Average Error: 0.0 → 0.0
Time: 10.2s
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 r20674 = f;
        double r20675 = n;
        double r20676 = r20674 + r20675;
        double r20677 = -r20676;
        double r20678 = r20674 - r20675;
        double r20679 = r20677 / r20678;
        return r20679;
}
↓
double f(double f, double n) {
        double r20680 = f;
        double r20681 = n;
        double r20682 = r20680 + r20681;
        double r20683 = -r20682;
        double r20684 = r20680 - r20681;
        double r20685 = r20683 / r20684;
        double r20686 = exp(r20685);
        double r20687 = log(r20686);
        return r20687;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))