Average Error: 0.0 → 0.0
Time: 3.9s
Precision: 64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(y \cdot 4, -z, x\right)\]
x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(y \cdot 4, -z, x\right)
double f(double x, double y, double z) {
        double r207649 = x;
        double r207650 = y;
        double r207651 = 4.0;
        double r207652 = r207650 * r207651;
        double r207653 = z;
        double r207654 = r207652 * r207653;
        double r207655 = r207649 - r207654;
        return r207655;
}
↓
double f(double x, double y, double z) {
        double r207656 = y;
        double r207657 = 4.0;
        double r207658 = r207656 * r207657;
        double r207659 = z;
        double r207660 = -r207659;
        double r207661 = x;
        double r207662 = fma(r207658, r207660, r207661);
        return r207662;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x - \left(y \cdot 4\right) \cdot z\]

  2. Taylor expanded around inf 0.0

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

  3. Simplified0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4) z)))