Average Error: 47.1 → 0.1
Time: 17.0s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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}
↓
\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r94398 = i;
        double r94399 = r94398 * r94398;
        double r94400 = r94399 * r94399;
        double r94401 = 2.0;
        double r94402 = r94401 * r94398;
        double r94403 = r94402 * r94402;
        double r94404 = r94400 / r94403;
        double r94405 = 1.0;
        double r94406 = r94403 - r94405;
        double r94407 = r94404 / r94406;
        return r94407;
}
↓
double f(double i) {
        double r94408 = i;
        double r94409 = 2.0;
        double r94410 = r94409 * r94409;
        double r94411 = r94408 / r94410;
        double r94412 = r94409 * r94408;
        double r94413 = r94409 * r94412;
        double r94414 = 1.0;
        double r94415 = r94414 / r94408;
        double r94416 = r94413 - r94415;
        double r94417 = r94411 / r94416;
        return r94417;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 47.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))