Average Error: 0.1 → 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 r885976 = x;
        double r885977 = 3.0;
        double r885978 = r885976 * r885977;
        double r885979 = y;
        double r885980 = r885978 * r885979;
        double r885981 = z;
        double r885982 = r885980 - r885981;
        return r885982;
}
↓
double f(double x, double y, double z) {
        double r885983 = x;
        double r885984 = 3.0;
        double r885985 = y;
        double r885986 = r885984 * r885985;
        double r885987 = r885983 * r885986;
        double r885988 = z;
        double r885989 = r885987 - r885988;
        return r885989;
}

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 2020036 
(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))