Average Error: 0.0 → 0
Time: 3.0s
Precision: 64
\[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]
\frac{x \cdot y}{2.0} - \frac{z}{8.0}
↓
\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)
double f(double x, double y, double z) {
        double r3326635 = x;
        double r3326636 = y;
        double r3326637 = r3326635 * r3326636;
        double r3326638 = 2.0;
        double r3326639 = r3326637 / r3326638;
        double r3326640 = z;
        double r3326641 = 8.0;
        double r3326642 = r3326640 / r3326641;
        double r3326643 = r3326639 - r3326642;
        return r3326643;
}
↓
double f(double x, double y, double z) {
        double r3326644 = x;
        double r3326645 = y;
        double r3326646 = 2.0;
        double r3326647 = r3326645 / r3326646;
        double r3326648 = z;
        double r3326649 = 8.0;
        double r3326650 = r3326648 / r3326649;
        double r3326651 = -r3326650;
        double r3326652 = fma(r3326644, r3326647, r3326651);
        return r3326652;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
  2. Using strategy rm

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

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2.0}} - \frac{z}{8.0}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2.0}} - \frac{z}{8.0}\]

  5. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2.0}, -\frac{z}{8.0}\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  (- (/ (* x y) 2.0) (/ z 8.0)))