Average Error: 0.0 → 0.0
Time: 16.6s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{\frac{-1}{f - n}}{\frac{1}{f + n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{\frac{-1}{f - n}}{\frac{1}{f + n}}
double f(double f, double n) {
        double r18697 = f;
        double r18698 = n;
        double r18699 = r18697 + r18698;
        double r18700 = -r18699;
        double r18701 = r18697 - r18698;
        double r18702 = r18700 / r18701;
        return r18702;
}
↓
double f(double f, double n) {
        double r18703 = -1.0;
        double r18704 = f;
        double r18705 = n;
        double r18706 = r18704 - r18705;
        double r18707 = r18703 / r18706;
        double r18708 = 1.0;
        double r18709 = r18704 + r18705;
        double r18710 = r18708 / r18709;
        double r18711 = r18707 / r18710;
        return r18711;
}

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-inv0.2

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

  7. Applied associate-/r*0.0

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

  8. Final simplification0.0

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

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))