Average Error: 46.0 → 0.2
Time: 23.0s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\frac{i}{i \cdot 16 - \frac{4.0}{i}}\]
\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{i}{i \cdot 16 - \frac{4.0}{i}}
double f(double i) {
        double r3091232 = i;
        double r3091233 = r3091232 * r3091232;
        double r3091234 = r3091233 * r3091233;
        double r3091235 = 2.0;
        double r3091236 = r3091235 * r3091232;
        double r3091237 = r3091236 * r3091236;
        double r3091238 = r3091234 / r3091237;
        double r3091239 = 1.0;
        double r3091240 = r3091237 - r3091239;
        double r3091241 = r3091238 / r3091240;
        return r3091241;
}
↓
double f(double i) {
        double r3091242 = i;
        double r3091243 = 16.0;
        double r3091244 = r3091242 * r3091243;
        double r3091245 = 4.0;
        double r3091246 = r3091245 / r3091242;
        double r3091247 = r3091244 - r3091246;
        double r3091248 = r3091242 / r3091247;
        return r3091248;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.0

    \[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]

  2. Simplified15.7

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

  4. Applied associate-/l*15.8

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

  5. Taylor expanded around 0 0.2

    \[\leadsto \frac{i}{\color{blue}{16 \cdot i - 4.0 \cdot \frac{1}{i}}}\]

  6. Simplified0.2

    \[\leadsto \frac{i}{\color{blue}{16 \cdot i - \frac{4.0}{i}}}\]

  7. Final simplification0.2

    \[\leadsto \frac{i}{i \cdot 16 - \frac{4.0}{i}}\]

Reproduce

herbie shell --seed 2019107 
(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)))