Average Error: 46.5 → 0.3
Time: 11.9s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}\]
\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}
↓
\frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}
double f(double i) {
        double r62582 = i;
        double r62583 = r62582 * r62582;
        double r62584 = r62583 * r62583;
        double r62585 = 2.0;
        double r62586 = r62585 * r62582;
        double r62587 = r62586 * r62586;
        double r62588 = r62584 / r62587;
        double r62589 = 1.0;
        double r62590 = r62587 - r62589;
        double r62591 = r62588 / r62590;
        return r62591;
}
↓
double f(double i) {
        double r62592 = 1.0;
        double r62593 = 2.0;
        double r62594 = r62593 * r62593;
        double r62595 = r62592 / r62594;
        double r62596 = 1.0;
        double r62597 = i;
        double r62598 = r62597 * r62597;
        double r62599 = r62596 / r62598;
        double r62600 = r62594 - r62599;
        double r62601 = r62595 / r62600;
        return r62601;
}

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. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{2 \cdot 2}}{2 \cdot 2 - \frac{1}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019195 +o rules:numerics
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2.0 i) (* 2.0 i))) (- (* (* 2.0 i) (* 2.0 i)) 1.0)))