Average Error: 0.0 → 0
Time: 845.0ms
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 r180225 = x;
        double r180226 = y;
        double r180227 = r180225 * r180226;
        double r180228 = 2.0;
        double r180229 = r180227 / r180228;
        double r180230 = z;
        double r180231 = 8.0;
        double r180232 = r180230 / r180231;
        double r180233 = r180229 - r180232;
        return r180233;
}
↓
double f(double x, double y, double z) {
        double r180234 = x;
        double r180235 = 1.0;
        double r180236 = r180234 / r180235;
        double r180237 = y;
        double r180238 = 2.0;
        double r180239 = r180237 / r180238;
        double r180240 = z;
        double r180241 = 8.0;
        double r180242 = r180240 / r180241;
        double r180243 = -r180242;
        double r180244 = fma(r180236, r180239, r180243);
        return r180244;
}

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

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

  6. Final simplification0

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

Reproduce

herbie shell --seed 2020062 +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)))