Average Error: 0.0 → 0.0
Time: 11.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{-\left(f + n\right)}{f - n}}\right)
double f(double f, double n) {
        double r29731 = f;
        double r29732 = n;
        double r29733 = r29731 + r29732;
        double r29734 = -r29733;
        double r29735 = r29731 - r29732;
        double r29736 = r29734 / r29735;
        return r29736;
}
↓
double f(double f, double n) {
        double r29737 = f;
        double r29738 = n;
        double r29739 = r29737 + r29738;
        double r29740 = -r29739;
        double r29741 = r29737 - r29738;
        double r29742 = r29740 / r29741;
        double r29743 = exp(r29742);
        double r29744 = log(r29743);
        return r29744;
}

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. Simplified0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))