Average Error: 0.0 → 0.0
Time: 906.0ms
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 r213410 = x;
        double r213411 = r213410 * r213410;
        double r213412 = y;
        double r213413 = 4.0;
        double r213414 = r213412 * r213413;
        double r213415 = z;
        double r213416 = r213414 * r213415;
        double r213417 = r213411 - r213416;
        return r213417;
}
↓
double f(double x, double y, double z) {
        double r213418 = x;
        double r213419 = y;
        double r213420 = 4.0;
        double r213421 = r213419 * r213420;
        double r213422 = z;
        double r213423 = r213421 * r213422;
        double r213424 = -r213423;
        double r213425 = fma(r213418, r213418, r213424);
        return r213425;
}

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 2020002 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))