Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)
double f(double x, double y, double z) {
        double r134520 = x;
        double r134521 = r134520 * r134520;
        double r134522 = y;
        double r134523 = 4.0;
        double r134524 = r134522 * r134523;
        double r134525 = z;
        double r134526 = r134524 * r134525;
        double r134527 = r134521 - r134526;
        return r134527;
}
↓
double f(double x, double y, double z) {
        double r134528 = x;
        double r134529 = y;
        double r134530 = 4.0;
        double r134531 = r134529 * r134530;
        double r134532 = z;
        double r134533 = r134531 * r134532;
        double r134534 = -r134533;
        double r134535 = fma(r134528, r134528, r134534);
        return r134535;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot x - \left(y \cdot 4\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, -\left(y \cdot 4\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))