Average Error: 46.4 → 0.4
Time: 16.9s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{1}{\frac{\left(i \cdot 2\right) \cdot 2 - \frac{1}{i}}{\frac{\frac{i}{2}}{2}}}\]
\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{1}{\frac{\left(i \cdot 2\right) \cdot 2 - \frac{1}{i}}{\frac{\frac{i}{2}}{2}}}
double f(double i) {
        double r72259 = i;
        double r72260 = r72259 * r72259;
        double r72261 = r72260 * r72260;
        double r72262 = 2.0;
        double r72263 = r72262 * r72259;
        double r72264 = r72263 * r72263;
        double r72265 = r72261 / r72264;
        double r72266 = 1.0;
        double r72267 = r72264 - r72266;
        double r72268 = r72265 / r72267;
        return r72268;
}
↓
double f(double i) {
        double r72269 = 1.0;
        double r72270 = i;
        double r72271 = 2.0;
        double r72272 = r72270 * r72271;
        double r72273 = r72272 * r72271;
        double r72274 = 1.0;
        double r72275 = r72274 / r72270;
        double r72276 = r72273 - r72275;
        double r72277 = r72270 / r72271;
        double r72278 = r72277 / r72271;
        double r72279 = r72276 / r72278;
        double r72280 = r72269 / r72279;
        return r72280;
}

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. Simplified0.1

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

  4. Applied clear-num0.4

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

  5. Simplified0.4

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

  6. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(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)))