Average Error: 0.0 → 0.0
Time: 13.5s
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 r422511 = f;
        double r422512 = n;
        double r422513 = r422511 + r422512;
        double r422514 = -r422513;
        double r422515 = r422511 - r422512;
        double r422516 = r422514 / r422515;
        return r422516;
}
↓
double f(double f, double n) {
        double r422517 = n;
        double r422518 = f;
        double r422519 = r422517 + r422518;
        double r422520 = -r422519;
        double r422521 = r422518 - r422517;
        double r422522 = r422520 / r422521;
        double r422523 = exp(r422522);
        double r422524 = log(r422523);
        return r422524;
}

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 2019153 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))