Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[\frac{x \cdot y}{2} - \frac{z}{8}\]
↓
\[\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)\]
\frac{x \cdot y}{2} - \frac{z}{8}
↓
\mathsf{fma}\left(x, \frac{y}{2}, -\frac{z}{8}\right)
double f(double x, double y, double z) {
        double r125373 = x;
        double r125374 = y;
        double r125375 = r125373 * r125374;
        double r125376 = 2.0;
        double r125377 = r125375 / r125376;
        double r125378 = z;
        double r125379 = 8.0;
        double r125380 = r125378 / r125379;
        double r125381 = r125377 - r125380;
        return r125381;
}
↓
double f(double x, double y, double z) {
        double r125382 = x;
        double r125383 = y;
        double r125384 = 2.0;
        double r125385 = r125383 / r125384;
        double r125386 = z;
        double r125387 = 8.0;
        double r125388 = r125386 / r125387;
        double r125389 = -r125388;
        double r125390 = fma(r125382, r125385, r125389);
        return r125390;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +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)))