Average Error: 0.0 → 0.0
Time: 3.6s
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 r14071 = f;
        double r14072 = n;
        double r14073 = r14071 + r14072;
        double r14074 = -r14073;
        double r14075 = r14071 - r14072;
        double r14076 = r14074 / r14075;
        return r14076;
}
↓
double f(double f, double n) {
        double r14077 = -1.0;
        double r14078 = f;
        double r14079 = n;
        double r14080 = r14078 + r14079;
        double r14081 = r14078 / r14080;
        double r14082 = r14081 * r14081;
        double r14083 = r14079 / r14080;
        double r14084 = r14083 * r14083;
        double r14085 = r14082 - r14084;
        double r14086 = r14077 / r14085;
        double r14087 = r14081 + r14083;
        double r14088 = r14086 * r14087;
        return r14088;
}

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 *-un-lft-identity0.0

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

  4. Applied distribute-lft-neg-in0.0

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

  5. Applied associate-/l*0.0

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

  7. Applied div-sub0.0

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

  9. Applied flip--0.0

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

  10. Applied associate-/r/0.0

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

  11. Simplified0.0

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

  12. 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 2020083 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))