Average Error: 46.9 → 0.2
Time: 18.5s
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 r59421 = i;
        double r59422 = r59421 * r59421;
        double r59423 = r59422 * r59422;
        double r59424 = 2.0;
        double r59425 = r59424 * r59421;
        double r59426 = r59425 * r59425;
        double r59427 = r59423 / r59426;
        double r59428 = 1.0;
        double r59429 = r59426 - r59428;
        double r59430 = r59427 / r59429;
        return r59430;
}
↓
double f(double i) {
        double r59431 = i;
        double r59432 = 2.0;
        double r59433 = r59432 * r59432;
        double r59434 = r59431 / r59433;
        double r59435 = 1.0;
        double r59436 = r59432 * r59431;
        double r59437 = r59432 * r59436;
        double r59438 = 1.0;
        double r59439 = r59438 / r59431;
        double r59440 = r59437 - r59439;
        double r59441 = r59435 / r59440;
        double r59442 = r59434 * r59441;
        return r59442;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.9

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

  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 2019347 
(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)))