \cdot x.im + -27\right)\\ \end{array} \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (*
  x.re_s
  (if (<= x.re_m 1.76e+19)
    (* (* x.im x.im) (* x.re_m -3.0))
    (-
     (* x.re_m (* x.re_m (- x.re_m 27.0)))
     (* x.im (+ (* x.re_m x.im) -27.0))))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 1.76e+19) {
		tmp = (x_46_im * x_46_im) * (x_46_re_m * -3.0);
	} else {
		tmp = (x_46_re_m * (x_46_re_m * (x_46_re_m - 27.0))) - (x_46_im * ((x_46_re_m * x_46_im) + -27.0));
	}
	return x_46_re_s * tmp;
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    real(8) :: tmp
    if (x_46re_m <= 1.76d+19) then
        tmp = (x_46im * x_46im) * (x_46re_m * (-3.0d0))
    else
        tmp = (x_46re_m * (x_46re_m * (x_46re_m - 27.0d0))) - (x_46im * ((x_46re_m * x_46im) + (-27.0d0)))
    end if
    code = x_46re_s * tmp
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	double tmp;
	if (x_46_re_m <= 1.76e+19) {
		tmp = (x_46_im * x_46_im) * (x_46_re_m * -3.0);
	} else {
		tmp = (x_46_re_m * (x_46_re_m * (x_46_re_m - 27.0))) - (x_46_im * ((x_46_re_m * x_46_im) + -27.0));
	}
	return x_46_re_s * tmp;
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	tmp = 0
	if x_46_re_m <= 1.76e+19:
		tmp = (x_46_im * x_46_im) * (x_46_re_m * -3.0)
	else:
		tmp = (x_46_re_m * (x_46_re_m * (x_46_re_m - 27.0))) - (x_46_im * ((x_46_re_m * x_46_im) + -27.0))
	return x_46_re_s * tmp

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0
	if (x_46_re_m <= 1.76e+19)
		tmp = Float64(Float64(x_46_im * x_46_im) * Float64(x_46_re_m * -3.0));
	else
		tmp = Float64(Float64(x_46_re_m * Float64(x_46_re_m * Float64(x_46_re_m - 27.0))) - Float64(x_46_im * Float64(Float64(x_46_re_m * x_46_im) + -27.0)));
	end
	return Float64(x_46_re_s * tmp)
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp_2 = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = 0.0;
	if (x_46_re_m <= 1.76e+19)
		tmp = (x_46_im * x_46_im) * (x_46_re_m * -3.0);
	else
		tmp = (x_46_re_m * (x_46_re_m * (x_46_re_m - 27.0))) - (x_46_im * ((x_46_re_m * x_46_im) + -27.0));
	end
	tmp_2 = x_46_re_s * tmp;
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * If[LessEqual[x$46$re$95$m, 1.76e+19], N[(N[(x$46$im * x$46$im), $MachinePrecision] * N[(x$46$re$95$m * -3.0), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$re$95$m * N[(x$46$re$95$m * N[(x$46$re$95$m - 27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(x$46$im * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] + -27.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.re < 1.76e19

   1. Initial program 88.5%

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

   3. Taylor expanded in x.im around inf 63.5%

      \[\leadsto \color{blue}{{x.im}^{2} \cdot \left(-1 \cdot x.re - 2 \cdot x.re\right)} \]
   4. Step-by-step derivation

      1. unpow2 63.5%

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

   5. Applied egg-rr 63.5%

      \[\leadsto \color{blue}{\left(x.im \cdot x.im\right)} \cdot \left(-1 \cdot x.re - 2 \cdot x.re\right) \]
   6. Step-by-step derivation

      1. distribute-rgt-out-- 63.5%

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

      2. metadata-eval 63.5%

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

   7. Applied egg-rr 63.5%

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

   if 1.76e19 < x.re

   1. Initial program 78.6%

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

      1. difference-of-squares 81.8%

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

   4. Applied egg-rr 81.8%

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

   6. Simplified 68.1%

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

   7. Taylor expanded in x.im around inf 63.5%

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

   9. Simplified 65.1%

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

       1. *-un-lft-identity 65.1%

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

       2. *-commutative 65.1%

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

       3. fma-define 65.1%

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

   11. Applied egg-rr 65.1%

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

   13. Simplified 65.0%

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

   14. Taylor expanded in x.im around 0 66.3%

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

4. Final simplification 64.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.re \leq 1.76 \cdot 10^{+19}:\\ \;\;\;\;\left(x.im \cdot x.im\right) \cdot \left(x.re \cdot -3\right)\\ \mathbf{else}:\\ \;\;\;\;x.re \cdot \left(x.re \cdot \left(x.re - 27\right)\right) - x.im \cdot \left(x.re \cdot x.im + -27\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 50.7% accurate, 2.7× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \left(\left(x.im \cdot x.im\right) \cdot \left(x.re\_m \cdot -3\right)\right) \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (* x.re_s (* (* x.im x.im) (* x.re_m -3.0))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * ((x_46_im * x_46_im) * (x_46_re_m * -3.0));
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    code = x_46re_s * ((x_46im * x_46im) * (x_46re_m * (-3.0d0)))
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * ((x_46_im * x_46_im) * (x_46_re_m * -3.0));
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	return x_46_re_s * ((x_46_im * x_46_im) * (x_46_re_m * -3.0))

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	return Float64(x_46_re_s * Float64(Float64(x_46_im * x_46_im) * Float64(x_46_re_m * -3.0)))
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = x_46_re_s * ((x_46_im * x_46_im) * (x_46_re_m * -3.0));
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * N[(N[(x$46$im * x$46$im), $MachinePrecision] * N[(x$46$re$95$m * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

3. Taylor expanded in x.im around inf 55.1%

   \[\leadsto \color{blue}{{x.im}^{2} \cdot \left(-1 \cdot x.re - 2 \cdot x.re\right)} \]
4. Step-by-step derivation

   1. unpow2 55.1%

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

5. Applied egg-rr 55.1%

   \[\leadsto \color{blue}{\left(x.im \cdot x.im\right)} \cdot \left(-1 \cdot x.re - 2 \cdot x.re\right) \]
6. Step-by-step derivation

   1. distribute-rgt-out-- 55.1%

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

   2. metadata-eval 55.1%

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

7. Applied egg-rr 55.1%

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

Alternative 7: 36.4% accurate, 2.7× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \left(x.im \cdot \left(x.im \cdot \left(x.re\_m \cdot -2\right)\right)\right) \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (* x.re_s (* x.im (* x.im (* x.re_m -2.0)))))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * (x_46_im * (x_46_im * (x_46_re_m * -2.0)));
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    code = x_46re_s * (x_46im * (x_46im * (x_46re_m * (-2.0d0))))
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * (x_46_im * (x_46_im * (x_46_re_m * -2.0)));
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	return x_46_re_s * (x_46_im * (x_46_im * (x_46_re_m * -2.0)))

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	return Float64(x_46_re_s * Float64(x_46_im * Float64(x_46_im * Float64(x_46_re_m * -2.0))))
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = x_46_re_s * (x_46_im * (x_46_im * (x_46_re_m * -2.0)));
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * N[(x$46$im * N[(x$46$im * N[(x$46$re$95$m * -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. difference-of-squares 88.1%

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

4. Applied egg-rr 88.1%

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

6. Simplified 55.6%

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

7. Taylor expanded in x.re around 0 31.0%

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

8. Taylor expanded in x.im around 0 34.6%

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

9. Taylor expanded in x.im around inf 37.4%

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

    1. *-commutative 37.4%

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

    2. *-commutative 37.4%

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

    3. *-commutative 37.4%

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

    4. associate-*r* 37.4%

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

11. Simplified 37.4%

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

Alternative 8: 19.6% accurate, 3.8× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \left(\left(x.re\_m \cdot x.im\right) \cdot -27\right) \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im)
 :precision binary64
 (* x.re_s (* (* x.re_m x.im) -27.0)))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * ((x_46_re_m * x_46_im) * -27.0);
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    code = x_46re_s * ((x_46re_m * x_46im) * (-27.0d0))
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * ((x_46_re_m * x_46_im) * -27.0);
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	return x_46_re_s * ((x_46_re_m * x_46_im) * -27.0)

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	return Float64(x_46_re_s * Float64(Float64(x_46_re_m * x_46_im) * -27.0))
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = x_46_re_s * ((x_46_re_m * x_46_im) * -27.0);
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * N[(N[(x$46$re$95$m * x$46$im), $MachinePrecision] * -27.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. difference-of-squares 88.1%

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

4. Applied egg-rr 88.1%

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

6. Simplified 55.6%

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

7. Taylor expanded in x.re around 0 31.0%

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

8. Taylor expanded in x.im around 0 34.6%

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

9. Taylor expanded in x.im around 0 20.3%

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

10. Final simplification 20.3%

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

Alternative 9: 3.6% accurate, 6.3× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot \left(x.im \cdot 27\right) \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im) :precision binary64 (* x.re_s (* x.im 27.0)))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * (x_46_im * 27.0);
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    code = x_46re_s * (x_46im * 27.0d0)
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * (x_46_im * 27.0);
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	return x_46_re_s * (x_46_im * 27.0)

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	return Float64(x_46_re_s * Float64(x_46_im * 27.0))
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = x_46_re_s * (x_46_im * 27.0);
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * N[(x$46$im * 27.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

   1. difference-of-squares 88.1%

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

4. Applied egg-rr 88.1%

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

6. Simplified 55.6%

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

7. Taylor expanded in x.re around 0 31.0%

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

   1. *-un-lft-identity 53.0%

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

   2. *-commutative 53.0%

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

   3. fma-define 53.0%

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

9. Applied egg-rr 31.0%

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

11. Simplified 16.7%

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

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

    \[\leadsto \color{blue}{27 \cdot x.im} \]
13. Step-by-step derivation

    1. *-commutative 3.6%

       \[\leadsto \color{blue}{x.im \cdot 27} \]

14. Simplified 3.6%

    \[\leadsto \color{blue}{x.im \cdot 27} \]
15. Add Preprocessing

Alternative 10: 2.7% accurate, 19.0× speedup

Math

\[\begin{array}{l} x.re\_m = \left|x.re\right| \\ x.re\_s = \mathsf{copysign}\left(1, x.re\right) \\ x.re\_s \cdot 8 \end{array} \]

FPCore

x.re\_m = (fabs.f64 x.re)
x.re\_s = (copysign.f64 #s(literal 1 binary64) x.re)
(FPCore (x.re_s x.re_m x.im) :precision binary64 (* x.re_s 8.0))

C

x.re\_m = fabs(x_46_re);
x.re\_s = copysign(1.0, x_46_re);
double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * 8.0;
}

Fortran

x.re\_m = abs(x_46re)
x.re\_s = copysign(1.0d0, x_46re)
real(8) function code(x_46re_s, x_46re_m, x_46im)
    real(8), intent (in) :: x_46re_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im
    code = x_46re_s * 8.0d0
end function

Java

x.re\_m = Math.abs(x_46_re);
x.re\_s = Math.copySign(1.0, x_46_re);
public static double code(double x_46_re_s, double x_46_re_m, double x_46_im) {
	return x_46_re_s * 8.0;
}

Python

x.re\_m = math.fabs(x_46_re)
x.re\_s = math.copysign(1.0, x_46_re)
def code(x_46_re_s, x_46_re_m, x_46_im):
	return x_46_re_s * 8.0

Julia

x.re\_m = abs(x_46_re)
x.re\_s = copysign(1.0, x_46_re)
function code(x_46_re_s, x_46_re_m, x_46_im)
	return Float64(x_46_re_s * 8.0)
end

MATLAB

x.re\_m = abs(x_46_re);
x.re\_s = sign(x_46_re) * abs(1.0);
function tmp = code(x_46_re_s, x_46_re_m, x_46_im)
	tmp = x_46_re_s * 8.0;
end

Wolfram

x.re\_m = N[Abs[x$46$re], $MachinePrecision]
x.re\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$re]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$re$95$s_, x$46$re$95$m_, x$46$im_] := N[(x$46$re$95$s * 8.0), $MachinePrecision]

Derivation

1. Initial program 86.1%

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

3. Simplified 82.7%

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

   1. flip-+ 21.6%

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

   2. unpow-prod-down 21.5%

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

   3. div-sub 21.5%

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

   4. pow2 21.5%

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

   5. pow-pow 21.5%

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

   6. metadata-eval 21.5%

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

   7. *-commutative 21.5%

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

   8. associate-*r* 21.5%

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

   9. associate-*l* 21.5%

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

   10. pow2 21.5%

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

6. Applied egg-rr 14.0%

   \[\leadsto \color{blue}{\frac{{x.re}^{6}}{{x.re}^{3} - {x.im}^{2} \cdot \left(-3 \cdot x.re\right)} - \frac{{x.re}^{2} \cdot \left({x.im}^{4} \cdot 9\right)}{{x.re}^{3} - {x.im}^{2} \cdot \left(-3 \cdot x.re\right)}} \]

8. Simplified 2.8%

   \[\leadsto \color{blue}{8} \]
9. Add Preprocessing

Developer Target 1: 87.4% 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 2024158 
(FPCore (x.re x.im)
  :name "math.cube on complex, real part"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (* x.re x.re) (- x.re x.im)) (* (* x.re x.im) (- x.re (* 3 x.im)))))

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