Average Error: 46.4 → 0.2
Time: 13.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(i \cdot \left(2 \cdot 2\right) - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{i}{\left(i \cdot \left(2 \cdot 2\right) - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r3557190 = i;
        double r3557191 = r3557190 * r3557190;
        double r3557192 = r3557191 * r3557191;
        double r3557193 = 2.0;
        double r3557194 = r3557193 * r3557190;
        double r3557195 = r3557194 * r3557194;
        double r3557196 = r3557192 / r3557195;
        double r3557197 = 1.0;
        double r3557198 = r3557195 - r3557197;
        double r3557199 = r3557196 / r3557198;
        return r3557199;
}
↓
double f(double i) {
        double r3557200 = i;
        double r3557201 = 2.0;
        double r3557202 = r3557201 * r3557201;
        double r3557203 = r3557200 * r3557202;
        double r3557204 = 1.0;
        double r3557205 = r3557204 / r3557200;
        double r3557206 = r3557203 - r3557205;
        double r3557207 = r3557206 * r3557202;
        double r3557208 = r3557200 / r3557207;
        return r3557208;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.4

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

  2. Simplified0.2

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

  3. Final simplification0.2

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

Reproduce

herbie shell --seed 2019171 
(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)))