Average Error: 0.1 → 0.1
Time: 36.4s
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 r519510 = x;
        double r519511 = 3.0;
        double r519512 = r519510 * r519511;
        double r519513 = y;
        double r519514 = r519512 * r519513;
        double r519515 = z;
        double r519516 = r519514 - r519515;
        return r519516;
}
↓
double f(double x, double y, double z) {
        double r519517 = x;
        double r519518 = y;
        double r519519 = 3.0;
        double r519520 = r519518 * r519519;
        double r519521 = r519517 * r519520;
        double r519522 = z;
        double r519523 = r519521 - r519522;
        return r519523;
}

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. 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 2019303 +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))