Average Error: 46.7 → 0.2
Time: 16.2s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]
\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{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}
double f(double i) {
        double r3319181 = i;
        double r3319182 = r3319181 * r3319181;
        double r3319183 = r3319182 * r3319182;
        double r3319184 = 2.0;
        double r3319185 = r3319184 * r3319181;
        double r3319186 = r3319185 * r3319185;
        double r3319187 = r3319183 / r3319186;
        double r3319188 = 1.0;
        double r3319189 = r3319186 - r3319188;
        double r3319190 = r3319187 / r3319189;
        return r3319190;
}
↓
double f(double i) {
        double r3319191 = i;
        double r3319192 = 4.0;
        double r3319193 = r3319192 * r3319191;
        double r3319194 = 1.0;
        double r3319195 = r3319194 / r3319191;
        double r3319196 = r3319193 - r3319195;
        double r3319197 = 2.0;
        double r3319198 = r3319197 * r3319197;
        double r3319199 = r3319196 * r3319198;
        double r3319200 = r3319191 / r3319199;
        return r3319200;
}

Error

Bits error versus i

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.7

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

  2. Simplified0.2

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

  3. Taylor expanded around 0 0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - 1 \cdot \frac{1}{i}\right)}}\]

  4. Simplified0.2

    \[\leadsto \frac{i}{\left(2 \cdot 2\right) \cdot \color{blue}{\left(4 \cdot i - \frac{1}{i}\right)}}\]

  5. Final simplification0.2

    \[\leadsto \frac{i}{\left(4 \cdot i - \frac{1}{i}\right) \cdot \left(2 \cdot 2\right)}\]

Reproduce

herbie shell --seed 2019172 
(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)))