Average Error: 0.0 → 0.0
Time: 4.4s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f - n}{f + n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f - n}{f + n}}
double f(double f, double n) {
        double r19120 = f;
        double r19121 = n;
        double r19122 = r19120 + r19121;
        double r19123 = -r19122;
        double r19124 = r19120 - r19121;
        double r19125 = r19123 / r19124;
        return r19125;
}
↓
double f(double f, double n) {
        double r19126 = -1.0;
        double r19127 = f;
        double r19128 = n;
        double r19129 = r19127 - r19128;
        double r19130 = r19127 + r19128;
        double r19131 = r19129 / r19130;
        double r19132 = r19126 / r19131;
        return r19132;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))