Average Error: 0.0 → 0
Time: 3.4s
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 r147746 = x;
        double r147747 = y;
        double r147748 = r147746 * r147747;
        double r147749 = 2.0;
        double r147750 = r147748 / r147749;
        double r147751 = z;
        double r147752 = 8.0;
        double r147753 = r147751 / r147752;
        double r147754 = r147750 - r147753;
        return r147754;
}
↓
double f(double x, double y, double z) {
        double r147755 = x;
        double r147756 = y;
        double r147757 = 2.0;
        double r147758 = r147756 / r147757;
        double r147759 = z;
        double r147760 = 8.0;
        double r147761 = r147759 / r147760;
        double r147762 = -r147761;
        double r147763 = fma(r147755, r147758, r147762);
        return r147763;
}

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

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2019303 +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)))