Average Error: 46.0 → 0.2
Time: 28.7s
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 r2657968 = i;
        double r2657969 = r2657968 * r2657968;
        double r2657970 = r2657969 * r2657969;
        double r2657971 = 2.0;
        double r2657972 = r2657971 * r2657968;
        double r2657973 = r2657972 * r2657972;
        double r2657974 = r2657970 / r2657973;
        double r2657975 = 1.0;
        double r2657976 = r2657973 - r2657975;
        double r2657977 = r2657974 / r2657976;
        return r2657977;
}
↓
double f(double i) {
        double r2657978 = i;
        double r2657979 = 16.0;
        double r2657980 = r2657978 * r2657979;
        double r2657981 = 4.0;
        double r2657982 = r2657981 / r2657978;
        double r2657983 = r2657980 - r2657982;
        double r2657984 = r2657978 / r2657983;
        return r2657984;
}

Error

Bits error versus i

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 46.0

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

  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 +o rules:numerics
(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)))