Average Error: 0.0 → 0.0
Time: 4.0s
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 r7595559 = x;
        double r7595560 = y;
        double r7595561 = r7595559 * r7595560;
        double r7595562 = 2.0;
        double r7595563 = r7595561 / r7595562;
        double r7595564 = z;
        double r7595565 = 8.0;
        double r7595566 = r7595564 / r7595565;
        double r7595567 = r7595563 - r7595566;
        return r7595567;
}
↓
double f(double x, double y, double z) {
        double r7595568 = x;
        double r7595569 = y;
        double r7595570 = 2.0;
        double r7595571 = r7595569 / r7595570;
        double r7595572 = z;
        double r7595573 = 8.0;
        double r7595574 = r7595572 / r7595573;
        double r7595575 = -r7595574;
        double r7595576 = fma(r7595568, r7595571, r7595575);
        return r7595576;
}

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 2019172 +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)))