Average Error: 46.2 → 0.3
Time: 17.1s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]
\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) - 1.0}
↓
\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}
double f(double i) {
        double r2025420 = i;
        double r2025421 = r2025420 * r2025420;
        double r2025422 = r2025421 * r2025421;
        double r2025423 = 2.0;
        double r2025424 = r2025423 * r2025420;
        double r2025425 = r2025424 * r2025424;
        double r2025426 = r2025422 / r2025425;
        double r2025427 = 1.0;
        double r2025428 = r2025425 - r2025427;
        double r2025429 = r2025426 / r2025428;
        return r2025429;
}
↓
double f(double i) {
        double r2025430 = 0.25;
        double r2025431 = 4.0;
        double r2025432 = 1.0;
        double r2025433 = i;
        double r2025434 = r2025433 * r2025433;
        double r2025435 = r2025432 / r2025434;
        double r2025436 = r2025431 - r2025435;
        double r2025437 = r2025430 / r2025436;
        return r2025437;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.2

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019132 
(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)))