Average Error: 0.0 → 0.1
Time: 3.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1}{f - n} \cdot \left(f + n\right)\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1}{f - n} \cdot \left(f + n\right)\right)\right)
double f(double f, double n) {
        double r14170 = f;
        double r14171 = n;
        double r14172 = r14170 + r14171;
        double r14173 = -r14172;
        double r14174 = r14170 - r14171;
        double r14175 = r14173 / r14174;
        return r14175;
}
↓
double f(double f, double n) {
        double r14176 = -1.0;
        double r14177 = f;
        double r14178 = n;
        double r14179 = r14177 - r14178;
        double r14180 = r14176 / r14179;
        double r14181 = r14177 + r14178;
        double r14182 = r14180 * r14181;
        double r14183 = expm1(r14182);
        double r14184 = log1p(r14183);
        return r14184;
}

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 flip--31.1

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

  6. Applied associate-/r/31.2

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

  7. Simplified0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\frac{-1}{f - n}} \cdot \left(f + n\right)\right)\right)\]

  8. Final simplification0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-1}{f - n} \cdot \left(f + n\right)\right)\right)\]

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))