Average Error: 0.2 → 0.1
Time: 3.0s
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 r630191 = x;
        double r630192 = 3.0;
        double r630193 = r630191 * r630192;
        double r630194 = y;
        double r630195 = r630193 * r630194;
        double r630196 = z;
        double r630197 = r630195 - r630196;
        return r630197;
}
↓
double f(double x, double y, double z) {
        double r630198 = x;
        double r630199 = 3.0;
        double r630200 = y;
        double r630201 = r630199 * r630200;
        double r630202 = r630198 * r630201;
        double r630203 = z;
        double r630204 = r630202 - r630203;
        return r630204;
}

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 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))