Average Error: 0.0 → 0.0
Time: 3.3s
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 r11144 = f;
        double r11145 = n;
        double r11146 = r11144 + r11145;
        double r11147 = -r11146;
        double r11148 = r11144 - r11145;
        double r11149 = r11147 / r11148;
        return r11149;
}
↓
double f(double f, double n) {
        double r11150 = 1.0;
        double r11151 = -r11150;
        double r11152 = f;
        double r11153 = n;
        double r11154 = r11152 + r11153;
        double r11155 = r11152 / r11154;
        double r11156 = r11153 / r11154;
        double r11157 = r11155 - r11156;
        double r11158 = r11151 / r11157;
        return r11158;
}

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 2019344 
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))