Average Error: 0.0 → 0.0
Time: 36.6s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f - n}{f + n}}\]
double f(double f, double n) {
        double r1265159 = f;
        double r1265160 = n;
        double r1265161 = r1265159 + r1265160;
        double r1265162 = -r1265161;
        double r1265163 = r1265159 - r1265160;
        double r1265164 = r1265162 / r1265163;
        return r1265164;
}
↓
double f(double f, double n) {
        double r1265165 = -1.0;
        double r1265166 = f;
        double r1265167 = n;
        double r1265168 = r1265166 - r1265167;
        double r1265169 = r1265166 + r1265167;
        double r1265170 = r1265168 / r1265169;
        double r1265171 = r1265165 / r1265170;
        return r1265171;
}


\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f - n}{f + n}}

Error

Bits error versus f

Bits error versus n

Derivation

  1. Initial program 0.0

    \[\frac{-\left(f + n\right)}{f - n}\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied distribute-lft-out0.0

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

  6. Applied distribute-lft-neg-in0.0

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

  7. Applied associate-/l*0.0

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

  8. Simplified0.0

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

  9. Final simplification0.0

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

Reproduce

herbie shell --seed 2019101 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))