Average Error: 46.5 → 0.2
Time: 34.3s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{4 \cdot i - \frac{1}{i}}\]
\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}}{4 \cdot i - \frac{1}{i}}
double f(double i) {
        double r3267360 = i;
        double r3267361 = r3267360 * r3267360;
        double r3267362 = r3267361 * r3267361;
        double r3267363 = 2.0;
        double r3267364 = r3267363 * r3267360;
        double r3267365 = r3267364 * r3267364;
        double r3267366 = r3267362 / r3267365;
        double r3267367 = 1.0;
        double r3267368 = r3267365 - r3267367;
        double r3267369 = r3267366 / r3267368;
        return r3267369;
}
↓
double f(double i) {
        double r3267370 = i;
        double r3267371 = 2.0;
        double r3267372 = r3267371 * r3267371;
        double r3267373 = r3267370 / r3267372;
        double r3267374 = 4.0;
        double r3267375 = r3267374 * r3267370;
        double r3267376 = 1.0;
        double r3267377 = r3267376 / r3267370;
        double r3267378 = r3267375 - r3267377;
        double r3267379 = r3267373 / r3267378;
        return r3267379;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.5

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

  2. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{4 \cdot i - 1 \cdot \frac{1}{i}}}\]

  4. Simplified0.2

    \[\leadsto \frac{\frac{i}{2 \cdot 2}}{\color{blue}{4 \cdot i - \frac{1}{i}}}\]

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019168 +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)))