Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, \frac{-z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, \frac{-z}{8}\right)
double f(double x, double y, double z) {
        double r115619 = x;
        double r115620 = y;
        double r115621 = r115619 * r115620;
        double r115622 = 2.0;
        double r115623 = r115621 / r115622;
        double r115624 = z;
        double r115625 = 8.0;
        double r115626 = r115624 / r115625;
        double r115627 = r115623 - r115626;
        return r115627;
}
↓
double f(double x, double y, double z) {
        double r115628 = x;
        double r115629 = y;
        double r115630 = 2.0;
        double r115631 = r115629 / r115630;
        double r115632 = z;
        double r115633 = -r115632;
        double r115634 = 8.0;
        double r115635 = r115633 / r115634;
        double r115636 = fma(r115628, r115631, r115635);
        return r115636;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2}} - \frac{z}{8}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2}} - \frac{z}{8}\]

  5. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)}\]

  6. Simplified0.0

    \[\leadsto \mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, \color{blue}{\frac{-z}{8}}\right)\]

  7. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2}, \frac{-z}{8}\right)\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))