Average Error: 45.3 → 0.1
Time: 16.0s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]
\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) - 1.0}
↓
\frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}
double f(double i) {
        double r1824153 = i;
        double r1824154 = r1824153 * r1824153;
        double r1824155 = r1824154 * r1824154;
        double r1824156 = 2.0;
        double r1824157 = r1824156 * r1824153;
        double r1824158 = r1824157 * r1824157;
        double r1824159 = r1824155 / r1824158;
        double r1824160 = 1.0;
        double r1824161 = r1824158 - r1824160;
        double r1824162 = r1824159 / r1824161;
        return r1824162;
}
↓
double f(double i) {
        double r1824163 = 0.25;
        double r1824164 = 2.0;
        double r1824165 = 1.0;
        double r1824166 = sqrt(r1824165);
        double r1824167 = i;
        double r1824168 = r1824166 / r1824167;
        double r1824169 = r1824164 - r1824168;
        double r1824170 = r1824163 / r1824169;
        double r1824171 = 1.0;
        double r1824172 = r1824164 + r1824168;
        double r1824173 = r1824171 / r1824172;
        double r1824174 = r1824170 * r1824173;
        return r1824174;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.3

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt0.4

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{\color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}}}{i \cdot i}}\]

  5. Applied times-frac0.5

    \[\leadsto \frac{\frac{1}{4}}{4 - \color{blue}{\frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}}\]

  6. Applied add-sqr-sqrt0.5

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\sqrt{4} \cdot \sqrt{4}} - \frac{\sqrt{1.0}}{i} \cdot \frac{\sqrt{1.0}}{i}}\]

  7. Applied difference-of-squares0.5

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}}\]

  8. Applied *-un-lft-identity0.5

    \[\leadsto \frac{\color{blue}{1 \cdot \frac{1}{4}}}{\left(\sqrt{4} + \frac{\sqrt{1.0}}{i}\right) \cdot \left(\sqrt{4} - \frac{\sqrt{1.0}}{i}\right)}\]

  9. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{1}{\sqrt{4} + \frac{\sqrt{1.0}}{i}} \cdot \frac{\frac{1}{4}}{\sqrt{4} - \frac{\sqrt{1.0}}{i}}}\]

  10. Final simplification0.1

    \[\leadsto \frac{\frac{1}{4}}{2 - \frac{\sqrt{1.0}}{i}} \cdot \frac{1}{2 + \frac{\sqrt{1.0}}{i}}\]

Reproduce

herbie shell --seed 2019135 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :pre (and (> i 0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1.0)))