Average Error: 46.8 → 0.4
Time: 2.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{16 - 4 \cdot \frac{1}{{i}^{2}}}\]
\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}{16 - 4 \cdot \frac{1}{{i}^{2}}}
double f(double i) {
        double r75062 = i;
        double r75063 = r75062 * r75062;
        double r75064 = r75063 * r75063;
        double r75065 = 2.0;
        double r75066 = r75065 * r75062;
        double r75067 = r75066 * r75066;
        double r75068 = r75064 / r75067;
        double r75069 = 1.0;
        double r75070 = r75067 - r75069;
        double r75071 = r75068 / r75070;
        return r75071;
}
↓
double f(double i) {
        double r75072 = 1.0;
        double r75073 = 16.0;
        double r75074 = 4.0;
        double r75075 = i;
        double r75076 = 2.0;
        double r75077 = pow(r75075, r75076);
        double r75078 = r75072 / r75077;
        double r75079 = r75074 * r75078;
        double r75080 = r75073 - r75079;
        double r75081 = r75072 / r75080;
        return r75081;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.8

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

  2. Simplified16.2

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

  4. Applied clear-num16.6

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

  5. Taylor expanded around 0 0.4

    \[\leadsto \frac{1}{\color{blue}{16 - 4 \cdot \frac{1}{{i}^{2}}}}\]

  6. Final simplification0.4

    \[\leadsto \frac{1}{16 - 4 \cdot \frac{1}{{i}^{2}}}\]

Reproduce

herbie shell --seed 2019346 
(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)))