Average Error: 0.0 → 0.0
Time: 1.5s
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 r150936 = x;
        double r150937 = y;
        double r150938 = r150936 * r150937;
        double r150939 = 2.0;
        double r150940 = r150938 / r150939;
        double r150941 = z;
        double r150942 = 8.0;
        double r150943 = r150941 / r150942;
        double r150944 = r150940 - r150943;
        return r150944;
}
↓
double f(double x, double y, double z) {
        double r150945 = x;
        double r150946 = y;
        double r150947 = 2.0;
        double r150948 = r150946 / r150947;
        double r150949 = z;
        double r150950 = 8.0;
        double r150951 = r150949 / r150950;
        double r150952 = -r150951;
        double r150953 = fma(r150945, r150948, r150952);
        return r150953;
}

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 2019174 +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)))