Average Error: 0.0 → 0.0
Time: 4.3s
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 r111352 = x;
        double r111353 = r111352 * r111352;
        double r111354 = y;
        double r111355 = 4.0;
        double r111356 = r111354 * r111355;
        double r111357 = z;
        double r111358 = r111356 * r111357;
        double r111359 = r111353 - r111358;
        return r111359;
}
↓
double f(double x, double y, double z) {
        double r111360 = x;
        double r111361 = y;
        double r111362 = 4.0;
        double r111363 = r111361 * r111362;
        double r111364 = z;
        double r111365 = r111363 * r111364;
        double r111366 = -r111365;
        double r111367 = fma(r111360, r111360, r111366);
        return r111367;
}

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 2019323 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))