Average Error: 46.5 → 0.0
Time: 28.4s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{\left(2 \cdot i - \sqrt{1}\right) \cdot 2} \cdot \frac{i}{\sqrt{1} + 2 \cdot i}\]
\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}
↓
\frac{\frac{i}{2}}{\left(2 \cdot i - \sqrt{1}\right) \cdot 2} \cdot \frac{i}{\sqrt{1} + 2 \cdot i}
double f(double i) {
        double r4877450 = i;
        double r4877451 = r4877450 * r4877450;
        double r4877452 = r4877451 * r4877451;
        double r4877453 = 2.0;
        double r4877454 = r4877453 * r4877450;
        double r4877455 = r4877454 * r4877454;
        double r4877456 = r4877452 / r4877455;
        double r4877457 = 1.0;
        double r4877458 = r4877455 - r4877457;
        double r4877459 = r4877456 / r4877458;
        return r4877459;
}
↓
double f(double i) {
        double r4877460 = i;
        double r4877461 = 2.0;
        double r4877462 = r4877460 / r4877461;
        double r4877463 = r4877461 * r4877460;
        double r4877464 = 1.0;
        double r4877465 = sqrt(r4877464);
        double r4877466 = r4877463 - r4877465;
        double r4877467 = r4877466 * r4877461;
        double r4877468 = r4877462 / r4877467;
        double r4877469 = r4877465 + r4877463;
        double r4877470 = r4877460 / r4877469;
        double r4877471 = r4877468 * r4877470;
        return r4877471;
}

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. Simplified15.3

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

  4. Applied add-sqr-sqrt15.3

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

  5. Applied difference-of-squares15.3

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

  6. Applied div-inv15.3

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

  7. Applied times-frac0.1

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

  8. Applied associate-*l*0.1

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

  9. Simplified0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2019200 +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)))