Average Error: 46.5 → 0.2
Time: 20.0s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r52423 = i;
        double r52424 = r52423 * r52423;
        double r52425 = r52424 * r52424;
        double r52426 = 2.0;
        double r52427 = r52426 * r52423;
        double r52428 = r52427 * r52427;
        double r52429 = r52425 / r52428;
        double r52430 = 1.0;
        double r52431 = r52428 - r52430;
        double r52432 = r52429 / r52431;
        return r52432;
}
↓
double f(double i) {
        double r52433 = i;
        double r52434 = 2.0;
        double r52435 = r52434 * r52434;
        double r52436 = r52433 / r52435;
        double r52437 = 1.0;
        double r52438 = r52434 * r52433;
        double r52439 = r52434 * r52438;
        double r52440 = 1.0;
        double r52441 = r52440 / r52433;
        double r52442 = r52439 - r52441;
        double r52443 = r52437 / r52442;
        double r52444 = r52436 * r52443;
        return r52444;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\frac{\frac{i}{2 \cdot 2}}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}}\]
  3. Using strategy rm

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))