Average Error: 0.0 → 0.0
Time: 854.0ms
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 r209362 = x;
        double r209363 = y;
        double r209364 = r209362 * r209363;
        double r209365 = 2.0;
        double r209366 = r209364 / r209365;
        double r209367 = z;
        double r209368 = 8.0;
        double r209369 = r209367 / r209368;
        double r209370 = r209366 - r209369;
        return r209370;
}
↓
double f(double x, double y, double z) {
        double r209371 = x;
        double r209372 = 1.0;
        double r209373 = r209371 / r209372;
        double r209374 = y;
        double r209375 = 2.0;
        double r209376 = r209374 / r209375;
        double r209377 = z;
        double r209378 = 8.0;
        double r209379 = r209377 / r209378;
        double r209380 = -r209379;
        double r209381 = fma(r209373, r209376, r209380);
        return r209381;
}

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-neg0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020025 +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)))