Average Error: 0.1 → 0.1
Time: 40.9s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[\mathsf{fma}\left(3 \cdot x, y, -z\right)\]
\left(x \cdot 3\right) \cdot y - z
↓
\mathsf{fma}\left(3 \cdot x, y, -z\right)
double f(double x, double y, double z) {
        double r16871194 = x;
        double r16871195 = 3.0;
        double r16871196 = r16871194 * r16871195;
        double r16871197 = y;
        double r16871198 = r16871196 * r16871197;
        double r16871199 = z;
        double r16871200 = r16871198 - r16871199;
        return r16871200;
}
↓
double f(double x, double y, double z) {
        double r16871201 = 3.0;
        double r16871202 = x;
        double r16871203 = r16871201 * r16871202;
        double r16871204 = y;
        double r16871205 = z;
        double r16871206 = -r16871205;
        double r16871207 = fma(r16871203, r16871204, r16871206);
        return r16871207;
}

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

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

Reproduce

herbie shell --seed 2019200 +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))