Average Error: 0.0 → 0
Time: 1.9s
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 r203838 = x;
        double r203839 = y;
        double r203840 = r203838 * r203839;
        double r203841 = 2.0;
        double r203842 = r203840 / r203841;
        double r203843 = z;
        double r203844 = 8.0;
        double r203845 = r203843 / r203844;
        double r203846 = r203842 - r203845;
        return r203846;
}
↓
double f(double x, double y, double z) {
        double r203847 = x;
        double r203848 = y;
        double r203849 = 2.0;
        double r203850 = r203848 / r203849;
        double r203851 = z;
        double r203852 = -r203851;
        double r203853 = 8.0;
        double r203854 = r203852 / r203853;
        double r203855 = fma(r203847, r203850, r203854);
        return r203855;
}

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

    \[\leadsto \frac{x \cdot y}{2} - \color{blue}{1 \cdot \frac{z}{8}}\]

  4. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot \frac{x \cdot y}{2}} - 1 \cdot \frac{z}{8}\]

  5. Applied distribute-lft-out--0.0

    \[\leadsto \color{blue}{1 \cdot \left(\frac{x \cdot y}{2} - \frac{z}{8}\right)}\]

  6. Simplified0

    \[\leadsto 1 \cdot \color{blue}{\mathsf{fma}\left(x, \frac{y}{2}, \frac{-z}{8}\right)}\]

  7. Final simplification0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, D"
  :precision binary64
  (- (/ (* x y) 2) (/ z 8)))