Average Error: 0.0 → 0.0
Time: 3.1s
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{f + n}{n - f}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{f + n}{n - f}
double f(double f, double n) {
        double r11534 = f;
        double r11535 = n;
        double r11536 = r11534 + r11535;
        double r11537 = -r11536;
        double r11538 = r11534 - r11535;
        double r11539 = r11537 / r11538;
        return r11539;
}
↓
double f(double f, double n) {
        double r11540 = f;
        double r11541 = n;
        double r11542 = r11540 + r11541;
        double r11543 = r11541 - r11540;
        double r11544 = r11542 / r11543;
        return r11544;
}

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 frac-2neg0.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  :precision binary64
  (/ (- (+ f n)) (- f n)))