Average Error: 0.2 → 0.1
Time: 2.3s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(3 \cdot y\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(3 \cdot y\right) - z
double f(double x, double y, double z) {
        double r696615 = x;
        double r696616 = 3.0;
        double r696617 = r696615 * r696616;
        double r696618 = y;
        double r696619 = r696617 * r696618;
        double r696620 = z;
        double r696621 = r696619 - r696620;
        return r696621;
}
↓
double f(double x, double y, double z) {
        double r696622 = x;
        double r696623 = 3.0;
        double r696624 = y;
        double r696625 = r696623 * r696624;
        double r696626 = r696622 * r696625;
        double r696627 = z;
        double r696628 = r696626 - r696627;
        return r696628;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.1
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.2

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

  3. Applied associate-*l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019356 
(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))