Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
\[x \cdot x - \left(y \cdot 4.0\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)\]
x \cdot x - \left(y \cdot 4.0\right) \cdot z
↓
\mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)
double f(double x, double y, double z) {
        double r7813143 = x;
        double r7813144 = r7813143 * r7813143;
        double r7813145 = y;
        double r7813146 = 4.0;
        double r7813147 = r7813145 * r7813146;
        double r7813148 = z;
        double r7813149 = r7813147 * r7813148;
        double r7813150 = r7813144 - r7813149;
        return r7813150;
}
↓
double f(double x, double y, double z) {
        double r7813151 = x;
        double r7813152 = z;
        double r7813153 = -r7813152;
        double r7813154 = 4.0;
        double r7813155 = y;
        double r7813156 = r7813154 * r7813155;
        double r7813157 = r7813153 * r7813156;
        double r7813158 = fma(r7813151, r7813151, r7813157);
        return r7813158;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot x - \left(y \cdot 4.0\right) \cdot z\]
  2. Using strategy rm

  3. Applied fma-neg0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, x, -\left(y \cdot 4.0\right) \cdot z\right)}\]

  4. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, x, \left(-z\right) \cdot \left(4.0 \cdot y\right)\right)\]

Reproduce

herbie shell --seed 2019158 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.QuadraticFormula:discriminant from Rasterific-0.6.1"
  (- (* x x) (* (* y 4.0) z)))