Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, B

Average Error: 0.2 → 0.2

Time: 1.8s

Precision: 64

Math

\[\left(x \cdot 3\right) \cdot y - z\]

↓

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

C

double f(double x, double y, double z) {
        double r657485 = x;
        double r657486 = 3.0;
        double r657487 = r657485 * r657486;
        double r657488 = y;
        double r657489 = r657487 * r657488;
        double r657490 = z;
        double r657491 = r657489 - r657490;
        return r657491;
}

↓

double f(double x, double y, double z) {
        double r657492 = x;
        double r657493 = 3.0;
        double r657494 = r657492 * r657493;
        double r657495 = y;
        double r657496 = z;
        double r657497 = -r657496;
        double r657498 = fma(r657494, r657495, r657497);
        return r657498;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original	0.2
Target	0.1
Herbie	0.2

\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

1. Initial program 0.2

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

3. Applied fma-neg 0.2

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

4. Final simplification 0.2

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

Reproduce

herbie shell --seed 2020001 +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))