Average Error: 45.8 → 0.1
Time: 23.7s
Precision: 64
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{4}}{i \cdot 4 - \frac{1.0}{i}}\]
double f(double i) {
        double r3596541 = i;
        double r3596542 = r3596541 * r3596541;
        double r3596543 = r3596542 * r3596542;
        double r3596544 = 2.0;
        double r3596545 = r3596544 * r3596541;
        double r3596546 = r3596545 * r3596545;
        double r3596547 = r3596543 / r3596546;
        double r3596548 = 1.0;
        double r3596549 = r3596546 - r3596548;
        double r3596550 = r3596547 / r3596549;
        return r3596550;
}
↓
double f(double i) {
        double r3596551 = i;
        double r3596552 = 4.0;
        double r3596553 = r3596551 / r3596552;
        double r3596554 = r3596551 * r3596552;
        double r3596555 = 1.0;
        double r3596556 = r3596555 / r3596551;
        double r3596557 = r3596554 - r3596556;
        double r3596558 = r3596553 / r3596557;
        return r3596558;
}


\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{i}{4}}{i \cdot 4 - \frac{1.0}{i}}

Error

Bits error versus i

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. Simplified15.6

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

  4. Applied times-frac15.6

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

  6. Applied pow115.6

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

  7. Applied pow115.6

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

  8. Applied pow-prod-down15.6

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019101 
(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)))