Average Error: 45.8 → 0.3
Time: 12.9s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]
\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{1}{4}}{4 - \frac{1.0}{i \cdot i}}
double f(double i) {
        double r3160468 = i;
        double r3160469 = r3160468 * r3160468;
        double r3160470 = r3160469 * r3160469;
        double r3160471 = 2.0;
        double r3160472 = r3160471 * r3160468;
        double r3160473 = r3160472 * r3160472;
        double r3160474 = r3160470 / r3160473;
        double r3160475 = 1.0;
        double r3160476 = r3160473 - r3160475;
        double r3160477 = r3160474 / r3160476;
        return r3160477;
}
↓
double f(double i) {
        double r3160478 = 0.25;
        double r3160479 = 4.0;
        double r3160480 = 1.0;
        double r3160481 = i;
        double r3160482 = r3160481 * r3160481;
        double r3160483 = r3160480 / r3160482;
        double r3160484 = r3160479 - r3160483;
        double r3160485 = r3160478 / r3160484;
        return r3160485;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.8

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]

  3. Final simplification0.3

    \[\leadsto \frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019163 
(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)))