Average Error: 0.0 → 0.0
Time: 11.6s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\log \left(e^{-\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{f + n}{f - n}\right)}^{3}\right)\right)}\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\log \left(e^{-\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{f + n}{f - n}\right)}^{3}\right)\right)}\right)}
double f(double f, double n) {
        double r26076 = f;
        double r26077 = n;
        double r26078 = r26076 + r26077;
        double r26079 = -r26078;
        double r26080 = r26076 - r26077;
        double r26081 = r26079 / r26080;
        return r26081;
}
↓
double f(double f, double n) {
        double r26082 = f;
        double r26083 = n;
        double r26084 = r26082 + r26083;
        double r26085 = r26082 - r26083;
        double r26086 = r26084 / r26085;
        double r26087 = 3.0;
        double r26088 = pow(r26086, r26087);
        double r26089 = expm1(r26088);
        double r26090 = log1p(r26089);
        double r26091 = -r26090;
        double r26092 = exp(r26091);
        double r26093 = log(r26092);
        double r26094 = cbrt(r26093);
        return r26094;
}

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 add-cbrt-cube41.7

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

  4. Applied add-cbrt-cube42.6

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

  5. Applied cbrt-undiv42.6

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

  6. Simplified0.0

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

  8. Applied add-log-exp0.0

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

  9. Simplified0.0

    \[\leadsto \sqrt[3]{\log \color{blue}{\left(e^{-{\left(\frac{f + n}{f - n}\right)}^{3}}\right)}}\]
  10. Using strategy rm

  11. Applied log1p-expm1-u0.0

    \[\leadsto \sqrt[3]{\log \left(e^{-\color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{f + n}{f - n}\right)}^{3}\right)\right)}}\right)}\]

  12. Simplified0.0

    \[\leadsto \sqrt[3]{\log \left(e^{-\mathsf{log1p}\left(\color{blue}{\mathsf{expm1}\left({\left(\frac{n + f}{f - n}\right)}^{3}\right)}\right)}\right)}\]

  13. Final simplification0.0

    \[\leadsto \sqrt[3]{\log \left(e^{-\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{f + n}{f - n}\right)}^{3}\right)\right)}\right)}\]

Reproduce

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