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

↓

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

double f(double f, double n) {
        double r5013001 = f;
        double r5013002 = n;
        double r5013003 = r5013001 + r5013002;
        double r5013004 = -r5013003;
        double r5013005 = r5013001 - r5013002;
        double r5013006 = r5013004 / r5013005;
        return r5013006;
}

↓

double f(double f, double n) {
        double r5013007 = -1.0;
        double r5013008 = f;
        double r5013009 = n;
        double r5013010 = r5013008 - r5013009;
        double r5013011 = r5013008 + r5013009;
        double r5013012 = r5013010 / r5013011;
        double r5013013 = r5013007 / r5013012;
        return r5013013;
}

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

↓

\frac{-1}{\frac{f - n}{f + n}}

Derivation

Initial program 0.0
\[\frac{-\left(f + n\right)}{f - n}\]
Using strategy rm
Applied *-un-lft-identity0.0
\[\leadsto \frac{-\color{blue}{1 \cdot \left(f + n\right)}}{f - n}\]
Applied distribute-lft-neg-in0.0
\[\leadsto \frac{\color{blue}{\left(-1\right) \cdot \left(f + n\right)}}{f - n}\]
Applied associate-/l*0.0
\[\leadsto \color{blue}{\frac{-1}{\frac{f - n}{f + n}}}\]
Simplified0.0
\[\leadsto \frac{\color{blue}{-1}}{\frac{f - n}{f + n}}\]
Final simplification0.0
\[\leadsto \frac{-1}{\frac{f - n}{f + n}}\]

Reproduce

herbie shell --seed 2019102 +o rules:numerics
(FPCore (f n)
  :name "subtraction fraction"
  (/ (- (+ f n)) (- f n)))

Error

Derivation

Reproduce