Average Error: 46.8 → 0.3
Time: 2.0m
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{\frac{1}{2}}{2}}{2 \cdot 2 - \frac{1}{i \cdot i}}\]
\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{\frac{1}{2}}{2}}{2 \cdot 2 - \frac{1}{i \cdot i}}
double f(double i) {
        double r299106 = i;
        double r299107 = r299106 * r299106;
        double r299108 = r299107 * r299107;
        double r299109 = 2.0;
        double r299110 = r299109 * r299106;
        double r299111 = r299110 * r299110;
        double r299112 = r299108 / r299111;
        double r299113 = 1.0;
        double r299114 = r299111 - r299113;
        double r299115 = r299112 / r299114;
        return r299115;
}
↓
double f(double i) {
        double r299116 = 1.0;
        double r299117 = 2.0;
        double r299118 = r299116 / r299117;
        double r299119 = r299118 / r299117;
        double r299120 = r299117 * r299117;
        double r299121 = 1.0;
        double r299122 = i;
        double r299123 = r299122 * r299122;
        double r299124 = r299121 / r299123;
        double r299125 = r299120 - r299124;
        double r299126 = r299119 / r299125;
        return r299126;
}

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. Simplified0.3

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

  3. Final simplification0.3

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

Reproduce

herbie shell --seed 2019198 
(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)))