Average Error: 45.6 → 0.0
Time: 20.8s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1.0}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1.0}}\]
\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{i}{2}}{i \cdot 2 - \sqrt{1.0}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1.0}}
double f(double i) {
        double r2316034 = i;
        double r2316035 = r2316034 * r2316034;
        double r2316036 = r2316035 * r2316035;
        double r2316037 = 2.0;
        double r2316038 = r2316037 * r2316034;
        double r2316039 = r2316038 * r2316038;
        double r2316040 = r2316036 / r2316039;
        double r2316041 = 1.0;
        double r2316042 = r2316039 - r2316041;
        double r2316043 = r2316040 / r2316042;
        return r2316043;
}
↓
double f(double i) {
        double r2316044 = i;
        double r2316045 = 2.0;
        double r2316046 = r2316044 / r2316045;
        double r2316047 = r2316044 * r2316045;
        double r2316048 = 1.0;
        double r2316049 = sqrt(r2316048);
        double r2316050 = r2316047 - r2316049;
        double r2316051 = r2316046 / r2316050;
        double r2316052 = r2316047 + r2316049;
        double r2316053 = r2316046 / r2316052;
        double r2316054 = r2316051 * r2316053;
        return r2316054;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.6

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

  2. Simplified15.5

    \[\leadsto \color{blue}{\frac{\frac{i}{2} \cdot \frac{i}{2}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}}\]
  3. Using strategy rm

  4. Applied add-sqr-sqrt15.5

    \[\leadsto \frac{\frac{i}{2} \cdot \frac{i}{2}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - \color{blue}{\sqrt{1.0} \cdot \sqrt{1.0}}}\]

  5. Applied difference-of-squares15.5

    \[\leadsto \frac{\frac{i}{2} \cdot \frac{i}{2}}{\color{blue}{\left(2 \cdot i + \sqrt{1.0}\right) \cdot \left(2 \cdot i - \sqrt{1.0}\right)}}\]

  6. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{\frac{i}{2}}{2 \cdot i + \sqrt{1.0}} \cdot \frac{\frac{i}{2}}{2 \cdot i - \sqrt{1.0}}}\]

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019134 
(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)))