Average Error: 0.2 → 0.1
Time: 2.0s
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 r907763 = x;
        double r907764 = 3.0;
        double r907765 = r907763 * r907764;
        double r907766 = y;
        double r907767 = r907765 * r907766;
        double r907768 = z;
        double r907769 = r907767 - r907768;
        return r907769;
}
↓
double f(double x, double y, double z) {
        double r907770 = x;
        double r907771 = 3.0;
        double r907772 = y;
        double r907773 = r907771 * r907772;
        double r907774 = r907770 * r907773;
        double r907775 = z;
        double r907776 = r907774 - r907775;
        return r907776;
}

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 2019354 +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))