Average Error: 0.3 → 0.3
Time: 1.5s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{x}{3 \cdot y}\]
\frac{x}{y \cdot 3}
↓
\frac{x}{3 \cdot y}
double f(double x, double y) {
        double r722224 = x;
        double r722225 = y;
        double r722226 = 3.0;
        double r722227 = r722225 * r722226;
        double r722228 = r722224 / r722227;
        return r722228;
}
↓
double f(double x, double y) {
        double r722229 = x;
        double r722230 = 3.0;
        double r722231 = y;
        double r722232 = r722230 * r722231;
        double r722233 = r722229 / r722232;
        return r722233;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.3
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.3

    \[\frac{x}{y \cdot 3}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.3

    \[\leadsto \frac{\color{blue}{1 \cdot x}}{y \cdot 3}\]

  4. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{1}{y} \cdot \frac{x}{3}}\]
  5. Using strategy rm

  6. Applied frac-times0.3

    \[\leadsto \color{blue}{\frac{1 \cdot x}{y \cdot 3}}\]

  7. Simplified0.3

    \[\leadsto \frac{\color{blue}{x}}{y \cdot 3}\]

  8. Simplified0.3

    \[\leadsto \frac{x}{\color{blue}{3 \cdot y}}\]

  9. Final simplification0.3

    \[\leadsto \frac{x}{3 \cdot y}\]

Reproduce

herbie shell --seed 2020033 +o rules:numerics
(FPCore (x y)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, C"
  :precision binary64

  :herbie-target
  (/ (/ x y) 3)

  (/ x (* y 3)))