Average Error: 0.6 → 0.2
Time: 4.0s
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 r448514 = 1.0;
        double r448515 = x;
        double r448516 = r448515 * r448515;
        double r448517 = r448514 / r448516;
        return r448517;
}
↓
double f(double x) {
        double r448518 = 1.0;
        double r448519 = x;
        double r448520 = r448518 / r448519;
        double r448521 = r448520 / r448519;
        return r448521;
}

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 2020001 +o rules:numerics
(FPCore (x)
  :name "Numeric.SpecFunctions:$slogFactorial from math-functions-0.1.5.2, A"
  :precision binary64

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

  (/ 1 (* x x)))