Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(\frac{x}{2}, y, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r154367 = x;
        double r154368 = y;
        double r154369 = r154367 * r154368;
        double r154370 = 2.0;
        double r154371 = r154369 / r154370;
        double r154372 = z;
        double r154373 = 8.0;
        double r154374 = r154372 / r154373;
        double r154375 = r154371 - r154374;
        return r154375;
}
↓
double f(double x, double y, double z) {
        double r154376 = x;
        double r154377 = 2.0;
        double r154378 = r154376 / r154377;
        double r154379 = y;
        double r154380 = z;
        double r154381 = 8.0;
        double r154382 = r154380 / r154381;
        double r154383 = -r154382;
        double r154384 = fma(r154378, r154379, r154383);
        return r154384;
}

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

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019303 +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)))