Average Error: 46.3 → 0.0
Time: 17.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}\]
\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{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}
double f(double i) {
        double r3308948 = i;
        double r3308949 = r3308948 * r3308948;
        double r3308950 = r3308949 * r3308949;
        double r3308951 = 2.0;
        double r3308952 = r3308951 * r3308948;
        double r3308953 = r3308952 * r3308952;
        double r3308954 = r3308950 / r3308953;
        double r3308955 = 1.0;
        double r3308956 = r3308953 - r3308955;
        double r3308957 = r3308954 / r3308956;
        return r3308957;
}
↓
double f(double i) {
        double r3308958 = i;
        double r3308959 = 2.0;
        double r3308960 = r3308958 / r3308959;
        double r3308961 = r3308958 * r3308959;
        double r3308962 = 1.0;
        double r3308963 = sqrt(r3308962);
        double r3308964 = r3308961 - r3308963;
        double r3308965 = r3308960 / r3308964;
        double r3308966 = r3308961 + r3308963;
        double r3308967 = r3308960 / r3308966;
        double r3308968 = r3308965 * r3308967;
        return r3308968;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.3

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

  2. Simplified15.2

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

  4. Applied associate-*l/15.6

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

  6. Applied add-sqr-sqrt15.6

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

  7. Applied difference-of-squares15.6

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

  8. Applied times-frac0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019174 
(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)))