Average Error: 0.5 → 0
Time: 3.5s
Precision: 64
\[\frac{1}{x \cdot x}\]
↓
\[{x}^{-2} \cdot 1\]
\frac{1}{x \cdot x}
↓
{x}^{-2} \cdot 1
double f(double x) {
        double r429094 = 1.0;
        double r429095 = x;
        double r429096 = r429095 * r429095;
        double r429097 = r429094 / r429096;
        return r429097;
}
↓
double f(double x) {
        double r429098 = x;
        double r429099 = -2.0;
        double r429100 = pow(r429098, r429099);
        double r429101 = 1.0;
        double r429102 = r429100 * r429101;
        return r429102;
}

Error

Bits error versus x

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Results

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Target

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

Derivation

  1. Initial program 0.5

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

  3. Applied div-inv0.5

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

  4. Simplified0.2

    \[\leadsto 1 \cdot \color{blue}{\frac{\frac{1}{x}}{x}}\]
  5. Using strategy rm

  6. Applied pow10.2

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

  7. Applied inv-pow0.2

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

  8. Applied pow-div0

    \[\leadsto 1 \cdot \color{blue}{{x}^{\left(-1 - 1\right)}}\]

  9. Simplified0

    \[\leadsto 1 \cdot {x}^{\color{blue}{-2}}\]

  10. Final simplification0

    \[\leadsto {x}^{-2} \cdot 1\]

Reproduce

herbie shell --seed 2019194 
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"

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

  (/ 1.0 (* x x)))