Average Error: 45.4 → 0.3
Time: 32.6s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{1}{\left(4 - \frac{1.0}{i \cdot i}\right) \cdot 4}\]
\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) - 1.0}
↓
\frac{1}{\left(4 - \frac{1.0}{i \cdot i}\right) \cdot 4}
double f(double i) {
        double r8595348 = i;
        double r8595349 = r8595348 * r8595348;
        double r8595350 = r8595349 * r8595349;
        double r8595351 = 2.0;
        double r8595352 = r8595351 * r8595348;
        double r8595353 = r8595352 * r8595352;
        double r8595354 = r8595350 / r8595353;
        double r8595355 = 1.0;
        double r8595356 = r8595353 - r8595355;
        double r8595357 = r8595354 / r8595356;
        return r8595357;
}
↓
double f(double i) {
        double r8595358 = 1.0;
        double r8595359 = 4.0;
        double r8595360 = 1.0;
        double r8595361 = i;
        double r8595362 = r8595361 * r8595361;
        double r8595363 = r8595360 / r8595362;
        double r8595364 = r8595359 - r8595363;
        double r8595365 = r8595364 * r8595359;
        double r8595366 = r8595358 / r8595365;
        return r8595366;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.4

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

  2. Simplified15.1

    \[\leadsto \color{blue}{\frac{i \cdot i}{\left(4 \cdot \left(i \cdot i\right) - 1.0\right) \cdot 4}}\]
  3. Using strategy rm

  4. Applied clear-num15.4

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019125 
(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)))