Average Error: 46.4 → 0.1
Time: 12.8s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{\left(i \cdot 2 - \sqrt{1}\right) \cdot 2} \cdot \frac{i}{i \cdot 2 + \sqrt{1}}\]
\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(i \cdot 2 - \sqrt{1}\right) \cdot 2} \cdot \frac{i}{i \cdot 2 + \sqrt{1}}
double f(double i) {
        double r3274464 = i;
        double r3274465 = r3274464 * r3274464;
        double r3274466 = r3274465 * r3274465;
        double r3274467 = 2.0;
        double r3274468 = r3274467 * r3274464;
        double r3274469 = r3274468 * r3274468;
        double r3274470 = r3274466 / r3274469;
        double r3274471 = 1.0;
        double r3274472 = r3274469 - r3274471;
        double r3274473 = r3274470 / r3274472;
        return r3274473;
}
↓
double f(double i) {
        double r3274474 = i;
        double r3274475 = 2.0;
        double r3274476 = r3274474 / r3274475;
        double r3274477 = r3274474 * r3274475;
        double r3274478 = 1.0;
        double r3274479 = sqrt(r3274478);
        double r3274480 = r3274477 - r3274479;
        double r3274481 = r3274480 * r3274475;
        double r3274482 = r3274476 / r3274481;
        double r3274483 = r3274477 + r3274479;
        double r3274484 = r3274474 / r3274483;
        double r3274485 = r3274482 * r3274484;
        return r3274485;
}

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. Simplified15.5

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

  4. Applied add-sqr-sqrt15.5

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

  5. Applied difference-of-squares15.5

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

  6. Applied div-inv15.5

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

  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. Using strategy rm

  10. Applied frac-times0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 
(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)))