Average Error: 0.0 → 0.0
Time: 1.7s
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 r155027 = x;
        double r155028 = y;
        double r155029 = r155027 * r155028;
        double r155030 = 2.0;
        double r155031 = r155029 / r155030;
        double r155032 = z;
        double r155033 = 8.0;
        double r155034 = r155032 / r155033;
        double r155035 = r155031 - r155034;
        return r155035;
}
↓
double f(double x, double y, double z) {
        double r155036 = x;
        double r155037 = y;
        double r155038 = 2.0;
        double r155039 = r155037 / r155038;
        double r155040 = z;
        double r155041 = 8.0;
        double r155042 = r155040 / r155041;
        double r155043 = -r155042;
        double r155044 = fma(r155036, r155039, r155043);
        return r155044;
}

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 2019194 +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)))