Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\frac{-1}{{\left(\frac{f - n}{f + n}\right)}^{3}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\frac{-1}{{\left(\frac{f - n}{f + n}\right)}^{3}}}
double f(double f, double n) {
        double r15960 = f;
        double r15961 = n;
        double r15962 = r15960 + r15961;
        double r15963 = -r15962;
        double r15964 = r15960 - r15961;
        double r15965 = r15963 / r15964;
        return r15965;
}
↓
double f(double f, double n) {
        double r15966 = -1.0;
        double r15967 = f;
        double r15968 = n;
        double r15969 = r15967 - r15968;
        double r15970 = r15967 + r15968;
        double r15971 = r15969 / r15970;
        double r15972 = 3.0;
        double r15973 = pow(r15971, r15972);
        double r15974 = r15966 / r15973;
        double r15975 = cbrt(r15974);
        return r15975;
}

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

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

  4. Applied distribute-lft-neg-in0.0

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

  5. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  6. Using strategy rm

  7. Applied add-cbrt-cube41.8

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

  8. Applied add-cbrt-cube41.7

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

  9. Applied cbrt-undiv41.7

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

  10. Applied add-cbrt-cube41.7

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

  11. Applied cbrt-undiv41.7

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))