Average Error: 0.0 → 0.0
Time: 1.4s
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 r150724 = x;
        double r150725 = y;
        double r150726 = r150724 * r150725;
        double r150727 = 2.0;
        double r150728 = r150726 / r150727;
        double r150729 = z;
        double r150730 = 8.0;
        double r150731 = r150729 / r150730;
        double r150732 = r150728 - r150731;
        return r150732;
}
↓
double f(double x, double y, double z) {
        double r150733 = x;
        double r150734 = y;
        double r150735 = 2.0;
        double r150736 = r150734 / r150735;
        double r150737 = z;
        double r150738 = 8.0;
        double r150739 = r150737 / r150738;
        double r150740 = -r150739;
        double r150741 = fma(r150733, r150736, r150740);
        return r150741;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019196 +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)))