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 r135393 = x;
        double r135394 = y;
        double r135395 = r135393 * r135394;
        double r135396 = 2.0;
        double r135397 = r135395 / r135396;
        double r135398 = z;
        double r135399 = 8.0;
        double r135400 = r135398 / r135399;
        double r135401 = r135397 - r135400;
        return r135401;
}
↓
double f(double x, double y, double z) {
        double r135402 = x;
        double r135403 = y;
        double r135404 = 2.0;
        double r135405 = r135403 / r135404;
        double r135406 = z;
        double r135407 = 8.0;
        double r135408 = r135406 / r135407;
        double r135409 = -r135408;
        double r135410 = fma(r135402, r135405, r135409);
        return r135410;
}

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

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied distribute-lft-out--0.0

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 +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)))