Average Error: 46.4 → 0.2
Time: 14.3s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \left(\sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}} \cdot \sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}\right)\]
\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}
↓
\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \left(\sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}} \cdot \sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}\right)
double f(double i) {
        double r2433299 = i;
        double r2433300 = r2433299 * r2433299;
        double r2433301 = r2433300 * r2433300;
        double r2433302 = 2.0;
        double r2433303 = r2433302 * r2433299;
        double r2433304 = r2433303 * r2433303;
        double r2433305 = r2433301 / r2433304;
        double r2433306 = 1.0;
        double r2433307 = r2433304 - r2433306;
        double r2433308 = r2433305 / r2433307;
        return r2433308;
}
↓
double f(double i) {
        double r2433309 = i;
        double r2433310 = 2.0;
        double r2433311 = r2433309 / r2433310;
        double r2433312 = r2433309 * r2433310;
        double r2433313 = 1.0;
        double r2433314 = sqrt(r2433313);
        double r2433315 = r2433312 - r2433314;
        double r2433316 = r2433311 / r2433315;
        double r2433317 = r2433312 + r2433314;
        double r2433318 = r2433311 / r2433317;
        double r2433319 = sqrt(r2433318);
        double r2433320 = r2433319 * r2433319;
        double r2433321 = r2433316 * r2433320;
        return r2433321;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.4

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]

  2. Simplified16.0

    \[\leadsto \color{blue}{\frac{\frac{i}{2} \cdot \frac{i}{2}}{\left(i \cdot 2\right) \cdot \left(i \cdot 2\right) - 1}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt16.0

    \[\leadsto \frac{\frac{i}{2} \cdot \frac{i}{2}}{\left(i \cdot 2\right) \cdot \left(i \cdot 2\right) - \color{blue}{\sqrt{1} \cdot \sqrt{1}}}\]

  5. Applied difference-of-squares16.0

    \[\leadsto \frac{\frac{i}{2} \cdot \frac{i}{2}}{\color{blue}{\left(i \cdot 2 + \sqrt{1}\right) \cdot \left(i \cdot 2 - \sqrt{1}\right)}}\]

  6. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}}}\]
  7. Using strategy rm

  8. Applied add-sqr-sqrt0.2

    \[\leadsto \color{blue}{\left(\sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}} \cdot \sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}\right)} \cdot \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}}\]

  9. Final simplification0.2

    \[\leadsto \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \left(\sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}} \cdot \sqrt{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}\right)\]

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))