Average Error: 0.1 → 0.1
Time: 17.0s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(y \cdot 3\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(y \cdot 3\right) - z
double f(double x, double y, double z) {
        double r460023 = x;
        double r460024 = 3.0;
        double r460025 = r460023 * r460024;
        double r460026 = y;
        double r460027 = r460025 * r460026;
        double r460028 = z;
        double r460029 = r460027 - r460028;
        return r460029;
}
↓
double f(double x, double y, double z) {
        double r460030 = x;
        double r460031 = y;
        double r460032 = 3.0;
        double r460033 = r460031 * r460032;
        double r460034 = r460030 * r460033;
        double r460035 = z;
        double r460036 = r460034 - r460035;
        return r460036;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(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))