Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left(\frac{1}{e^{\frac{f + n}{f - n}}}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left(\frac{1}{e^{\frac{f + n}{f - n}}}\right)
double f(double f, double n) {
        double r18404 = f;
        double r18405 = n;
        double r18406 = r18404 + r18405;
        double r18407 = -r18406;
        double r18408 = r18404 - r18405;
        double r18409 = r18407 / r18408;
        return r18409;
}
↓
double f(double f, double n) {
        double r18410 = 1.0;
        double r18411 = f;
        double r18412 = n;
        double r18413 = r18411 + r18412;
        double r18414 = r18411 - r18412;
        double r18415 = r18413 / r18414;
        double r18416 = exp(r18415);
        double r18417 = r18410 / r18416;
        double r18418 = log(r18417);
        return r18418;
}

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{f - n}{-\left(f + n\right)}}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

    \[\leadsto \color{blue}{\log \left(e^{\frac{1}{\frac{f - n}{-\left(f + n\right)}}}\right)}\]

  6. Simplified0.0

    \[\leadsto \log \color{blue}{\left(\frac{1}{e^{\frac{f + n}{f - n}}}\right)}\]

  7. Final simplification0.0

    \[\leadsto \log \left(\frac{1}{e^{\frac{f + n}{f - n}}}\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))