Average Error: 45.7 → 0.5
Time: 19.6s
Precision: 64
\[i \gt 0\]
\[\frac{\frac{\left(i \cdot i\right) \cdot \left(i \cdot i\right)}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right)}}{\left(2 \cdot i\right) \cdot \left(2 \cdot i\right) - 1.0}\]
↓
\[\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]
\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}
↓
\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}
double f(double i) {
        double r1681261 = i;
        double r1681262 = r1681261 * r1681261;
        double r1681263 = r1681262 * r1681262;
        double r1681264 = 2.0;
        double r1681265 = r1681264 * r1681261;
        double r1681266 = r1681265 * r1681265;
        double r1681267 = r1681263 / r1681266;
        double r1681268 = 1.0;
        double r1681269 = r1681266 - r1681268;
        double r1681270 = r1681267 / r1681269;
        return r1681270;
}
↓
double f(double i) {
        double r1681271 = 0.25;
        double r1681272 = cbrt(r1681271);
        double r1681273 = r1681272 * r1681272;
        double r1681274 = 4.0;
        double r1681275 = 1.0;
        double r1681276 = i;
        double r1681277 = r1681276 * r1681276;
        double r1681278 = r1681275 / r1681277;
        double r1681279 = r1681274 - r1681278;
        double r1681280 = r1681272 / r1681279;
        double r1681281 = r1681273 * r1681280;
        return r1681281;
}

Error

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 45.7

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

  2. Simplified0.4

    \[\leadsto \color{blue}{\frac{\frac{1}{4}}{4 - \frac{1.0}{i \cdot i}}}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.4

    \[\leadsto \frac{\frac{1}{4}}{\color{blue}{1 \cdot \left(4 - \frac{1.0}{i \cdot i}\right)}}\]

  5. Applied add-cube-cbrt0.4

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \sqrt[3]{\frac{1}{4}}}}{1 \cdot \left(4 - \frac{1.0}{i \cdot i}\right)}\]

  6. Applied times-frac0.5

    \[\leadsto \color{blue}{\frac{\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}}{1} \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}}\]

  7. Simplified0.5

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right)} \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]

  8. Final simplification0.5

    \[\leadsto \left(\sqrt[3]{\frac{1}{4}} \cdot \sqrt[3]{\frac{1}{4}}\right) \cdot \frac{\sqrt[3]{\frac{1}{4}}}{4 - \frac{1.0}{i \cdot i}}\]

Reproduce

herbie shell --seed 2019146 +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)))