Average Error: 0.0 → 0.0
Time: 13.7s
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 r25336 = f;
        double r25337 = n;
        double r25338 = r25336 + r25337;
        double r25339 = -r25338;
        double r25340 = r25336 - r25337;
        double r25341 = r25339 / r25340;
        return r25341;
}
↓
double f(double f, double n) {
        double r25342 = -1.0;
        double r25343 = f;
        double r25344 = n;
        double r25345 = r25343 + r25344;
        double r25346 = r25343 / r25345;
        double r25347 = r25344 / r25345;
        double r25348 = r25346 - r25347;
        double r25349 = r25342 / r25348;
        return r25349;
}

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 add-log-exp0.0

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

  5. Applied neg-mul-10.0

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

  6. Applied associate-/l*0.0

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

  8. Applied div-sub0.0

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

  10. Applied flip--0.0

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

  11. Applied associate-/r/0.0

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

  12. Applied exp-prod0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019297 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))