Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\left(x \cdot 3.0\right) \cdot y - z\]
↓
\[\mathsf{fma}\left(x \cdot 3.0, y, -z\right)\]
\left(x \cdot 3.0\right) \cdot y - z
↓
\mathsf{fma}\left(x \cdot 3.0, y, -z\right)
double f(double x, double y, double z) {
        double r33630605 = x;
        double r33630606 = 3.0;
        double r33630607 = r33630605 * r33630606;
        double r33630608 = y;
        double r33630609 = r33630607 * r33630608;
        double r33630610 = z;
        double r33630611 = r33630609 - r33630610;
        return r33630611;
}
↓
double f(double x, double y, double z) {
        double r33630612 = x;
        double r33630613 = 3.0;
        double r33630614 = r33630612 * r33630613;
        double r33630615 = y;
        double r33630616 = z;
        double r33630617 = -r33630616;
        double r33630618 = fma(r33630614, r33630615, r33630617);
        return r33630618;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.2
Herbie0.1
\[x \cdot \left(3.0 \cdot y\right) - z\]

Derivation

  1. Initial program 0.1

    \[\left(x \cdot 3.0\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied fma-neg0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(x \cdot 3.0, y, -z\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{fma}\left(x \cdot 3.0, y, -z\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, B"

  :herbie-target
  (- (* x (* 3.0 y)) z)

  (- (* (* x 3.0) y) z))