Average Error: 0.2 → 0.1
Time: 22.1s
Precision: 64
\[\left(x \cdot 3\right) \cdot y - z\]
↓
\[x \cdot \left(y \cdot 3\right) - z\]
\left(x \cdot 3\right) \cdot y - z
↓
x \cdot \left(y \cdot 3\right) - z
double f(double x, double y, double z) {
        double r495766 = x;
        double r495767 = 3.0;
        double r495768 = r495766 * r495767;
        double r495769 = y;
        double r495770 = r495768 * r495769;
        double r495771 = z;
        double r495772 = r495770 - r495771;
        return r495772;
}
↓
double f(double x, double y, double z) {
        double r495773 = x;
        double r495774 = y;
        double r495775 = 3.0;
        double r495776 = r495774 * r495775;
        double r495777 = r495773 * r495776;
        double r495778 = z;
        double r495779 = r495777 - r495778;
        return r495779;
}

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. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019304 
(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))