Average Error: 0.0 → 0.0
Time: 7.8s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{1}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{1}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}
double f(double f, double n) {
        double r32200 = f;
        double r32201 = n;
        double r32202 = r32200 + r32201;
        double r32203 = -r32202;
        double r32204 = r32200 - r32201;
        double r32205 = r32203 / r32204;
        return r32205;
}
↓
double f(double f, double n) {
        double r32206 = 1.0;
        double r32207 = f;
        double r32208 = n;
        double r32209 = r32207 + r32208;
        double r32210 = -r32209;
        double r32211 = r32207 / r32210;
        double r32212 = r32208 / r32210;
        double r32213 = r32211 - r32212;
        double r32214 = r32206 / r32213;
        return r32214;
}

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 clear-num0.0

    \[\leadsto \color{blue}{\frac{1}{\frac{f - n}{-\left(f + n\right)}}}\]
  4. Using strategy rm

  5. Applied div-sub0.0

    \[\leadsto \frac{1}{\color{blue}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}}\]

  6. Final simplification0.0

    \[\leadsto \frac{1}{\frac{f}{-\left(f + n\right)} - \frac{n}{-\left(f + n\right)}}\]

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))