Average Error: 0.1 → 0.1
Time: 21.3s
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 r48276 = x;
        double r48277 = 3.0;
        double r48278 = r48276 * r48277;
        double r48279 = y;
        double r48280 = r48278 * r48279;
        double r48281 = z;
        double r48282 = r48280 - r48281;
        return r48282;
}
↓
double f(double x, double y, double z) {
        double r48283 = x;
        double r48284 = y;
        double r48285 = 3.0;
        double r48286 = r48284 * r48285;
        double r48287 = r48283 * r48286;
        double r48288 = z;
        double r48289 = r48287 - r48288;
        return r48289;
}

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 2019310 
(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))