Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, D

Average Error: 0.0 → 0

Time: 5.5s

Precision: 64

Math

\[\frac{x \cdot y}{2} - \frac{z}{8}\]

↓

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

C

double f(double x, double y, double z) {
        double r121397 = x;
        double r121398 = y;
        double r121399 = r121397 * r121398;
        double r121400 = 2.0;
        double r121401 = r121399 / r121400;
        double r121402 = z;
        double r121403 = 8.0;
        double r121404 = r121402 / r121403;
        double r121405 = r121401 - r121404;
        return r121405;
}

↓

double f(double x, double y, double z) {
        double r121406 = x;
        double r121407 = y;
        double r121408 = 2.0;
        double r121409 = r121407 / r121408;
        double r121410 = z;
        double r121411 = 8.0;
        double r121412 = r121410 / r121411;
        double r121413 = -r121412;
        double r121414 = fma(r121406, r121409, r121413);
        return r121414;
}

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-identity 0.0

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

4. Applied times-frac 0.0

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

5. Applied fma-neg 0

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

6. Final simplification 0

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

Reproduce

herbie shell --seed 2019323 +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)))