Average Error: 0.0 → 0.0
Time: 3.7s
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 r16060 = f;
        double r16061 = n;
        double r16062 = r16060 + r16061;
        double r16063 = -r16062;
        double r16064 = r16060 - r16061;
        double r16065 = r16063 / r16064;
        return r16065;
}
↓
double f(double f, double n) {
        double r16066 = -1.0;
        double r16067 = f;
        double r16068 = n;
        double r16069 = r16067 - r16068;
        double r16070 = r16067 + r16068;
        double r16071 = r16069 / r16070;
        double r16072 = r16066 / r16071;
        return r16072;
}

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 2020060 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))