Average Error: 0.0 → 0.0
Time: 3.8s
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 r121498 = x;
        double r121499 = y;
        double r121500 = r121498 * r121499;
        double r121501 = 2.0;
        double r121502 = r121500 / r121501;
        double r121503 = z;
        double r121504 = 8.0;
        double r121505 = r121503 / r121504;
        double r121506 = r121502 - r121505;
        return r121506;
}
↓
double f(double x, double y, double z) {
        double r121507 = x;
        double r121508 = y;
        double r121509 = 2.0;
        double r121510 = r121508 / r121509;
        double r121511 = z;
        double r121512 = 8.0;
        double r121513 = r121511 / r121512;
        double r121514 = -r121513;
        double r121515 = fma(r121507, r121510, r121514);
        return r121515;
}

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 2019322 +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)))