Average Error: 0.0 → 0.0
Time: 3.9s
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 r15217 = f;
        double r15218 = n;
        double r15219 = r15217 + r15218;
        double r15220 = -r15219;
        double r15221 = r15217 - r15218;
        double r15222 = r15220 / r15221;
        return r15222;
}
↓
double f(double f, double n) {
        double r15223 = -1.0;
        double r15224 = f;
        double r15225 = n;
        double r15226 = r15224 + r15225;
        double r15227 = r15224 / r15226;
        double r15228 = r15227 * r15227;
        double r15229 = r15225 / r15226;
        double r15230 = r15229 * r15229;
        double r15231 = r15228 - r15230;
        double r15232 = r15223 / r15231;
        double r15233 = r15227 + r15229;
        double r15234 = r15232 * r15233;
        return r15234;
}

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-sub0.0

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

  8. Applied flip--0.0

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

  9. Applied associate-/r/0.0

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

  10. 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 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))