Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f}{f + n} \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \frac{n}{f + n}} \cdot \left(\frac{f}{f + n} + \frac{n}{f + n}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f}{f + n} \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \frac{n}{f + n}} \cdot \left(\frac{f}{f + n} + \frac{n}{f + n}\right)
double f(double f, double n) {
        double r13189 = f;
        double r13190 = n;
        double r13191 = r13189 + r13190;
        double r13192 = -r13191;
        double r13193 = r13189 - r13190;
        double r13194 = r13192 / r13193;
        return r13194;
}
↓
double f(double f, double n) {
        double r13195 = -1.0;
        double r13196 = f;
        double r13197 = n;
        double r13198 = r13196 + r13197;
        double r13199 = r13196 / r13198;
        double r13200 = r13199 * r13199;
        double r13201 = r13197 / r13198;
        double r13202 = r13201 * r13201;
        double r13203 = r13200 - r13202;
        double r13204 = r13195 / r13203;
        double r13205 = r13199 + r13201;
        double r13206 = r13204 * r13205;
        return r13206;
}

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 neg-mul-10.0

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

  4. Applied associate-/l*0.0

    \[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto \frac{-1}{\color{blue}{\frac{f}{f + n} - \frac{n}{f + n}}}\]
  7. Using strategy rm

  8. Applied flip--0.0

    \[\leadsto \frac{-1}{\color{blue}{\frac{\frac{f}{f + n} \cdot \frac{f}{f + n} - \frac{n}{f + n} \cdot \frac{n}{f + n}}{\frac{f}{f + n} + \frac{n}{f + n}}}}\]

  9. Applied associate-/r/0.0

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

  10. Final simplification0.0

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

Reproduce

herbie shell --seed 2020049 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))