Average Error: 0.6 → 0.2
Time: 3.3s
Precision: 64
\[\frac{1}{x \cdot x}\]
↓
\[\frac{\frac{1}{x}}{x}\]
\frac{1}{x \cdot x}
↓
\frac{\frac{1}{x}}{x}
double f(double x) {
        double r425843 = 1.0;
        double r425844 = x;
        double r425845 = r425844 * r425844;
        double r425846 = r425843 / r425845;
        return r425846;
}
↓
double f(double x) {
        double r425847 = 1.0;
        double r425848 = x;
        double r425849 = r425847 / r425848;
        double r425850 = r425849 / r425848;
        return r425850;
}

Error

Bits error versus x

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Results

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Target

Original0.6
Target0.2
Herbie0.2
\[\frac{\frac{1}{x}}{x}\]

Derivation

  1. Initial program 0.6

    \[\frac{1}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020060 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (/ (/ 1 x) x)

  (/ 1 (* x x)))