Average Error: 0.1 → 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 r606804 = x;
        double r606805 = 3.0;
        double r606806 = r606804 * r606805;
        double r606807 = y;
        double r606808 = r606806 * r606807;
        double r606809 = z;
        double r606810 = r606808 - r606809;
        return r606810;
}
↓
double f(double x, double y, double z) {
        double r606811 = x;
        double r606812 = 3.0;
        double r606813 = y;
        double r606814 = r606812 * r606813;
        double r606815 = r606811 * r606814;
        double r606816 = z;
        double r606817 = r606815 - r606816;
        return r606817;
}

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 +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))