Average Error: 0.2 → 0.2
Time: 1.9s
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 r805757 = x;
        double r805758 = 3.0;
        double r805759 = r805757 * r805758;
        double r805760 = y;
        double r805761 = r805759 * r805760;
        double r805762 = z;
        double r805763 = r805761 - r805762;
        return r805763;
}
↓
double f(double x, double y, double z) {
        double r805764 = x;
        double r805765 = 3.0;
        double r805766 = y;
        double r805767 = r805765 * r805766;
        double r805768 = r805764 * r805767;
        double r805769 = z;
        double r805770 = r805768 - r805769;
        return r805770;
}

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
Target0.2
Herbie0.2
\[x \cdot \left(3 \cdot y\right) - z\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot 3\right) \cdot y - z\]
  2. Using strategy rm

  3. Applied associate-*l*0.2

    \[\leadsto \color{blue}{x \cdot \left(3 \cdot y\right)} - z\]

  4. Final simplification0.2

    \[\leadsto x \cdot \left(3 \cdot y\right) - z\]

Reproduce

herbie shell --seed 2020081 +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))