Average Error: 0.1 → 0.1
Time: 9.2s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[\mathsf{fma}\left(x \cdot 3, y, -z\right)\]
\left(x \cdot 3\right) \cdot y - z
↓
\mathsf{fma}\left(x \cdot 3, y, -z\right)
double f(double x, double y, double z) {
        double r497112 = x;
        double r497113 = 3.0;
        double r497114 = r497112 * r497113;
        double r497115 = y;
        double r497116 = r497114 * r497115;
        double r497117 = z;
        double r497118 = r497116 - r497117;
        return r497118;
}
↓
double f(double x, double y, double z) {
        double r497119 = x;
        double r497120 = 3.0;
        double r497121 = r497119 * r497120;
        double r497122 = y;
        double r497123 = z;
        double r497124 = -r497123;
        double r497125 = fma(r497121, r497122, r497124);
        return r497125;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied fma-neg0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 3, y, -z\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x \cdot 3, y, -z\right)\]

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (* x (* 3 y)) z)

  (- (* (* x 3) y) z))