Average Error: 0.0 → 0.0
Time: 5.8s
Precision: 64
\[x \cdot x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)\]
x \cdot x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(x, x, -z \cdot \left(y \cdot 4\right)\right)
double f(double x, double y, double z) {
        double r215017 = x;
        double r215018 = r215017 * r215017;
        double r215019 = y;
        double r215020 = 4.0;
        double r215021 = r215019 * r215020;
        double r215022 = z;
        double r215023 = r215021 * r215022;
        double r215024 = r215018 - r215023;
        return r215024;
}
↓
double f(double x, double y, double z) {
        double r215025 = x;
        double r215026 = z;
        double r215027 = y;
        double r215028 = 4.0;
        double r215029 = r215027 * r215028;
        double r215030 = r215026 * r215029;
        double r215031 = -r215030;
        double r215032 = fma(r215025, r215025, r215031);
        return r215032;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))