Average Error: 0.0 → 0.0
Time: 10.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(-\frac{f + n}{f - n}\right)}^{3}}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\sqrt[3]{{\left(-\frac{f + n}{f - n}\right)}^{3}}\right)\right)
double f(double f, double n) {
        double r18803 = f;
        double r18804 = n;
        double r18805 = r18803 + r18804;
        double r18806 = -r18805;
        double r18807 = r18803 - r18804;
        double r18808 = r18806 / r18807;
        return r18808;
}
↓
double f(double f, double n) {
        double r18809 = f;
        double r18810 = n;
        double r18811 = r18809 + r18810;
        double r18812 = r18809 - r18810;
        double r18813 = r18811 / r18812;
        double r18814 = -r18813;
        double r18815 = 3.0;
        double r18816 = pow(r18814, r18815);
        double r18817 = cbrt(r18816);
        double r18818 = expm1(r18817);
        double r18819 = log1p(r18818);
        return r18819;
}

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 log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\]
  4. Using strategy rm

  5. Applied add-cbrt-cube42.0

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

  6. Applied add-cbrt-cube42.8

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

  7. Applied cbrt-undiv42.8

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))