Average Error: 0.0 → 0.0
Time: 4.1s
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 r8161062 = x;
        double r8161063 = y;
        double r8161064 = r8161062 * r8161063;
        double r8161065 = 2.0;
        double r8161066 = r8161064 / r8161065;
        double r8161067 = z;
        double r8161068 = 8.0;
        double r8161069 = r8161067 / r8161068;
        double r8161070 = r8161066 - r8161069;
        return r8161070;
}
↓
double f(double x, double y, double z) {
        double r8161071 = x;
        double r8161072 = y;
        double r8161073 = 2.0;
        double r8161074 = r8161072 / r8161073;
        double r8161075 = z;
        double r8161076 = 8.0;
        double r8161077 = r8161075 / r8161076;
        double r8161078 = -r8161077;
        double r8161079 = fma(r8161071, r8161074, r8161078);
        return r8161079;
}

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

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

  4. Applied times-frac0.0

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

  5. Applied fma-neg0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +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)))