Average Error: 46.4 → 0.0
Time: 16.7s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}\]
\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}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}
double f(double i) {
        double r4067208 = i;
        double r4067209 = r4067208 * r4067208;
        double r4067210 = r4067209 * r4067209;
        double r4067211 = 2.0;
        double r4067212 = r4067211 * r4067208;
        double r4067213 = r4067212 * r4067212;
        double r4067214 = r4067210 / r4067213;
        double r4067215 = 1.0;
        double r4067216 = r4067213 - r4067215;
        double r4067217 = r4067214 / r4067216;
        return r4067217;
}
↓
double f(double i) {
        double r4067218 = i;
        double r4067219 = 2.0;
        double r4067220 = r4067218 / r4067219;
        double r4067221 = r4067218 * r4067219;
        double r4067222 = 1.0;
        double r4067223 = sqrt(r4067222);
        double r4067224 = r4067221 - r4067223;
        double r4067225 = r4067220 / r4067224;
        double r4067226 = r4067221 + r4067223;
        double r4067227 = r4067220 / r4067226;
        double r4067228 = r4067225 * r4067227;
        return r4067228;
}

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 associate-*l/15.9

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

  6. Applied add-sqr-sqrt15.9

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

  7. Applied difference-of-squares15.9

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

  8. Applied times-frac0.0

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

  9. Final simplification0.0

    \[\leadsto \frac{\frac{i}{2}}{i \cdot 2 - \sqrt{1}} \cdot \frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}\]

Reproduce

herbie shell --seed 2019171 
(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)))