Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)
double f(double f, double n) {
        double r14065 = f;
        double r14066 = n;
        double r14067 = r14065 + r14066;
        double r14068 = -r14067;
        double r14069 = r14065 - r14066;
        double r14070 = r14068 / r14069;
        return r14070;
}
↓
double f(double f, double n) {
        double r14071 = f;
        double r14072 = n;
        double r14073 = r14071 + r14072;
        double r14074 = -r14073;
        double r14075 = r14071 - r14072;
        double r14076 = r14074 / r14075;
        double r14077 = expm1(r14076);
        double r14078 = log1p(r14077);
        return r14078;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020057 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))