Average Error: 0.0 → 0.0
Time: 16.8s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f}{f + n} - \frac{1}{\frac{f + n}{n}}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f}{f + n} - \frac{1}{\frac{f + n}{n}}}
double f(double f, double n) {
        double r25085 = f;
        double r25086 = n;
        double r25087 = r25085 + r25086;
        double r25088 = -r25087;
        double r25089 = r25085 - r25086;
        double r25090 = r25088 / r25089;
        return r25090;
}
↓
double f(double f, double n) {
        double r25091 = -1.0;
        double r25092 = f;
        double r25093 = n;
        double r25094 = r25092 + r25093;
        double r25095 = r25092 / r25094;
        double r25096 = 1.0;
        double r25097 = r25094 / r25093;
        double r25098 = r25096 / r25097;
        double r25099 = r25095 - r25098;
        double r25100 = r25091 / r25099;
        return r25100;
}

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. Using strategy rm

  8. Applied clear-num0.0

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

  9. Final simplification0.0

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

Reproduce

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