Average Error: 46.7 → 0.2
Time: 20.1s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(2 \cdot 2\right) \cdot \left(2 \cdot \left(2 \cdot i\right) - \frac{1}{i}\right)}\]
\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{i}{\left(2 \cdot 2\right) \cdot \left(2 \cdot \left(2 \cdot i\right) - \frac{1}{i}\right)}
double f(double i) {
        double r58093 = i;
        double r58094 = r58093 * r58093;
        double r58095 = r58094 * r58094;
        double r58096 = 2.0;
        double r58097 = r58096 * r58093;
        double r58098 = r58097 * r58097;
        double r58099 = r58095 / r58098;
        double r58100 = 1.0;
        double r58101 = r58098 - r58100;
        double r58102 = r58099 / r58101;
        return r58102;
}
↓
double f(double i) {
        double r58103 = i;
        double r58104 = 2.0;
        double r58105 = r58104 * r58104;
        double r58106 = r58104 * r58103;
        double r58107 = r58104 * r58106;
        double r58108 = 1.0;
        double r58109 = r58108 / r58103;
        double r58110 = r58107 - r58109;
        double r58111 = r58105 * r58110;
        double r58112 = r58103 / r58111;
        return r58112;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  2. Simplified0.1

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

  4. Applied div-inv0.2

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

  6. Applied frac-times0.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 
(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)))