Average Error: 0.0 → 0.0
Time: 3.9s
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 r116499 = x;
        double r116500 = r116499 * r116499;
        double r116501 = y;
        double r116502 = 4.0;
        double r116503 = r116501 * r116502;
        double r116504 = z;
        double r116505 = r116503 * r116504;
        double r116506 = r116500 - r116505;
        return r116506;
}
↓
double f(double x, double y, double z) {
        double r116507 = x;
        double r116508 = y;
        double r116509 = 4.0;
        double r116510 = r116508 * r116509;
        double r116511 = z;
        double r116512 = r116510 * r116511;
        double r116513 = -r116512;
        double r116514 = fma(r116507, r116507, r116513);
        return r116514;
}

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 2019350 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))