Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r251661 = x;
        double r251662 = y;
        double r251663 = r251661 * r251662;
        double r251664 = 2.0;
        double r251665 = r251663 / r251664;
        double r251666 = z;
        double r251667 = 8.0;
        double r251668 = r251666 / r251667;
        double r251669 = r251665 - r251668;
        return r251669;
}
↓
double f(double x, double y, double z) {
        double r251670 = x;
        double r251671 = 1.0;
        double r251672 = r251670 / r251671;
        double r251673 = y;
        double r251674 = 2.0;
        double r251675 = r251673 / r251674;
        double r251676 = z;
        double r251677 = 8.0;
        double r251678 = r251676 / r251677;
        double r251679 = -r251678;
        double r251680 = fma(r251672, r251675, r251679);
        return r251680;
}

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

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

Reproduce

herbie shell --seed 2020083 +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)))