Average Error: 3.9 → 2.1
Time: 2.0s
Precision: binary64
\[re \cdot re - im \cdot im \]
↓
\[\begin{array}{l} \mathbf{if}\;re \cdot re \leq 3.6361091965505894 \cdot 10^{+301}:\\ \;\;\;\;re \cdot re - im \cdot im\\ \mathbf{else}:\\ \;\;\;\;{re}^{2}\\ \end{array} \]
re \cdot re - im \cdot im
↓
\begin{array}{l}
\mathbf{if}\;re \cdot re \leq 3.6361091965505894 \cdot 10^{+301}:\\
\;\;\;\;re \cdot re - im \cdot im\\

\mathbf{else}:\\
\;\;\;\;{re}^{2}\\


\end{array}

(FPCore re_sqr (re im) :precision binary64 (- (* re re) (* im im)))
↓
(FPCore re_sqr (re im)
 :precision binary64
 (if (<= (* re re) 3.6361091965505894e+301)
   (- (* re re) (* im im))
   (pow re 2.0)))
double re_sqr(double re, double im) {
	return (re * re) - (im * im);
}
↓
double re_sqr(double re, double im) {
	double tmp;
	if ((re * re) <= 3.6361091965505894e+301) {
		tmp = (re * re) - (im * im);
	} else {
		tmp = pow(re, 2.0);
	}
	return tmp;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if (*.f64 re re) < 3.63610919655058944e301

    1. Initial program 0.0

      \[re \cdot re - im \cdot im \]

    if 3.63610919655058944e301 < (*.f64 re re)

    1. Initial program 15.4

      \[re \cdot re - im \cdot im \]

    2. Taylor expanded in re around inf 8.3

      \[\leadsto \color{blue}{{re}^{2}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification2.1

    \[\leadsto \begin{array}{l} \mathbf{if}\;re \cdot re \leq 3.6361091965505894 \cdot 10^{+301}:\\ \;\;\;\;re \cdot re - im \cdot im\\ \mathbf{else}:\\ \;\;\;\;{re}^{2}\\ \end{array} \]

Reproduce

herbie shell --seed 2022068 
(FPCore re_sqr (re im)
  :name "math.square on complex, real part"
  :precision binary64
  (- (* re re) (* im im)))