Average Error: 46.6 → 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 r84930 = i;
        double r84931 = r84930 * r84930;
        double r84932 = r84931 * r84931;
        double r84933 = 2.0;
        double r84934 = r84933 * r84930;
        double r84935 = r84934 * r84934;
        double r84936 = r84932 / r84935;
        double r84937 = 1.0;
        double r84938 = r84935 - r84937;
        double r84939 = r84936 / r84938;
        return r84939;
}
↓
double f(double i) {
        double r84940 = 1.0;
        double r84941 = 16.0;
        double r84942 = 4.0;
        double r84943 = i;
        double r84944 = 2.0;
        double r84945 = pow(r84943, r84944);
        double r84946 = r84940 / r84945;
        double r84947 = r84942 * r84946;
        double r84948 = r84941 - r84947;
        double r84949 = r84940 / r84948;
        return r84949;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.6

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

  2. Simplified16.6

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

  4. Applied clear-num17.0

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

  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 2020083 
(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)))