Average Error: 0.2 → 0.1
Time: 1.6s
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 r765576 = x;
        double r765577 = 3.0;
        double r765578 = r765576 * r765577;
        double r765579 = y;
        double r765580 = r765578 * r765579;
        double r765581 = z;
        double r765582 = r765580 - r765581;
        return r765582;
}
↓
double f(double x, double y, double z) {
        double r765583 = x;
        double r765584 = 3.0;
        double r765585 = y;
        double r765586 = r765584 * r765585;
        double r765587 = r765583 * r765586;
        double r765588 = z;
        double r765589 = r765587 - r765588;
        return r765589;
}

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 +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))