Average Error: 46.7 → 0.1
Time: 21.9s
Precision: 64
\[i \gt 0.0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1}\]
↓
\[\frac{i}{2} \cdot \frac{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}{i \cdot 2 - \sqrt{1}}\]
\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{i}{2} \cdot \frac{\frac{\frac{i}{2}}{i \cdot 2 + \sqrt{1}}}{i \cdot 2 - \sqrt{1}}
double f(double i) {
        double r3280020 = i;
        double r3280021 = r3280020 * r3280020;
        double r3280022 = r3280021 * r3280021;
        double r3280023 = 2.0;
        double r3280024 = r3280023 * r3280020;
        double r3280025 = r3280024 * r3280024;
        double r3280026 = r3280022 / r3280025;
        double r3280027 = 1.0;
        double r3280028 = r3280025 - r3280027;
        double r3280029 = r3280026 / r3280028;
        return r3280029;
}
↓
double f(double i) {
        double r3280030 = i;
        double r3280031 = 2.0;
        double r3280032 = r3280030 / r3280031;
        double r3280033 = r3280030 * r3280031;
        double r3280034 = 1.0;
        double r3280035 = sqrt(r3280034);
        double r3280036 = r3280033 + r3280035;
        double r3280037 = r3280032 / r3280036;
        double r3280038 = r3280033 - r3280035;
        double r3280039 = r3280037 / r3280038;
        double r3280040 = r3280032 * r3280039;
        return r3280040;
}

Error

Bits error versus i

Try it out

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. Simplified15.4

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

  4. Applied add-sqr-sqrt15.4

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

  5. Applied difference-of-squares15.4

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

  6. Applied associate-/r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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)))