Average Error: 0.0 → 0.0
Time: 4.3s
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 r8061043 = x;
        double r8061044 = y;
        double r8061045 = r8061043 * r8061044;
        double r8061046 = 2.0;
        double r8061047 = r8061045 / r8061046;
        double r8061048 = z;
        double r8061049 = 8.0;
        double r8061050 = r8061048 / r8061049;
        double r8061051 = r8061047 - r8061050;
        return r8061051;
}
↓
double f(double x, double y, double z) {
        double r8061052 = x;
        double r8061053 = y;
        double r8061054 = 2.0;
        double r8061055 = r8061053 / r8061054;
        double r8061056 = z;
        double r8061057 = 8.0;
        double r8061058 = r8061056 / r8061057;
        double r8061059 = -r8061058;
        double r8061060 = fma(r8061052, r8061055, r8061059);
        return r8061060;
}

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-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2.0}, -\frac{z}{8.0}\right)}\]

  6. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]

Reproduce

herbie shell --seed 2019163 +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)))