Average Error: 0.0 → 0.0
Time: 1.6s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(z \cdot \left(-4\right), y, x \cdot x\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(z \cdot \left(-4\right), y, x \cdot x\right)
double f(double x, double y, double z) {
        double r115312 = x;
        double r115313 = r115312 * r115312;
        double r115314 = y;
        double r115315 = 4.0;
        double r115316 = r115314 * r115315;
        double r115317 = z;
        double r115318 = r115316 * r115317;
        double r115319 = r115313 - r115318;
        return r115319;
}
↓
double f(double x, double y, double z) {
        double r115320 = z;
        double r115321 = 4.0;
        double r115322 = -r115321;
        double r115323 = r115320 * r115322;
        double r115324 = y;
        double r115325 = x;
        double r115326 = r115325 * r115325;
        double r115327 = fma(r115323, r115324, r115326);
        return r115327;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))