Average Error: 0.2 → 0.1
Time: 1.4s
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 r718440 = x;
        double r718441 = 3.0;
        double r718442 = r718440 * r718441;
        double r718443 = y;
        double r718444 = r718442 * r718443;
        double r718445 = z;
        double r718446 = r718444 - r718445;
        return r718446;
}
↓
double f(double x, double y, double z) {
        double r718447 = x;
        double r718448 = 3.0;
        double r718449 = y;
        double r718450 = r718448 * r718449;
        double r718451 = r718447 * r718450;
        double r718452 = z;
        double r718453 = r718451 - r718452;
        return r718453;
}

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 2020046 
(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))