Average Error: 0.0 → 0.0
Time: 1.4m
Precision: 64
\[\frac{-\left(f + n\right)}{f - n}\]
↓
\[\frac{-1}{\frac{f - n}{f + n}}\]
\frac{-\left(f + n\right)}{f - n}
↓
\frac{-1}{\frac{f - n}{f + n}}
double f(double f, double n) {
        double r2778720 = f;
        double r2778721 = n;
        double r2778722 = r2778720 + r2778721;
        double r2778723 = -r2778722;
        double r2778724 = r2778720 - r2778721;
        double r2778725 = r2778723 / r2778724;
        return r2778725;
}
↓
double f(double f, double n) {
        double r2778726 = -1.0;
        double r2778727 = f;
        double r2778728 = n;
        double r2778729 = r2778727 - r2778728;
        double r2778730 = r2778727 + r2778728;
        double r2778731 = r2778729 / r2778730;
        double r2778732 = r2778726 / r2778731;
        return r2778732;
}

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 *-un-lft-identity0.0

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

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

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

  8. Applied distribute-lft-out0.0

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

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

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

  10. Applied times-frac0.0

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

  11. Applied associate-/r*0.0

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

  12. Simplified0.0

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

  13. Final simplification0.0

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

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))