Average Error: 46.0 → 0.3
Time: 19.4s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{\left(4 - \frac{1.0}{i \cdot i}\right) \cdot 4}\]
\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}{\left(4 - \frac{1.0}{i \cdot i}\right) \cdot 4}
double f(double i) {
        double r2001406 = i;
        double r2001407 = r2001406 * r2001406;
        double r2001408 = r2001407 * r2001407;
        double r2001409 = 2.0;
        double r2001410 = r2001409 * r2001406;
        double r2001411 = r2001410 * r2001410;
        double r2001412 = r2001408 / r2001411;
        double r2001413 = 1.0;
        double r2001414 = r2001411 - r2001413;
        double r2001415 = r2001412 / r2001414;
        return r2001415;
}
↓
double f(double i) {
        double r2001416 = 1.0;
        double r2001417 = 4.0;
        double r2001418 = 1.0;
        double r2001419 = i;
        double r2001420 = r2001419 * r2001419;
        double r2001421 = r2001418 / r2001420;
        double r2001422 = r2001417 - r2001421;
        double r2001423 = r2001422 * r2001417;
        double r2001424 = r2001416 / r2001423;
        return r2001424;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.0

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

  2. Simplified15.9

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

  4. Applied clear-num16.2

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019128 
(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)))