Average Error: 46.7 → 0.2
Time: 18.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r3465246 = i;
        double r3465247 = r3465246 * r3465246;
        double r3465248 = r3465247 * r3465247;
        double r3465249 = 2.0;
        double r3465250 = r3465249 * r3465246;
        double r3465251 = r3465250 * r3465250;
        double r3465252 = r3465248 / r3465251;
        double r3465253 = 1.0;
        double r3465254 = r3465251 - r3465253;
        double r3465255 = r3465252 / r3465254;
        return r3465255;
}
↓
double f(double i) {
        double r3465256 = i;
        double r3465257 = 4.0;
        double r3465258 = r3465257 * r3465256;
        double r3465259 = 1.0;
        double r3465260 = r3465259 / r3465256;
        double r3465261 = r3465258 - r3465260;
        double r3465262 = 2.0;
        double r3465263 = r3465262 * r3465262;
        double r3465264 = r3465261 * r3465263;
        double r3465265 = r3465256 / r3465264;
        return r3465265;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  2. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - 1 \cdot \frac{1}{i}\right)}}\]

  4. Simplified0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - \frac{1}{i}\right)}}\]

  5. Final simplification0.2

    \[\leadsto \frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]

Reproduce

herbie shell --seed 2019169 
(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)))