Average Error: 0.2 → 0.2
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 r783315 = x;
        double r783316 = 3.0;
        double r783317 = r783315 * r783316;
        double r783318 = y;
        double r783319 = r783317 * r783318;
        double r783320 = z;
        double r783321 = r783319 - r783320;
        return r783321;
}
↓
double f(double x, double y, double z) {
        double r783322 = x;
        double r783323 = 3.0;
        double r783324 = y;
        double r783325 = r783323 * r783324;
        double r783326 = r783322 * r783325;
        double r783327 = z;
        double r783328 = r783326 - r783327;
        return r783328;
}

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

Derivation

  1. Initial program 0.2

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

  3. Applied associate-*l*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020020 
(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))