Average Error: 0.0 → 0.0
Time: 2.9s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f}{f + n} - \frac{n}{f + n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f}{f + n} - \frac{n}{f + n}}
double f(double f, double n) {
        double r10087 = f;
        double r10088 = n;
        double r10089 = r10087 + r10088;
        double r10090 = -r10089;
        double r10091 = r10087 - r10088;
        double r10092 = r10090 / r10091;
        return r10092;
}
↓
double f(double f, double n) {
        double r10093 = 1.0;
        double r10094 = -r10093;
        double r10095 = f;
        double r10096 = n;
        double r10097 = r10095 + r10096;
        double r10098 = r10095 / r10097;
        double r10099 = r10096 / r10097;
        double r10100 = r10098 - r10099;
        double r10101 = r10094 / r10100;
        return r10101;
}

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 log1p-expm1-u0.0

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{-\left(f + n\right)}{f - n}\right)\right)}\]
  4. Using strategy rm

  5. Applied log1p-expm10.0

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

  7. Applied *-un-lft-identity0.0

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

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

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

  9. Applied associate-/l*0.0

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

  11. Applied div-sub0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))