Average Error: 0.0 → 0.0
Time: 4.9s
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 r46903989 = x;
        double r46903990 = y;
        double r46903991 = r46903989 * r46903990;
        double r46903992 = 2.0;
        double r46903993 = r46903991 / r46903992;
        double r46903994 = z;
        double r46903995 = 8.0;
        double r46903996 = r46903994 / r46903995;
        double r46903997 = r46903993 - r46903996;
        return r46903997;
}
↓
double f(double x, double y, double z) {
        double r46903998 = x;
        double r46903999 = y;
        double r46904000 = 2.0;
        double r46904001 = r46903999 / r46904000;
        double r46904002 = z;
        double r46904003 = 8.0;
        double r46904004 = r46904002 / r46904003;
        double r46904005 = -r46904004;
        double r46904006 = fma(r46903998, r46904001, r46904005);
        return r46904006;
}

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 2019173 +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)))