Average Error: 45.1 → 0.5
Time: 19.7s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{\frac{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}{i}}\]
\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) - 1.0}
↓
\frac{1}{\frac{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}{i}}
double f(double i) {
        double r4888480 = i;
        double r4888481 = r4888480 * r4888480;
        double r4888482 = r4888481 * r4888481;
        double r4888483 = 2.0;
        double r4888484 = r4888483 * r4888480;
        double r4888485 = r4888484 * r4888484;
        double r4888486 = r4888482 / r4888485;
        double r4888487 = 1.0;
        double r4888488 = r4888485 - r4888487;
        double r4888489 = r4888486 / r4888488;
        return r4888489;
}
↓
double f(double i) {
        double r4888490 = 1.0;
        double r4888491 = i;
        double r4888492 = 4.0;
        double r4888493 = r4888491 * r4888492;
        double r4888494 = 1.0;
        double r4888495 = r4888494 / r4888491;
        double r4888496 = r4888493 - r4888495;
        double r4888497 = r4888496 * r4888492;
        double r4888498 = r4888497 / r4888491;
        double r4888499 = r4888490 / r4888498;
        return r4888499;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.1

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.1

    \[\leadsto \color{blue}{\frac{i}{4 \cdot \left(4 \cdot i - \frac{1.0}{i}\right)}}\]
  3. Using strategy rm

  4. Applied clear-num0.5

    \[\leadsto \color{blue}{\frac{1}{\frac{4 \cdot \left(4 \cdot i - \frac{1.0}{i}\right)}{i}}}\]

  5. Final simplification0.5

    \[\leadsto \frac{1}{\frac{\left(i \cdot 4 - \frac{1.0}{i}\right) \cdot 4}{i}}\]

Reproduce

herbie shell --seed 2019162 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))