Average Error: 0.0 → 0.0
Time: 14.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\left(\left(f + n\right) \cdot \left(\frac{1}{f - n} \cdot \frac{f + n}{f - n}\right)\right) \cdot \frac{-1}{\frac{f - n}{f + n}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\left(\left(f + n\right) \cdot \left(\frac{1}{f - n} \cdot \frac{f + n}{f - n}\right)\right) \cdot \frac{-1}{\frac{f - n}{f + n}}}
double f(double f, double n) {
        double r1261176 = f;
        double r1261177 = n;
        double r1261178 = r1261176 + r1261177;
        double r1261179 = -r1261178;
        double r1261180 = r1261176 - r1261177;
        double r1261181 = r1261179 / r1261180;
        return r1261181;
}
↓
double f(double f, double n) {
        double r1261182 = f;
        double r1261183 = n;
        double r1261184 = r1261182 + r1261183;
        double r1261185 = 1.0;
        double r1261186 = r1261182 - r1261183;
        double r1261187 = r1261185 / r1261186;
        double r1261188 = r1261184 / r1261186;
        double r1261189 = r1261187 * r1261188;
        double r1261190 = r1261184 * r1261189;
        double r1261191 = -1.0;
        double r1261192 = r1261186 / r1261184;
        double r1261193 = r1261191 / r1261192;
        double r1261194 = r1261190 * r1261193;
        double r1261195 = cbrt(r1261194);
        return r1261195;
}

Error

Bits error versus f

Bits error versus n

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \frac{-\left(f + n\right)}{\color{blue}{1 \cdot \left(f - n\right)}}\]

  4. Applied associate-/r*0.0

    \[\leadsto \color{blue}{\frac{\frac{-\left(f + n\right)}{1}}{f - n}}\]

  5. Simplified0.0

    \[\leadsto \frac{\color{blue}{-\left(n + f\right)}}{f - n}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{-\left(n + f\right)}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}\right) \cdot \frac{-\left(n + f\right)}{f - n}}}\]
  8. Using strategy rm

  9. Applied neg-mul-10.0

    \[\leadsto \sqrt[3]{\left(\frac{-\left(n + f\right)}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}\right) \cdot \frac{\color{blue}{-1 \cdot \left(n + f\right)}}{f - n}}\]

  10. Applied associate-/l*0.0

    \[\leadsto \sqrt[3]{\left(\frac{-\left(n + f\right)}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}\right) \cdot \color{blue}{\frac{-1}{\frac{f - n}{n + f}}}}\]
  11. Using strategy rm

  12. Applied div-inv0.0

    \[\leadsto \sqrt[3]{\left(\color{blue}{\left(\left(-\left(n + f\right)\right) \cdot \frac{1}{f - n}\right)} \cdot \frac{-\left(n + f\right)}{f - n}\right) \cdot \frac{-1}{\frac{f - n}{n + f}}}\]

  13. Applied associate-*l*0.0

    \[\leadsto \sqrt[3]{\color{blue}{\left(\left(-\left(n + f\right)\right) \cdot \left(\frac{1}{f - n} \cdot \frac{-\left(n + f\right)}{f - n}\right)\right)} \cdot \frac{-1}{\frac{f - n}{n + f}}}\]

  14. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(\left(f + n\right) \cdot \left(\frac{1}{f - n} \cdot \frac{f + n}{f - n}\right)\right) \cdot \frac{-1}{\frac{f - n}{f + n}}}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))