Average Error: 0.1 → 0
Time: 860.0ms
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 r190334 = x;
        double r190335 = y;
        double r190336 = r190334 * r190335;
        double r190337 = 2.0;
        double r190338 = r190336 / r190337;
        double r190339 = z;
        double r190340 = 8.0;
        double r190341 = r190339 / r190340;
        double r190342 = r190338 - r190341;
        return r190342;
}
↓
double f(double x, double y, double z) {
        double r190343 = x;
        double r190344 = 1.0;
        double r190345 = r190343 / r190344;
        double r190346 = y;
        double r190347 = 2.0;
        double r190348 = r190346 / r190347;
        double r190349 = z;
        double r190350 = 8.0;
        double r190351 = r190349 / r190350;
        double r190352 = -r190351;
        double r190353 = fma(r190345, r190348, r190352);
        return r190353;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[\frac{x \cdot y}{2} - \frac{z}{8}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.1

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

  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 2020036 +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)))