Average Error: 0.1 → 0.1
Time: 8.4s
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 r508504 = x;
        double r508505 = 3.0;
        double r508506 = r508504 * r508505;
        double r508507 = y;
        double r508508 = r508506 * r508507;
        double r508509 = z;
        double r508510 = r508508 - r508509;
        return r508510;
}
↓
double f(double x, double y, double z) {
        double r508511 = x;
        double r508512 = 3.0;
        double r508513 = y;
        double r508514 = r508512 * r508513;
        double r508515 = r508511 * r508514;
        double r508516 = z;
        double r508517 = r508515 - r508516;
        return r508517;
}

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 2019305 
(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))