Average Error: 46.3 → 0.4
Time: 21.0s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{1}{\left(2 \cdot 2 - \frac{1}{i \cdot i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r68545 = i;
        double r68546 = r68545 * r68545;
        double r68547 = r68546 * r68546;
        double r68548 = 2.0;
        double r68549 = r68548 * r68545;
        double r68550 = r68549 * r68549;
        double r68551 = r68547 / r68550;
        double r68552 = 1.0;
        double r68553 = r68550 - r68552;
        double r68554 = r68551 / r68553;
        return r68554;
}
↓
double f(double i) {
        double r68555 = 1.0;
        double r68556 = 2.0;
        double r68557 = r68556 * r68556;
        double r68558 = 1.0;
        double r68559 = i;
        double r68560 = r68559 * r68559;
        double r68561 = r68558 / r68560;
        double r68562 = r68557 - r68561;
        double r68563 = r68562 * r68557;
        double r68564 = r68555 / r68563;
        return r68564;
}

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. Simplified0.4

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

  3. Final simplification0.4

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(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)))