Average Error: 0.0 → 0
Time: 994.0ms
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 r174547 = x;
        double r174548 = y;
        double r174549 = r174547 * r174548;
        double r174550 = 2.0;
        double r174551 = r174549 / r174550;
        double r174552 = z;
        double r174553 = 8.0;
        double r174554 = r174552 / r174553;
        double r174555 = r174551 - r174554;
        return r174555;
}
↓
double f(double x, double y, double z) {
        double r174556 = x;
        double r174557 = 1.0;
        double r174558 = r174556 / r174557;
        double r174559 = y;
        double r174560 = 2.0;
        double r174561 = r174559 / r174560;
        double r174562 = z;
        double r174563 = 8.0;
        double r174564 = r174562 / r174563;
        double r174565 = -r174564;
        double r174566 = fma(r174558, r174561, r174565);
        return r174566;
}

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 2020100 +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)))