Average Error: 0.0 → 0.0
Time: 4.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\log \left({\left(e^{\frac{1}{\frac{f}{-\left(f + n\right)} \cdot \frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}}}\right)}^{\left(\frac{f}{-\left(f + n\right)} + \frac{n}{-\left(f + n\right)}\right)}\right)\]
\frac{-\left(f + n\right)}{f - n}
↓
\log \left({\left(e^{\frac{1}{\frac{f}{-\left(f + n\right)} \cdot \frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)} \cdot \frac{n}{-\left(f + n\right)}}}\right)}^{\left(\frac{f}{-\left(f + n\right)} + \frac{n}{-\left(f + n\right)}\right)}\right)
double f(double f, double n) {
        double r15011 = f;
        double r15012 = n;
        double r15013 = r15011 + r15012;
        double r15014 = -r15013;
        double r15015 = r15011 - r15012;
        double r15016 = r15014 / r15015;
        return r15016;
}
↓
double f(double f, double n) {
        double r15017 = 1.0;
        double r15018 = f;
        double r15019 = n;
        double r15020 = r15018 + r15019;
        double r15021 = -r15020;
        double r15022 = r15018 / r15021;
        double r15023 = r15022 * r15022;
        double r15024 = r15019 / r15021;
        double r15025 = r15024 * r15024;
        double r15026 = r15023 - r15025;
        double r15027 = r15017 / r15026;
        double r15028 = exp(r15027);
        double r15029 = r15022 + r15024;
        double r15030 = pow(r15028, r15029);
        double r15031 = log(r15030);
        return r15031;
}

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 div-sub0.0

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

  7. Applied add-log-exp0.0

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

  9. Applied flip--0.0

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

  10. Applied associate-/r/0.0

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

  11. Applied exp-prod0.0

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

  12. Final simplification0.0

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

Reproduce

herbie shell --seed 2020059 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))