Average Error: 0.0 → 0
Time: 3.1s
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 r10547061 = x;
        double r10547062 = y;
        double r10547063 = r10547061 * r10547062;
        double r10547064 = 2.0;
        double r10547065 = r10547063 / r10547064;
        double r10547066 = z;
        double r10547067 = 8.0;
        double r10547068 = r10547066 / r10547067;
        double r10547069 = r10547065 - r10547068;
        return r10547069;
}
↓
double f(double x, double y, double z) {
        double r10547070 = x;
        double r10547071 = y;
        double r10547072 = 2.0;
        double r10547073 = r10547071 / r10547072;
        double r10547074 = z;
        double r10547075 = 8.0;
        double r10547076 = r10547074 / r10547075;
        double r10547077 = -r10547076;
        double r10547078 = fma(r10547070, r10547073, r10547077);
        return r10547078;
}

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 2019164 +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)))