Average Error: 45.9 → 0.1
Time: 24.6s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]
\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) - 1.0}
↓
\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}
double f(double i) {
        double r2899294 = i;
        double r2899295 = r2899294 * r2899294;
        double r2899296 = r2899295 * r2899295;
        double r2899297 = 2.0;
        double r2899298 = r2899297 * r2899294;
        double r2899299 = r2899298 * r2899298;
        double r2899300 = r2899296 / r2899299;
        double r2899301 = 1.0;
        double r2899302 = r2899299 - r2899301;
        double r2899303 = r2899300 / r2899302;
        return r2899303;
}
↓
double f(double i) {
        double r2899304 = 0.25;
        double r2899305 = 2.0;
        double r2899306 = 1.0;
        double r2899307 = sqrt(r2899306);
        double r2899308 = i;
        double r2899309 = r2899307 / r2899308;
        double r2899310 = r2899305 - r2899309;
        double r2899311 = r2899304 / r2899310;
        double r2899312 = 1.0;
        double r2899313 = r2899305 + r2899309;
        double r2899314 = r2899312 / r2899313;
        double r2899315 = r2899311 * r2899314;
        return r2899315;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.9

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.3

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{\color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}}}{i \cdot i}}\]

  5. Applied times-frac0.4

    \[\leadsto \frac{\frac{1}{4}}{4 - \color{blue}{\frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}}\]

  6. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\sqrt{4} \cdot \sqrt{4}} - \frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}\]

  7. Applied difference-of-squares0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}}\]

  8. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{4}}}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}\]

  9. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{\sqrt{4} + \frac{\sqrt{1.0}}{i}} \cdot \frac{\frac{1}{4}}{\sqrt{4} - \frac{\sqrt{1.0}}{i}}}\]

  10. Final simplification0.1

    \[\leadsto \frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]

Reproduce

herbie shell --seed 2019143 +o rules:numerics
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))