Average Error: 0.2 → 0.1
Time: 1.7s
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 r702790 = x;
        double r702791 = 3.0;
        double r702792 = r702790 * r702791;
        double r702793 = y;
        double r702794 = r702792 * r702793;
        double r702795 = z;
        double r702796 = r702794 - r702795;
        return r702796;
}
↓
double f(double x, double y, double z) {
        double r702797 = x;
        double r702798 = 3.0;
        double r702799 = y;
        double r702800 = r702798 * r702799;
        double r702801 = r702797 * r702800;
        double r702802 = z;
        double r702803 = r702801 - r702802;
        return r702803;
}

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 2019354 
(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))