math.cube on complex, imaginary part

Percentage Accurate: 82.8% → 99.7%

Time: 9.3s

Alternatives: 10

Speedup: 1.4×

• 44.0% of points produce a very large (infinite) output. You may want to add a precondition.

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 82.8% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;x.im\_m \leq 9 \cdot 10^{+88}:\\ \;\;\;\;\left(x.re\_m \cdot \left(x.im\_m \cdot x.re\_m\right)\right) \cdot 3 - {x.im\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right) + -3\\ \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (*
  x.im_s
  (if (<= x.im_m 9e+88)
    (- (* (* x.re_m (* x.im_m x.re_m)) 3.0) (pow x.im_m 3.0))
    (+ (* x.im_m (* x.im_m (- x.re_m x.im_m))) -3.0))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 9e+88) {
		tmp = ((x_46_re_m * (x_46_im_m * x_46_re_m)) * 3.0) - pow(x_46_im_m, 3.0);
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    real(8) :: tmp
    if (x_46im_m <= 9d+88) then
        tmp = ((x_46re_m * (x_46im_m * x_46re_m)) * 3.0d0) - (x_46im_m ** 3.0d0)
    else
        tmp = (x_46im_m * (x_46im_m * (x_46re_m - x_46im_m))) + (-3.0d0)
    end if
    code = x_46im_s * tmp
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 9e+88) {
		tmp = ((x_46_re_m * (x_46_im_m * x_46_re_m)) * 3.0) - Math.pow(x_46_im_m, 3.0);
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	tmp = 0
	if x_46_im_m <= 9e+88:
		tmp = ((x_46_re_m * (x_46_im_m * x_46_re_m)) * 3.0) - math.pow(x_46_im_m, 3.0)
	else:
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0
	if (x_46_im_m <= 9e+88)
		tmp = Float64(Float64(Float64(x_46_re_m * Float64(x_46_im_m * x_46_re_m)) * 3.0) - (x_46_im_m ^ 3.0));
	else
		tmp = Float64(Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m))) + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0;
	if (x_46_im_m <= 9e+88)
		tmp = ((x_46_re_m * (x_46_im_m * x_46_re_m)) * 3.0) - (x_46_im_m ^ 3.0);
	else
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := N[(x$46$im$95$s * If[LessEqual[x$46$im$95$m, 9e+88], N[(N[(N[(x$46$re$95$m * N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision] * 3.0), $MachinePrecision] - N[Power[x$46$im$95$m, 3.0], $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -3.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.im < 9e88

   1. Initial program 80.1%

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

   3. Simplified 90.8%

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

   if 9e88 < x.im

   1. Initial program 71.7%

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

      1. difference-of-squares 76.1%

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

      2. *-commutative 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in x.re around 0 67.4%

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

   6. Taylor expanded in x.re around 0 67.4%

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

   8. Simplified 91.3%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 9 \cdot 10^{+88}:\\ \;\;\;\;\left(x.re \cdot \left(x.im \cdot x.re\right)\right) \cdot 3 - {x.im}^{3}\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ \begin{array}{l} t_0 := x.im\_m \cdot \left(x.re\_m \cdot x.re\_m - x.im\_m \cdot x.im\_m\right)\\ t_1 := t\_0 + x.re\_m \cdot \left(x.im\_m \cdot x.re\_m + x.im\_m \cdot x.re\_m\right)\\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;t\_1 \leq 2 \cdot 10^{+307}:\\ \;\;\;\;t\_0 + x.re\_m \cdot \left(\left(x.im\_m \cdot x.re\_m\right) \cdot 2\right)\\ \mathbf{elif}\;t\_1 \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\left(x.im\_m \cdot x.re\_m\right) \cdot 3, x.re\_m, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right) + -3\\ \end{array} \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (let* ((t_0 (* x.im_m (- (* x.re_m x.re_m) (* x.im_m x.im_m))))
        (t_1 (+ t_0 (* x.re_m (+ (* x.im_m x.re_m) (* x.im_m x.re_m))))))
   (*
    x.im_s
    (if (<= t_1 2e+307)
      (+ t_0 (* x.re_m (* (* x.im_m x.re_m) 2.0)))
      (if (<= t_1 INFINITY)
        (fma (* (* x.im_m x.re_m) 3.0) x.re_m -1.0)
        (+ (* x.im_m (* x.im_m (- x.re_m x.im_m))) -3.0))))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double t_0 = x_46_im_m * ((x_46_re_m * x_46_re_m) - (x_46_im_m * x_46_im_m));
	double t_1 = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) + (x_46_im_m * x_46_re_m)));
	double tmp;
	if (t_1 <= 2e+307) {
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	} else if (t_1 <= ((double) INFINITY)) {
		tmp = fma(((x_46_im_m * x_46_re_m) * 3.0), x_46_re_m, -1.0);
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	t_0 = Float64(x_46_im_m * Float64(Float64(x_46_re_m * x_46_re_m) - Float64(x_46_im_m * x_46_im_m)))
	t_1 = Float64(t_0 + Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) + Float64(x_46_im_m * x_46_re_m))))
	tmp = 0.0
	if (t_1 <= 2e+307)
		tmp = Float64(t_0 + Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) * 2.0)));
	elseif (t_1 <= Inf)
		tmp = fma(Float64(Float64(x_46_im_m * x_46_re_m) * 3.0), x_46_re_m, -1.0);
	else
		tmp = Float64(Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m))) + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := Block[{t$95$0 = N[(x$46$im$95$m * N[(N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision] - N[(x$46$im$95$m * x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(t$95$0 + N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] + N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$46$im$95$s * If[LessEqual[t$95$1, 2e+307], N[(t$95$0 + N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$1, Infinity], N[(N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] * 3.0), $MachinePrecision] * x$46$re$95$m + -1.0), $MachinePrecision], N[(N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -3.0), $MachinePrecision]]]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)) < 1.99999999999999997e307

   1. Initial program 91.9%

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

      1. *-commutative 91.9%

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

      2. count-2 91.9%

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

      3. *-commutative 91.9%

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

   4. Applied egg-rr 91.9%

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

   if 1.99999999999999997e307 < (+.f64 (*.f64 (-.f64 (*.f64 x.re x.re) (*.f64 x.im x.im)) x.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)) < +inf.0

   1. Initial program 79.3%

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

   3. Simplified 93.1%

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

      1. *-commutative 93.1%

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

      2. fma-neg 93.1%

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

      3. associate-*r* 93.1%

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

      4. *-commutative 93.1%

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

      5. associate-*l* 93.1%

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

   6. Applied egg-rr 93.1%

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

   7. Taylor expanded in x.im around 0 93.1%

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

   9. Simplified 66.3%

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

   10. Taylor expanded in x.re around 0 66.3%

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

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

   1. Initial program 0.0%

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

      1. difference-of-squares 22.6%

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

      2. *-commutative 22.6%

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

   4. Applied egg-rr 22.6%

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

   5. Taylor expanded in x.re around 0 16.1%

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

   6. Taylor expanded in x.re around 0 16.1%

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

   8. Simplified 93.5%

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

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(x.im \cdot x.re + x.im \cdot x.re\right) \leq 2 \cdot 10^{+307}:\\ \;\;\;\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.im \cdot x.re\right) \cdot 2\right)\\ \mathbf{elif}\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(x.im \cdot x.re + x.im \cdot x.re\right) \leq \infty:\\ \;\;\;\;\mathsf{fma}\left(\left(x.im \cdot x.re\right) \cdot 3, x.re, -1\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.7% accurate, 0.2× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;x.im\_m \leq 8 \cdot 10^{+88}:\\ \;\;\;\;x.re\_m \cdot \left(\left(x.im\_m \cdot x.re\_m\right) \cdot 3\right) - {x.im\_m}^{3}\\ \mathbf{else}:\\ \;\;\;\;x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right) + -3\\ \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (*
  x.im_s
  (if (<= x.im_m 8e+88)
    (- (* x.re_m (* (* x.im_m x.re_m) 3.0)) (pow x.im_m 3.0))
    (+ (* x.im_m (* x.im_m (- x.re_m x.im_m))) -3.0))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 8e+88) {
		tmp = (x_46_re_m * ((x_46_im_m * x_46_re_m) * 3.0)) - pow(x_46_im_m, 3.0);
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    real(8) :: tmp
    if (x_46im_m <= 8d+88) then
        tmp = (x_46re_m * ((x_46im_m * x_46re_m) * 3.0d0)) - (x_46im_m ** 3.0d0)
    else
        tmp = (x_46im_m * (x_46im_m * (x_46re_m - x_46im_m))) + (-3.0d0)
    end if
    code = x_46im_s * tmp
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 8e+88) {
		tmp = (x_46_re_m * ((x_46_im_m * x_46_re_m) * 3.0)) - Math.pow(x_46_im_m, 3.0);
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	tmp = 0
	if x_46_im_m <= 8e+88:
		tmp = (x_46_re_m * ((x_46_im_m * x_46_re_m) * 3.0)) - math.pow(x_46_im_m, 3.0)
	else:
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0
	if (x_46_im_m <= 8e+88)
		tmp = Float64(Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) * 3.0)) - (x_46_im_m ^ 3.0));
	else
		tmp = Float64(Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m))) + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0;
	if (x_46_im_m <= 8e+88)
		tmp = (x_46_re_m * ((x_46_im_m * x_46_re_m) * 3.0)) - (x_46_im_m ^ 3.0);
	else
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := N[(x$46$im$95$s * If[LessEqual[x$46$im$95$m, 8e+88], N[(N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision] - N[Power[x$46$im$95$m, 3.0], $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -3.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.im < 7.99999999999999968e88

   1. Initial program 80.1%

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

   3. Simplified 90.7%

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

   5. Taylor expanded in x.im around 0 90.7%

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

   if 7.99999999999999968e88 < x.im

   1. Initial program 71.7%

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

      1. difference-of-squares 76.1%

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

      2. *-commutative 76.1%

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

   4. Applied egg-rr 76.1%

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

   5. Taylor expanded in x.re around 0 67.4%

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

   6. Taylor expanded in x.re around 0 67.4%

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

   8. Simplified 91.3%

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

4. Final simplification 90.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 8 \cdot 10^{+88}:\\ \;\;\;\;x.re \cdot \left(\left(x.im \cdot x.re\right) \cdot 3\right) - {x.im}^{3}\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 94.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ \begin{array}{l} t_0 := x.im\_m \cdot \left(x.re\_m \cdot x.re\_m - x.im\_m \cdot x.im\_m\right)\\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;t\_0 + x.re\_m \cdot \left(x.im\_m \cdot x.re\_m + x.im\_m \cdot x.re\_m\right) \leq \infty:\\ \;\;\;\;t\_0 + x.re\_m \cdot \left(\left(x.im\_m \cdot x.re\_m\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right) + -3\\ \end{array} \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (let* ((t_0 (* x.im_m (- (* x.re_m x.re_m) (* x.im_m x.im_m)))))
   (*
    x.im_s
    (if (<=
         (+ t_0 (* x.re_m (+ (* x.im_m x.re_m) (* x.im_m x.re_m))))
         INFINITY)
      (+ t_0 (* x.re_m (* (* x.im_m x.re_m) 2.0)))
      (+ (* x.im_m (* x.im_m (- x.re_m x.im_m))) -3.0)))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double t_0 = x_46_im_m * ((x_46_re_m * x_46_re_m) - (x_46_im_m * x_46_im_m));
	double tmp;
	if ((t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) + (x_46_im_m * x_46_re_m)))) <= ((double) INFINITY)) {
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double t_0 = x_46_im_m * ((x_46_re_m * x_46_re_m) - (x_46_im_m * x_46_im_m));
	double tmp;
	if ((t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) + (x_46_im_m * x_46_re_m)))) <= Double.POSITIVE_INFINITY) {
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	t_0 = x_46_im_m * ((x_46_re_m * x_46_re_m) - (x_46_im_m * x_46_im_m))
	tmp = 0
	if (t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) + (x_46_im_m * x_46_re_m)))) <= math.inf:
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0))
	else:
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	t_0 = Float64(x_46_im_m * Float64(Float64(x_46_re_m * x_46_re_m) - Float64(x_46_im_m * x_46_im_m)))
	tmp = 0.0
	if (Float64(t_0 + Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) + Float64(x_46_im_m * x_46_re_m)))) <= Inf)
		tmp = Float64(t_0 + Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) * 2.0)));
	else
		tmp = Float64(Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m))) + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	t_0 = x_46_im_m * ((x_46_re_m * x_46_re_m) - (x_46_im_m * x_46_im_m));
	tmp = 0.0;
	if ((t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) + (x_46_im_m * x_46_re_m)))) <= Inf)
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	else
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := Block[{t$95$0 = N[(x$46$im$95$m * N[(N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision] - N[(x$46$im$95$m * x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$46$im$95$s * If[LessEqual[N[(t$95$0 + N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] + N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], Infinity], N[(t$95$0 + N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -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.im) (*.f64 (+.f64 (*.f64 x.re x.im) (*.f64 x.im x.re)) x.re)) < +inf.0

   1. Initial program 89.4%

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

      1. *-commutative 89.4%

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

      2. count-2 89.4%

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

      3. *-commutative 89.4%

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

   4. Applied egg-rr 89.4%

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

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

   1. Initial program 0.0%

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

      1. difference-of-squares 22.6%

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

      2. *-commutative 22.6%

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

   4. Applied egg-rr 22.6%

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

   5. Taylor expanded in x.re around 0 16.1%

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

   6. Taylor expanded in x.re around 0 16.1%

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

   8. Simplified 93.5%

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

4. Final simplification 89.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(x.im \cdot x.re + x.im \cdot x.re\right) \leq \infty:\\ \;\;\;\;x.im \cdot \left(x.re \cdot x.re - x.im \cdot x.im\right) + x.re \cdot \left(\left(x.im \cdot x.re\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ \begin{array}{l} t_0 := x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right)\\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;x.im\_m \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;3 \cdot \left(x.im\_m \cdot \left(x.re\_m \cdot x.re\_m\right)\right)\\ \mathbf{elif}\;x.im\_m \leq 1.95 \cdot 10^{+78}:\\ \;\;\;\;t\_0 + x.re\_m \cdot \left(\left(x.im\_m \cdot x.re\_m\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0 + -3\\ \end{array} \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (let* ((t_0 (* x.im_m (* x.im_m (- x.re_m x.im_m)))))
   (*
    x.im_s
    (if (<= x.im_m 5.5e-30)
      (* 3.0 (* x.im_m (* x.re_m x.re_m)))
      (if (<= x.im_m 1.95e+78)
        (+ t_0 (* x.re_m (* (* x.im_m x.re_m) 2.0)))
        (+ t_0 -3.0))))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double t_0 = x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m));
	double tmp;
	if (x_46_im_m <= 5.5e-30) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else if (x_46_im_m <= 1.95e+78) {
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	} else {
		tmp = t_0 + -3.0;
	}
	return x_46_im_s * tmp;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x_46im_m * (x_46im_m * (x_46re_m - x_46im_m))
    if (x_46im_m <= 5.5d-30) then
        tmp = 3.0d0 * (x_46im_m * (x_46re_m * x_46re_m))
    else if (x_46im_m <= 1.95d+78) then
        tmp = t_0 + (x_46re_m * ((x_46im_m * x_46re_m) * 2.0d0))
    else
        tmp = t_0 + (-3.0d0)
    end if
    code = x_46im_s * tmp
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double t_0 = x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m));
	double tmp;
	if (x_46_im_m <= 5.5e-30) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else if (x_46_im_m <= 1.95e+78) {
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	} else {
		tmp = t_0 + -3.0;
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	t_0 = x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))
	tmp = 0
	if x_46_im_m <= 5.5e-30:
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m))
	elif x_46_im_m <= 1.95e+78:
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0))
	else:
		tmp = t_0 + -3.0
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	t_0 = Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m)))
	tmp = 0.0
	if (x_46_im_m <= 5.5e-30)
		tmp = Float64(3.0 * Float64(x_46_im_m * Float64(x_46_re_m * x_46_re_m)));
	elseif (x_46_im_m <= 1.95e+78)
		tmp = Float64(t_0 + Float64(x_46_re_m * Float64(Float64(x_46_im_m * x_46_re_m) * 2.0)));
	else
		tmp = Float64(t_0 + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	t_0 = x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m));
	tmp = 0.0;
	if (x_46_im_m <= 5.5e-30)
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	elseif (x_46_im_m <= 1.95e+78)
		tmp = t_0 + (x_46_re_m * ((x_46_im_m * x_46_re_m) * 2.0));
	else
		tmp = t_0 + -3.0;
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := Block[{t$95$0 = N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, N[(x$46$im$95$s * If[LessEqual[x$46$im$95$m, 5.5e-30], N[(3.0 * N[(x$46$im$95$m * N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x$46$im$95$m, 1.95e+78], N[(t$95$0 + N[(x$46$re$95$m * N[(N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision] * 2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(t$95$0 + -3.0), $MachinePrecision]]]), $MachinePrecision]]

Derivation

1. Split input into 3 regimes

2. if x.im < 5.49999999999999976e-30

   1. Initial program 77.6%

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

   3. Simplified 89.6%

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

   5. Taylor expanded in x.re around inf 60.4%

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

      1. unpow2 60.4%

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

   7. Applied egg-rr 60.4%

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

   if 5.49999999999999976e-30 < x.im < 1.9500000000000002e78

   1. Initial program 99.5%

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

      1. difference-of-squares 99.5%

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

      2. *-commutative 99.5%

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

   4. Applied egg-rr 99.5%

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

   5. Taylor expanded in x.re around 0 81.2%

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

      1. *-commutative 99.5%

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

      2. count-2 99.5%

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

      3. *-commutative 99.5%

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

   7. Applied egg-rr 81.2%

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

   if 1.9500000000000002e78 < x.im

   1. Initial program 73.5%

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

      1. difference-of-squares 77.6%

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

      2. *-commutative 77.6%

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

   4. Applied egg-rr 77.6%

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

   5. Taylor expanded in x.re around 0 69.4%

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

   6. Taylor expanded in x.re around 0 69.4%

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

   8. Simplified 91.8%

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

4. Final simplification 68.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 5.5 \cdot 10^{-30}:\\ \;\;\;\;3 \cdot \left(x.im \cdot \left(x.re \cdot x.re\right)\right)\\ \mathbf{elif}\;x.im \leq 1.95 \cdot 10^{+78}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + x.re \cdot \left(\left(x.im \cdot x.re\right) \cdot 2\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 83.7% accurate, 1.4× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;x.im\_m \leq 3100000000:\\ \;\;\;\;3 \cdot \left(x.im\_m \cdot \left(x.re\_m \cdot x.re\_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x.im\_m \cdot \left(x.im\_m \cdot \left(x.re\_m - x.im\_m\right)\right) + -3\\ \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (*
  x.im_s
  (if (<= x.im_m 3100000000.0)
    (* 3.0 (* x.im_m (* x.re_m x.re_m)))
    (+ (* x.im_m (* x.im_m (- x.re_m x.im_m))) -3.0))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 3100000000.0) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    real(8) :: tmp
    if (x_46im_m <= 3100000000.0d0) then
        tmp = 3.0d0 * (x_46im_m * (x_46re_m * x_46re_m))
    else
        tmp = (x_46im_m * (x_46im_m * (x_46re_m - x_46im_m))) + (-3.0d0)
    end if
    code = x_46im_s * tmp
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 3100000000.0) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else {
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	tmp = 0
	if x_46_im_m <= 3100000000.0:
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m))
	else:
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0
	if (x_46_im_m <= 3100000000.0)
		tmp = Float64(3.0 * Float64(x_46_im_m * Float64(x_46_re_m * x_46_re_m)));
	else
		tmp = Float64(Float64(x_46_im_m * Float64(x_46_im_m * Float64(x_46_re_m - x_46_im_m))) + -3.0);
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0;
	if (x_46_im_m <= 3100000000.0)
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	else
		tmp = (x_46_im_m * (x_46_im_m * (x_46_re_m - x_46_im_m))) + -3.0;
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := N[(x$46$im$95$s * If[LessEqual[x$46$im$95$m, 3100000000.0], N[(3.0 * N[(x$46$im$95$m * N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x$46$im$95$m * N[(x$46$im$95$m * N[(x$46$re$95$m - x$46$im$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -3.0), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.im < 3.1e9

   1. Initial program 78.1%

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

   3. Simplified 89.8%

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

   5. Taylor expanded in x.re around inf 60.4%

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

      1. unpow2 60.4%

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

   7. Applied egg-rr 60.4%

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

   if 3.1e9 < x.im

   1. Initial program 79.9%

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

      1. difference-of-squares 83.0%

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

      2. *-commutative 83.0%

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

   4. Applied egg-rr 83.0%

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

   5. Taylor expanded in x.re around 0 72.1%

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

   6. Taylor expanded in x.re around 0 72.1%

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

   8. Simplified 85.7%

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

4. Final simplification 66.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 3100000000:\\ \;\;\;\;3 \cdot \left(x.im \cdot \left(x.re \cdot x.re\right)\right)\\ \mathbf{else}:\\ \;\;\;\;x.im \cdot \left(x.im \cdot \left(x.re - x.im\right)\right) + -3\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 63.6% accurate, 1.6× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ x.im\_s \cdot \begin{array}{l} \mathbf{if}\;x.im\_m \leq 6.2 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot \left(x.im\_m \cdot \left(x.re\_m \cdot x.re\_m\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 - x.im\_m \cdot \left(x.im\_m \cdot x.re\_m\right)\\ \end{array} \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m)
 :precision binary64
 (*
  x.im_s
  (if (<= x.im_m 6.2e+135)
    (* 3.0 (* x.im_m (* x.re_m x.re_m)))
    (- -1.0 (* x.im_m (* x.im_m x.re_m))))))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 6.2e+135) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else {
		tmp = -1.0 - (x_46_im_m * (x_46_im_m * x_46_re_m));
	}
	return x_46_im_s * tmp;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    real(8) :: tmp
    if (x_46im_m <= 6.2d+135) then
        tmp = 3.0d0 * (x_46im_m * (x_46re_m * x_46re_m))
    else
        tmp = (-1.0d0) - (x_46im_m * (x_46im_m * x_46re_m))
    end if
    code = x_46im_s * tmp
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	double tmp;
	if (x_46_im_m <= 6.2e+135) {
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	} else {
		tmp = -1.0 - (x_46_im_m * (x_46_im_m * x_46_re_m));
	}
	return x_46_im_s * tmp;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	tmp = 0
	if x_46_im_m <= 6.2e+135:
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m))
	else:
		tmp = -1.0 - (x_46_im_m * (x_46_im_m * x_46_re_m))
	return x_46_im_s * tmp

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0
	if (x_46_im_m <= 6.2e+135)
		tmp = Float64(3.0 * Float64(x_46_im_m * Float64(x_46_re_m * x_46_re_m)));
	else
		tmp = Float64(-1.0 - Float64(x_46_im_m * Float64(x_46_im_m * x_46_re_m)));
	end
	return Float64(x_46_im_s * tmp)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp_2 = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = 0.0;
	if (x_46_im_m <= 6.2e+135)
		tmp = 3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m));
	else
		tmp = -1.0 - (x_46_im_m * (x_46_im_m * x_46_re_m));
	end
	tmp_2 = x_46_im_s * tmp;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := N[(x$46$im$95$s * If[LessEqual[x$46$im$95$m, 6.2e+135], N[(3.0 * N[(x$46$im$95$m * N[(x$46$re$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(-1.0 - N[(x$46$im$95$m * N[(x$46$im$95$m * x$46$re$95$m), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]), $MachinePrecision]

Derivation

1. Split input into 2 regimes

2. if x.im < 6.20000000000000044e135

   1. Initial program 80.8%

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

   3. Simplified 89.7%

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

   5. Taylor expanded in x.re around inf 58.1%

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

      1. unpow2 58.1%

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

   7. Applied egg-rr 58.1%

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

   if 6.20000000000000044e135 < x.im

   1. Initial program 65.8%

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

      1. difference-of-squares 71.1%

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

      2. *-commutative 71.1%

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

   4. Applied egg-rr 71.1%

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

   5. Taylor expanded in x.re around 0 94.7%

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

   7. Simplified 40.0%

      \[\leadsto \color{blue}{-1 + x.im \cdot \left(x.re \cdot \left(-x.im\right)\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 55.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x.im \leq 6.2 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot \left(x.im \cdot \left(x.re \cdot x.re\right)\right)\\ \mathbf{else}:\\ \;\;\;\;-1 - x.im \cdot \left(x.im \cdot x.re\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 51.2% accurate, 2.7× speedup

Math

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

FPCore

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

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * (3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m)));
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    code = x_46im_s * (3.0d0 * (x_46im_m * (x_46re_m * x_46re_m)))
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * (3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m)));
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	return x_46_im_s * (3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m)))

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	return Float64(x_46_im_s * Float64(3.0 * Float64(x_46_im_m * Float64(x_46_re_m * x_46_re_m))))
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = x_46_im_s * (3.0 * (x_46_im_m * (x_46_re_m * x_46_re_m)));
end

Wolfram

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

Derivation

1. Initial program 78.6%

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

3. Simplified 86.1%

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

5. Taylor expanded in x.re around inf 50.3%

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

   1. unpow2 50.3%

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

7. Applied egg-rr 50.3%

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

Alternative 9: 2.8% accurate, 19.0× speedup

Math

\[\begin{array}{l} x.re_m = \left|x.re\right| \\ x.im\_m = \left|x.im\right| \\ x.im\_s = \mathsf{copysign}\left(1, x.im\right) \\ x.im\_s \cdot 0.1 \end{array} \]

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m) :precision binary64 (* x.im_s 0.1))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * 0.1;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    code = x_46im_s * 0.1d0
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * 0.1;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	return x_46_im_s * 0.1

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	return Float64(x_46_im_s * 0.1)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = x_46_im_s * 0.1;
end

Wolfram

x.re_m = N[Abs[x$46$re], $MachinePrecision]
x.im\_m = N[Abs[x$46$im], $MachinePrecision]
x.im\_s = N[With[{TMP1 = Abs[1.0], TMP2 = Sign[x$46$im]}, TMP1 * If[TMP2 == 0, 1, TMP2]], $MachinePrecision]
code[x$46$im$95$s_, x$46$re$95$m_, x$46$im$95$m_] := N[(x$46$im$95$s * 0.1), $MachinePrecision]

Derivation

1. Initial program 78.6%

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

3. Simplified 86.1%

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

   1. sub-neg 86.1%

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

   2. flip3-+ 15.0%

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

   3. associate-*r* 15.0%

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

   4. *-commutative 15.0%

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

   5. associate-*l* 14.9%

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

   6. associate-*r* 13.5%

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

   7. associate-*l* 13.5%

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

   8. pow2 13.5%

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

6. Applied egg-rr 9.5%

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

8. Simplified 2.7%

   \[\leadsto \color{blue}{0.1} \]
9. Add Preprocessing

Alternative 10: 2.7% accurate, 19.0× speedup

Math

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

FPCore

x.re_m = (fabs.f64 x.re)
x.im\_m = (fabs.f64 x.im)
x.im\_s = (copysign.f64 #s(literal 1 binary64) x.im)
(FPCore (x.im_s x.re_m x.im_m) :precision binary64 (* x.im_s -1.0))

C

x.re_m = fabs(x_46_re);
x.im\_m = fabs(x_46_im);
x.im\_s = copysign(1.0, x_46_im);
double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * -1.0;
}

Fortran

x.re_m = abs(x_46re)
x.im\_m = abs(x_46im)
x.im\_s = copysign(1.0d0, x_46im)
real(8) function code(x_46im_s, x_46re_m, x_46im_m)
    real(8), intent (in) :: x_46im_s
    real(8), intent (in) :: x_46re_m
    real(8), intent (in) :: x_46im_m
    code = x_46im_s * (-1.0d0)
end function

Java

x.re_m = Math.abs(x_46_re);
x.im\_m = Math.abs(x_46_im);
x.im\_s = Math.copySign(1.0, x_46_im);
public static double code(double x_46_im_s, double x_46_re_m, double x_46_im_m) {
	return x_46_im_s * -1.0;
}

Python

x.re_m = math.fabs(x_46_re)
x.im\_m = math.fabs(x_46_im)
x.im\_s = math.copysign(1.0, x_46_im)
def code(x_46_im_s, x_46_re_m, x_46_im_m):
	return x_46_im_s * -1.0

Julia

x.re_m = abs(x_46_re)
x.im\_m = abs(x_46_im)
x.im\_s = copysign(1.0, x_46_im)
function code(x_46_im_s, x_46_re_m, x_46_im_m)
	return Float64(x_46_im_s * -1.0)
end

MATLAB

x.re_m = abs(x_46_re);
x.im\_m = abs(x_46_im);
x.im\_s = sign(x_46_im) * abs(1.0);
function tmp = code(x_46_im_s, x_46_re_m, x_46_im_m)
	tmp = x_46_im_s * -1.0;
end

Wolfram

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

Derivation

1. Initial program 78.6%

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

   1. difference-of-squares 81.3%

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

   2. *-commutative 81.3%

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

4. Applied egg-rr 81.3%

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

5. Taylor expanded in x.re around 0 55.2%

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

7. Simplified 16.3%

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

8. Taylor expanded in x.im around 0 2.7%

   \[\leadsto \color{blue}{-1} \]
9. Add Preprocessing

Developer Target 1: 91.7% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024137 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  :precision binary64

  :alt
  (! :herbie-platform default (+ (* (* x.re x.im) (* 2 x.re)) (* (* x.im (- x.re x.im)) (+ x.re x.im))))

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