Average Error: 0.6 → 0.2
Time: 17.0s
Precision: 64
\[\frac{1.0}{x \cdot x}\]
↓
\[\frac{\frac{1.0}{x}}{x}\]
\frac{1.0}{x \cdot x}
↓
\frac{\frac{1.0}{x}}{x}
double f(double x) {
        double r18121468 = 1.0;
        double r18121469 = x;
        double r18121470 = r18121469 * r18121469;
        double r18121471 = r18121468 / r18121470;
        return r18121471;
}
↓
double f(double x) {
        double r18121472 = 1.0;
        double r18121473 = x;
        double r18121474 = r18121472 / r18121473;
        double r18121475 = r18121474 / r18121473;
        return r18121475;
}

Error

Bits error versus x

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Results

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Target

Original0.6
Target0.2
Herbie0.2
\[\frac{\frac{1.0}{x}}{x}\]

Derivation

  1. Initial program 0.6

    \[\frac{1.0}{x \cdot x}\]
  2. Using strategy rm

  3. Applied associate-/r*0.2

    \[\leadsto \color{blue}{\frac{\frac{1.0}{x}}{x}}\]

  4. Final simplification0.2

    \[\leadsto \frac{\frac{1.0}{x}}{x}\]

Reproduce

herbie shell --seed 2019168 +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)))