Average Error: 0.4 → 0.3
Time: 12.3s
Precision: 64
\[\frac{\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.im\right)}{\left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.re\right)}\]
↓
\[\left(\mathsf{qma}\left(\left(\left(\left(x.re - x.im\right) \cdot \left(\left(x.im + x.re\right) \cdot x.im\right)\right)\right), \left(x.re \cdot \left(x.im + x.im\right)\right), x.re\right)\right)\]
\frac{\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.im\right)}{\left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.re\right)}
↓
\left(\mathsf{qma}\left(\left(\left(\left(x.re - x.im\right) \cdot \left(\left(x.im + x.re\right) \cdot x.im\right)\right)\right), \left(x.re \cdot \left(x.im + x.im\right)\right), x.re\right)\right)
double f(double x_re, double x_im) {
        double r741100 = x_re;
        double r741101 = r741100 * r741100;
        double r741102 = x_im;
        double r741103 = r741102 * r741102;
        double r741104 = r741101 - r741103;
        double r741105 = r741104 * r741102;
        double r741106 = r741100 * r741102;
        double r741107 = r741102 * r741100;
        double r741108 = r741106 + r741107;
        double r741109 = r741108 * r741100;
        double r741110 = r741105 + r741109;
        return r741110;
}
↓
double f(double x_re, double x_im) {
        double r741111 = x_re;
        double r741112 = x_im;
        double r741113 = r741111 - r741112;
        double r741114 = r741112 + r741111;
        double r741115 = r741114 * r741112;
        double r741116 = r741113 * r741115;
        double r741117 = /*Error: no posit support in C */;
        double r741118 = r741112 + r741112;
        double r741119 = r741111 * r741118;
        double r741120 = /*Error: no posit support in C */;
        double r741121 = /*Error: no posit support in C */;
        return r741121;
}

Error

Bits error versus x.re

Bits error versus x.im

Derivation

  1. Initial program 0.4

    \[\frac{\left(\left(\left(x.re \cdot x.re\right) - \left(x.im \cdot x.im\right)\right) \cdot x.im\right)}{\left(\left(\frac{\left(x.re \cdot x.im\right)}{\left(x.im \cdot x.re\right)}\right) \cdot x.re\right)}\]
  2. Using strategy rm

  3. Applied introduce-quire0.4

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

  4. Applied insert-quire-fdp-add0.3

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

  5. Simplified0.3

    \[\leadsto \color{blue}{\left(\mathsf{qma}\left(\left(\left(\left(x.re - x.im\right) \cdot \left(\left(\frac{x.im}{x.re}\right) \cdot x.im\right)\right)\right), \left(\frac{\left(x.re \cdot x.im\right)}{\left(x.re \cdot x.im\right)}\right), x.re\right)\right)}\]
  6. Using strategy rm

  7. Applied distribute-lft-out0.3

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

  8. Final simplification0.3

    \[\leadsto \left(\mathsf{qma}\left(\left(\left(\left(x.re - x.im\right) \cdot \left(\left(x.im + x.re\right) \cdot x.im\right)\right)\right), \left(x.re \cdot \left(x.im + x.im\right)\right), x.re\right)\right)\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x.re x.im)
  :name "math.cube on complex, imaginary part"
  (+.p16 (*.p16 (-.p16 (*.p16 x.re x.re) (*.p16 x.im x.im)) x.im) (*.p16 (+.p16 (*.p16 x.re x.im) (*.p16 x.im x.re)) x.re)))