Average Error: 46.5 → 0.2
Time: 19.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}\]
\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}
↓
\frac{i}{2 \cdot 2} \cdot \frac{1}{2 \cdot \left(2 \cdot i\right) - \frac{1}{i}}
double f(double i) {
        double r42369 = i;
        double r42370 = r42369 * r42369;
        double r42371 = r42370 * r42370;
        double r42372 = 2.0;
        double r42373 = r42372 * r42369;
        double r42374 = r42373 * r42373;
        double r42375 = r42371 / r42374;
        double r42376 = 1.0;
        double r42377 = r42374 - r42376;
        double r42378 = r42375 / r42377;
        return r42378;
}
↓
double f(double i) {
        double r42379 = i;
        double r42380 = 2.0;
        double r42381 = r42380 * r42380;
        double r42382 = r42379 / r42381;
        double r42383 = 1.0;
        double r42384 = r42380 * r42379;
        double r42385 = r42380 * r42384;
        double r42386 = 1.0;
        double r42387 = r42386 / r42379;
        double r42388 = r42385 - r42387;
        double r42389 = r42383 / r42388;
        double r42390 = r42382 * r42389;
        return r42390;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.5

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

  2. Simplified0.1

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

  4. Applied div-inv0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (i)
  :name "Octave 3.8, jcobi/4, as called"
  :precision binary64
  :pre (and (> i 0.0))
  (/ (/ (* (* i i) (* i i)) (* (* 2 i) (* 2 i))) (- (* (* 2 i) (* 2 i)) 1)))