Average Error: 0.0 → 0
Time: 4.7s
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 r10032647 = x;
        double r10032648 = y;
        double r10032649 = r10032647 * r10032648;
        double r10032650 = 2.0;
        double r10032651 = r10032649 / r10032650;
        double r10032652 = z;
        double r10032653 = 8.0;
        double r10032654 = r10032652 / r10032653;
        double r10032655 = r10032651 - r10032654;
        return r10032655;
}
↓
double f(double x, double y, double z) {
        double r10032656 = x;
        double r10032657 = y;
        double r10032658 = 2.0;
        double r10032659 = r10032657 / r10032658;
        double r10032660 = z;
        double r10032661 = 8.0;
        double r10032662 = r10032660 / r10032661;
        double r10032663 = -r10032662;
        double r10032664 = fma(r10032656, r10032659, r10032663);
        return r10032664;
}

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 2019162 +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)))