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 r943902 = x;
        double r943903 = 3.0;
        double r943904 = r943902 * r943903;
        double r943905 = y;
        double r943906 = r943904 * r943905;
        double r943907 = z;
        double r943908 = r943906 - r943907;
        return r943908;
}
↓
double f(double x, double y, double z) {
        double r943909 = x;
        double r943910 = 3.0;
        double r943911 = y;
        double r943912 = r943910 * r943911;
        double r943913 = r943909 * r943912;
        double r943914 = z;
        double r943915 = r943913 - r943914;
        return r943915;
}

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 2020034 
(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))