Average Error: 0.0 → 0.0
Time: 16.8s
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 r24191 = f;
        double r24192 = n;
        double r24193 = r24191 + r24192;
        double r24194 = -r24193;
        double r24195 = r24191 - r24192;
        double r24196 = r24194 / r24195;
        return r24196;
}
↓
double f(double f, double n) {
        double r24197 = -1.0;
        double r24198 = f;
        double r24199 = n;
        double r24200 = r24198 + r24199;
        double r24201 = r24198 / r24200;
        double r24202 = r24199 / r24200;
        double r24203 = r24201 - r24202;
        double r24204 = r24197 / r24203;
        return r24204;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))