Average Error: 0.0 → 0
Time: 4.2s
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 r6958375 = x;
        double r6958376 = y;
        double r6958377 = r6958375 * r6958376;
        double r6958378 = 2.0;
        double r6958379 = r6958377 / r6958378;
        double r6958380 = z;
        double r6958381 = 8.0;
        double r6958382 = r6958380 / r6958381;
        double r6958383 = r6958379 - r6958382;
        return r6958383;
}
↓
double f(double x, double y, double z) {
        double r6958384 = x;
        double r6958385 = y;
        double r6958386 = 2.0;
        double r6958387 = r6958385 / r6958386;
        double r6958388 = z;
        double r6958389 = 8.0;
        double r6958390 = r6958388 / r6958389;
        double r6958391 = -r6958390;
        double r6958392 = fma(r6958384, r6958387, r6958391);
        return r6958392;
}

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 2019168 +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)))