Average Error: 46.3 → 0.1
Time: 13.6s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2 \cdot 2}}{\left(2 \cdot 2\right) \cdot i - \frac{1}{i}}\]
\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{\frac{i}{2 \cdot 2}}{\left(2 \cdot 2\right) \cdot i - \frac{1}{i}}
double f(double i) {
        double r67481 = i;
        double r67482 = r67481 * r67481;
        double r67483 = r67482 * r67482;
        double r67484 = 2.0;
        double r67485 = r67484 * r67481;
        double r67486 = r67485 * r67485;
        double r67487 = r67483 / r67486;
        double r67488 = 1.0;
        double r67489 = r67486 - r67488;
        double r67490 = r67487 / r67489;
        return r67490;
}
↓
double f(double i) {
        double r67491 = i;
        double r67492 = 2.0;
        double r67493 = r67492 * r67492;
        double r67494 = r67491 / r67493;
        double r67495 = r67493 * r67491;
        double r67496 = 1.0;
        double r67497 = r67496 / r67491;
        double r67498 = r67495 - r67497;
        double r67499 = r67494 / r67498;
        return r67499;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  2. Simplified0.2

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

  4. Applied associate-/r*0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))