Average Error: 46.7 → 0.4
Time: 16.5s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\left(2 \cdot 2 - \frac{\frac{1}{i}}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{\frac{1}{i}}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r54804 = i;
        double r54805 = r54804 * r54804;
        double r54806 = r54805 * r54805;
        double r54807 = 2.0;
        double r54808 = r54807 * r54804;
        double r54809 = r54808 * r54808;
        double r54810 = r54806 / r54809;
        double r54811 = 1.0;
        double r54812 = r54809 - r54811;
        double r54813 = r54810 / r54812;
        return r54813;
}
↓
double f(double i) {
        double r54814 = 1.0;
        double r54815 = 2.0;
        double r54816 = r54815 * r54815;
        double r54817 = 1.0;
        double r54818 = i;
        double r54819 = r54817 / r54818;
        double r54820 = r54819 / r54818;
        double r54821 = r54816 - r54820;
        double r54822 = r54821 * r54816;
        double r54823 = r54814 / r54822;
        return r54823;
}

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. Simplified0.4

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

  4. Applied associate-/r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2019326 +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)))