Average Error: 10.6 → 0.2
Time: 8.4s
Precision: 64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{1}{\frac{y}{x}}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{1}{\frac{y}{x}}}{y}
double f(double x, double y) {
        double r13623427 = x;
        double r13623428 = y;
        double r13623429 = r13623428 * r13623428;
        double r13623430 = r13623427 / r13623429;
        return r13623430;
}
↓
double f(double x, double y) {
        double r13623431 = 1.0;
        double r13623432 = y;
        double r13623433 = x;
        double r13623434 = r13623432 / r13623433;
        double r13623435 = r13623431 / r13623434;
        double r13623436 = r13623435 / r13623432;
        return r13623436;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original10.6
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.6

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

  3. Applied associate-/r*0.2

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

  5. Applied clear-num0.6

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

  7. Applied associate-/r/0.6

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

  8. Applied associate-/r*0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"

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

  (/ x (* y y)))