Average Error: 0.0 → 0.0
Time: 1.0s
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 r229376 = x;
        double r229377 = r229376 * r229376;
        double r229378 = y;
        double r229379 = 4.0;
        double r229380 = r229378 * r229379;
        double r229381 = z;
        double r229382 = r229380 * r229381;
        double r229383 = r229377 - r229382;
        return r229383;
}
↓
double f(double x, double y, double z) {
        double r229384 = x;
        double r229385 = y;
        double r229386 = 4.0;
        double r229387 = r229385 * r229386;
        double r229388 = z;
        double r229389 = r229387 * r229388;
        double r229390 = -r229389;
        double r229391 = fma(r229384, r229384, r229390);
        return r229391;
}

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 2020047 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  :precision binary64
  (- (* x x) (* (* y 4) z)))