Average Error: 0.3 → 0.7
Time: 2.1s
Precision: 64
\[\frac{x}{y \cdot 3}\]
↓
\[\frac{1}{\frac{1}{\frac{\frac{x}{y}}{3}}}\]
\frac{x}{y \cdot 3}
↓
\frac{1}{\frac{1}{\frac{\frac{x}{y}}{3}}}
double f(double x, double y) {
        double r862041 = x;
        double r862042 = y;
        double r862043 = 3.0;
        double r862044 = r862042 * r862043;
        double r862045 = r862041 / r862044;
        return r862045;
}
↓
double f(double x, double y) {
        double r862046 = 1.0;
        double r862047 = x;
        double r862048 = y;
        double r862049 = r862047 / r862048;
        double r862050 = 3.0;
        double r862051 = r862049 / r862050;
        double r862052 = r862046 / r862051;
        double r862053 = r862046 / r862052;
        return r862053;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.3
Target0.2
Herbie0.7
\[\frac{\frac{x}{y}}{3}\]

Derivation

  1. Initial program 0.3

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

  3. Applied associate-/r*0.2

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

  5. Applied clear-num0.7

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

  7. Applied clear-num0.7

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

  8. Final simplification0.7

    \[\leadsto \frac{1}{\frac{1}{\frac{\frac{x}{y}}{3}}}\]

Reproduce

herbie shell --seed 2020100 +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)))