Average Error: 46.8 → 0.3
Time: 14.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}\]
\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{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}
double f(double i) {
        double r59347 = i;
        double r59348 = r59347 * r59347;
        double r59349 = r59348 * r59348;
        double r59350 = 2.0;
        double r59351 = r59350 * r59347;
        double r59352 = r59351 * r59351;
        double r59353 = r59349 / r59352;
        double r59354 = 1.0;
        double r59355 = r59352 - r59354;
        double r59356 = r59353 / r59355;
        return r59356;
}
↓
double f(double i) {
        double r59357 = 1.0;
        double r59358 = 2.0;
        double r59359 = r59358 * r59358;
        double r59360 = r59357 / r59359;
        double r59361 = 1.0;
        double r59362 = i;
        double r59363 = r59362 * r59362;
        double r59364 = r59361 / r59363;
        double r59365 = r59359 - r59364;
        double r59366 = r59360 / r59365;
        return r59366;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.8

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019198 +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)))