Average Error: 0.1 → 0.1
Time: 10.8s
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 r393392 = x;
        double r393393 = 3.0;
        double r393394 = r393392 * r393393;
        double r393395 = y;
        double r393396 = r393394 * r393395;
        double r393397 = z;
        double r393398 = r393396 - r393397;
        return r393398;
}
↓
double f(double x, double y, double z) {
        double r393399 = x;
        double r393400 = 3.0;
        double r393401 = r393399 * r393400;
        double r393402 = y;
        double r393403 = z;
        double r393404 = -r393403;
        double r393405 = fma(r393401, r393402, r393404);
        return r393405;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.2
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 2019212 +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))