Average Error: 0.0 → 0.1
Time: 12.3s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{f - n} \cdot f + \frac{-n}{f - n}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{f - n} \cdot f + \frac{-n}{f - n}
double f(double f, double n) {
        double r1007385 = f;
        double r1007386 = n;
        double r1007387 = r1007385 + r1007386;
        double r1007388 = -r1007387;
        double r1007389 = r1007385 - r1007386;
        double r1007390 = r1007388 / r1007389;
        return r1007390;
}
↓
double f(double f, double n) {
        double r1007391 = -1.0;
        double r1007392 = f;
        double r1007393 = n;
        double r1007394 = r1007392 - r1007393;
        double r1007395 = r1007391 / r1007394;
        double r1007396 = r1007395 * r1007392;
        double r1007397 = -r1007393;
        double r1007398 = r1007397 / r1007394;
        double r1007399 = r1007396 + r1007398;
        return r1007399;
}

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 flip--31.0

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

  4. Applied associate-/r/31.1

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

  5. Simplified0.2

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

  7. Applied distribute-rgt-in0.2

    \[\leadsto \color{blue}{f \cdot \frac{-1}{f - n} + n \cdot \frac{-1}{f - n}}\]
  8. Using strategy rm

  9. Applied associate-*r/0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))