Average Error: 0.0 → 0.0
Time: 21.7s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(e^{\frac{-\left(n + f\right)}{f - n}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(e^{\frac{-\left(n + f\right)}{f - n}}\right)
double f(double f, double n) {
        double r968358 = f;
        double r968359 = n;
        double r968360 = r968358 + r968359;
        double r968361 = -r968360;
        double r968362 = r968358 - r968359;
        double r968363 = r968361 / r968362;
        return r968363;
}
↓
double f(double f, double n) {
        double r968364 = n;
        double r968365 = f;
        double r968366 = r968364 + r968365;
        double r968367 = -r968366;
        double r968368 = r968365 - r968364;
        double r968369 = r968367 / r968368;
        double r968370 = exp(r968369);
        double r968371 = log(r968370);
        return r968371;
}

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

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

Reproduce

herbie shell --seed 2019171 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))