Average Error: 0.0 → 0
Time: 9.2s
Precision: 64
\[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]
\frac{x \cdot y}{2.0} - \frac{z}{8.0}
↓
\mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)
double f(double x, double y, double z) {
        double r12038390 = x;
        double r12038391 = y;
        double r12038392 = r12038390 * r12038391;
        double r12038393 = 2.0;
        double r12038394 = r12038392 / r12038393;
        double r12038395 = z;
        double r12038396 = 8.0;
        double r12038397 = r12038395 / r12038396;
        double r12038398 = r12038394 - r12038397;
        return r12038398;
}
↓
double f(double x, double y, double z) {
        double r12038399 = x;
        double r12038400 = y;
        double r12038401 = 2.0;
        double r12038402 = r12038400 / r12038401;
        double r12038403 = z;
        double r12038404 = 8.0;
        double r12038405 = r12038403 / r12038404;
        double r12038406 = -r12038405;
        double r12038407 = fma(r12038399, r12038402, r12038406);
        return r12038407;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[\frac{x \cdot y}{2.0} - \frac{z}{8.0}\]
  2. Using strategy rm

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

    \[\leadsto \frac{x \cdot y}{\color{blue}{1 \cdot 2.0}} - \frac{z}{8.0}\]

  4. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{x}{1} \cdot \frac{y}{2.0}} - \frac{z}{8.0}\]

  5. Applied fma-neg0

    \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{x}{1}, \frac{y}{2.0}, -\frac{z}{8.0}\right)}\]

  6. Final simplification0

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{2.0}, -\frac{z}{8.0}\right)\]

Reproduce

herbie shell --seed 2019165 +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)))