Average Error: 0.0 → 0.0
Time: 4.4s
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 r13656260 = x;
        double r13656261 = y;
        double r13656262 = r13656260 * r13656261;
        double r13656263 = 2.0;
        double r13656264 = r13656262 / r13656263;
        double r13656265 = z;
        double r13656266 = 8.0;
        double r13656267 = r13656265 / r13656266;
        double r13656268 = r13656264 - r13656267;
        return r13656268;
}
↓
double f(double x, double y, double z) {
        double r13656269 = x;
        double r13656270 = y;
        double r13656271 = 2.0;
        double r13656272 = r13656270 / r13656271;
        double r13656273 = z;
        double r13656274 = 8.0;
        double r13656275 = r13656273 / r13656274;
        double r13656276 = -r13656275;
        double r13656277 = fma(r13656269, r13656272, r13656276);
        return r13656277;
}

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 2019174 +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)))