Average Error: 0.1 → 0.1
Time: 2.0s
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 r820347 = x;
        double r820348 = 3.0;
        double r820349 = r820347 * r820348;
        double r820350 = y;
        double r820351 = r820349 * r820350;
        double r820352 = z;
        double r820353 = r820351 - r820352;
        return r820353;
}
↓
double f(double x, double y, double z) {
        double r820354 = x;
        double r820355 = 3.0;
        double r820356 = r820354 * r820355;
        double r820357 = y;
        double r820358 = z;
        double r820359 = -r820358;
        double r820360 = fma(r820356, r820357, r820359);
        return r820360;
}

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 2019353 +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))