Average Error: 45.8 → 0.2
Time: 22.5s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{\frac{i}{4}}{i \cdot 4 - \frac{1.0}{i}}\]
\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{i}{4}}{i \cdot 4 - \frac{1.0}{i}}
double f(double i) {
        double r3833067 = i;
        double r3833068 = r3833067 * r3833067;
        double r3833069 = r3833068 * r3833068;
        double r3833070 = 2.0;
        double r3833071 = r3833070 * r3833067;
        double r3833072 = r3833071 * r3833071;
        double r3833073 = r3833069 / r3833072;
        double r3833074 = 1.0;
        double r3833075 = r3833072 - r3833074;
        double r3833076 = r3833073 / r3833075;
        return r3833076;
}
↓
double f(double i) {
        double r3833077 = i;
        double r3833078 = 4.0;
        double r3833079 = r3833077 / r3833078;
        double r3833080 = r3833077 * r3833078;
        double r3833081 = 1.0;
        double r3833082 = r3833081 / r3833077;
        double r3833083 = r3833080 - r3833082;
        double r3833084 = r3833079 / r3833083;
        return r3833084;
}

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. Simplified15.1

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

  4. Applied times-frac15.2

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

  6. Applied pow115.2

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

  7. Applied pow115.2

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

  8. Applied pow-prod-down15.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019124 
(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)))