Average Error: 0.2 → 0.1
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 r884923 = x;
        double r884924 = 3.0;
        double r884925 = r884923 * r884924;
        double r884926 = y;
        double r884927 = r884925 * r884926;
        double r884928 = z;
        double r884929 = r884927 - r884928;
        return r884929;
}
↓
double f(double x, double y, double z) {
        double r884930 = x;
        double r884931 = 3.0;
        double r884932 = y;
        double r884933 = r884931 * r884932;
        double r884934 = r884930 * r884933;
        double r884935 = z;
        double r884936 = r884934 - r884935;
        return r884936;
}

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 2020056 +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))