Average Error: 10.0 → 0.2
Time: 18.6s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{x}{y}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{x}{y}}{y}
double f(double x, double y) {
        double r329953 = x;
        double r329954 = y;
        double r329955 = r329954 * r329954;
        double r329956 = r329953 / r329955;
        return r329956;
}
↓
double f(double x, double y) {
        double r329957 = x;
        double r329958 = y;
        double r329959 = r329957 / r329958;
        double r329960 = r329959 / r329958;
        return r329960;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.0
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.0

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

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))