Average Error: 0.0 → 0.1
Time: 9.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)\right)}\]
\frac{-\left(f + n\right)}{f - n}
↓
\sqrt[3]{\mathsf{log1p}\left(\mathsf{expm1}\left({\left(\frac{-\left(f + n\right)}{f - n}\right)}^{3}\right)\right)}
double f(double f, double n) {
        double r15297 = f;
        double r15298 = n;
        double r15299 = r15297 + r15298;
        double r15300 = -r15299;
        double r15301 = r15297 - r15298;
        double r15302 = r15300 / r15301;
        return r15302;
}
↓
double f(double f, double n) {
        double r15303 = f;
        double r15304 = n;
        double r15305 = r15303 + r15304;
        double r15306 = -r15305;
        double r15307 = r15303 - r15304;
        double r15308 = r15306 / r15307;
        double r15309 = 3.0;
        double r15310 = pow(r15308, r15309);
        double r15311 = expm1(r15310);
        double r15312 = log1p(r15311);
        double r15313 = cbrt(r15312);
        return r15313;
}

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-cube41.5

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

  4. Applied add-cbrt-cube42.3

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

  5. Applied cbrt-undiv42.3

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

  6. Simplified0.0

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

  8. Applied log1p-expm1-u0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))