Average Error: 0.0 → 0.0
Time: 3.9s
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 r14124 = f;
        double r14125 = n;
        double r14126 = r14124 + r14125;
        double r14127 = -r14126;
        double r14128 = r14124 - r14125;
        double r14129 = r14127 / r14128;
        return r14129;
}
↓
double f(double f, double n) {
        double r14130 = -1.0;
        double r14131 = f;
        double r14132 = n;
        double r14133 = r14131 + r14132;
        double r14134 = r14131 / r14133;
        double r14135 = r14132 / r14133;
        double r14136 = r14134 - r14135;
        double r14137 = r14130 / r14136;
        return r14137;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))