Average Error: 0.1 → 0.1
Time: 1.8s
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 r996768 = x;
        double r996769 = 3.0;
        double r996770 = r996768 * r996769;
        double r996771 = y;
        double r996772 = r996770 * r996771;
        double r996773 = z;
        double r996774 = r996772 - r996773;
        return r996774;
}
↓
double f(double x, double y, double z) {
        double r996775 = x;
        double r996776 = 3.0;
        double r996777 = y;
        double r996778 = r996776 * r996777;
        double r996779 = r996775 * r996778;
        double r996780 = z;
        double r996781 = r996779 - r996780;
        return r996781;
}

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

Original0.1
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 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 2020025 
(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))