Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\right)
double f(double f, double n) {
        double r28559 = f;
        double r28560 = n;
        double r28561 = r28559 + r28560;
        double r28562 = -r28561;
        double r28563 = r28559 - r28560;
        double r28564 = r28562 / r28563;
        return r28564;
}
↓
double f(double f, double n) {
        double r28565 = f;
        double r28566 = n;
        double r28567 = r28565 + r28566;
        double r28568 = -r28567;
        double r28569 = r28565 - r28566;
        double r28570 = r28568 / r28569;
        double r28571 = expm1(r28570);
        double r28572 = log1p(r28571);
        double r28573 = exp(r28572);
        double r28574 = log(r28573);
        return r28574;
}

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-log-exp0.0

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

  5. Applied log1p-expm1-u0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019212 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))