Average Error: 0.0 → 0.0
Time: 3.7s
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 r125751 = x;
        double r125752 = y;
        double r125753 = 4.0;
        double r125754 = r125752 * r125753;
        double r125755 = z;
        double r125756 = r125754 * r125755;
        double r125757 = r125751 - r125756;
        return r125757;
}
↓
double f(double x, double y, double z) {
        double r125758 = y;
        double r125759 = 4.0;
        double r125760 = r125758 * r125759;
        double r125761 = z;
        double r125762 = -r125761;
        double r125763 = x;
        double r125764 = fma(r125760, r125762, r125763);
        return r125764;
}

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 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:quadForm from diagrams-solve-0.1, A"
  :precision binary64
  (- x (* (* y 4) z)))