Average Error: 0.0 → 0.0
Time: 4.0s
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 r13148666 = x;
        double r13148667 = y;
        double r13148668 = r13148666 * r13148667;
        double r13148669 = 2.0;
        double r13148670 = r13148668 / r13148669;
        double r13148671 = z;
        double r13148672 = 8.0;
        double r13148673 = r13148671 / r13148672;
        double r13148674 = r13148670 - r13148673;
        return r13148674;
}
↓
double f(double x, double y, double z) {
        double r13148675 = x;
        double r13148676 = y;
        double r13148677 = 2.0;
        double r13148678 = r13148676 / r13148677;
        double r13148679 = z;
        double r13148680 = 8.0;
        double r13148681 = r13148679 / r13148680;
        double r13148682 = -r13148681;
        double r13148683 = fma(r13148675, r13148678, r13148682);
        return r13148683;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019172 +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)))