Average Error: 0.0 → 0.0
Time: 11.9s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4 \cdot y\right)\right)
double f(double x, double y, double z) {
        double r7392184 = x;
        double r7392185 = r7392184 * r7392184;
        double r7392186 = y;
        double r7392187 = 4.0;
        double r7392188 = r7392186 * r7392187;
        double r7392189 = z;
        double r7392190 = r7392188 * r7392189;
        double r7392191 = r7392185 - r7392190;
        return r7392191;
}
↓
double f(double x, double y, double z) {
        double r7392192 = x;
        double r7392193 = z;
        double r7392194 = -r7392193;
        double r7392195 = 4.0;
        double r7392196 = y;
        double r7392197 = r7392195 * r7392196;
        double r7392198 = r7392194 * r7392197;
        double r7392199 = fma(r7392192, r7392192, r7392198);
        return r7392199;
}

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

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))