Average Error: 0.0 → 0
Time: 1.0s
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 r176413 = x;
        double r176414 = y;
        double r176415 = r176413 * r176414;
        double r176416 = 2.0;
        double r176417 = r176415 / r176416;
        double r176418 = z;
        double r176419 = 8.0;
        double r176420 = r176418 / r176419;
        double r176421 = r176417 - r176420;
        return r176421;
}
↓
double f(double x, double y, double z) {
        double r176422 = x;
        double r176423 = 1.0;
        double r176424 = r176422 / r176423;
        double r176425 = y;
        double r176426 = 2.0;
        double r176427 = r176425 / r176426;
        double r176428 = z;
        double r176429 = 8.0;
        double r176430 = r176428 / r176429;
        double r176431 = -r176430;
        double r176432 = fma(r176424, r176427, r176431);
        return r176432;
}

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 2020001 +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)))