Average Error: 46.3 → 0.1
Time: 18.0s
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 r41476 = i;
        double r41477 = r41476 * r41476;
        double r41478 = r41477 * r41477;
        double r41479 = 2.0;
        double r41480 = r41479 * r41476;
        double r41481 = r41480 * r41480;
        double r41482 = r41478 / r41481;
        double r41483 = 1.0;
        double r41484 = r41481 - r41483;
        double r41485 = r41482 / r41484;
        return r41485;
}
↓
double f(double i) {
        double r41486 = i;
        double r41487 = 2.0;
        double r41488 = r41487 * r41487;
        double r41489 = r41486 / r41488;
        double r41490 = r41487 * r41486;
        double r41491 = r41487 * r41490;
        double r41492 = 1.0;
        double r41493 = r41492 / r41486;
        double r41494 = r41491 - r41493;
        double r41495 = r41489 / r41494;
        return r41495;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  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 2019325 
(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)))