Average Error: 0.0 → 0.0
Time: 2.8s
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 r150382 = x;
        double r150383 = r150382 * r150382;
        double r150384 = y;
        double r150385 = 4.0;
        double r150386 = r150384 * r150385;
        double r150387 = z;
        double r150388 = r150386 * r150387;
        double r150389 = r150383 - r150388;
        return r150389;
}
↓
double f(double x, double y, double z) {
        double r150390 = x;
        double r150391 = y;
        double r150392 = 4.0;
        double r150393 = r150391 * r150392;
        double r150394 = z;
        double r150395 = r150393 * r150394;
        double r150396 = -r150395;
        double r150397 = fma(r150390, r150390, r150396);
        return r150397;
}

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 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))