Average Error: 0.5 → 0.2
Time: 16.9s
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 r352383 = 1.0;
        double r352384 = x;
        double r352385 = r352384 * r352384;
        double r352386 = r352383 / r352385;
        return r352386;
}
↓
double f(double x) {
        double r352387 = 1.0;
        double r352388 = x;
        double r352389 = r352387 / r352388;
        double r352390 = r352389 / r352388;
        return r352390;
}

Error

Bits error versus x

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Results

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Target

Original0.5
Target0.2
Herbie0.2
\[\frac{\frac{1}{x}}{x}\]

Derivation

  1. Initial program 0.5

    \[\frac{1}{x \cdot x}\]
  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 2019199 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

  :herbie-target
  (/ (/ 1.0 x) x)

  (/ 1.0 (* x x)))