Average Error: 0.0 → 0.0
Time: 1.2s
Precision: 64
\[x - \left(y \cdot 4\right) \cdot z\]
↓
\[\mathsf{fma}\left(4 \cdot y, -z, x\right)\]
x - \left(y \cdot 4\right) \cdot z
↓
\mathsf{fma}\left(4 \cdot y, -z, x\right)
double f(double x, double y, double z) {
        double r132702 = x;
        double r132703 = y;
        double r132704 = 4.0;
        double r132705 = r132703 * r132704;
        double r132706 = z;
        double r132707 = r132705 * r132706;
        double r132708 = r132702 - r132707;
        return r132708;
}
↓
double f(double x, double y, double z) {
        double r132709 = 4.0;
        double r132710 = y;
        double r132711 = r132709 * r132710;
        double r132712 = z;
        double r132713 = -r132712;
        double r132714 = x;
        double r132715 = fma(r132711, r132713, r132714);
        return r132715;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  (- x (* (* y 4.0) z)))