\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

↓

\[\frac{{k}^{m}}{\frac{1}{a} + \frac{k}{a} \cdot \left(10 + k\right)}\]

double f(double a, double k, double m) {
        double r50701528 = a;
        double r50701529 = k;
        double r50701530 = m;
        double r50701531 = pow(r50701529, r50701530);
        double r50701532 = r50701528 * r50701531;
        double r50701533 = 1.0;
        double r50701534 = 10.0;
        double r50701535 = r50701534 * r50701529;
        double r50701536 = r50701533 + r50701535;
        double r50701537 = r50701529 * r50701529;
        double r50701538 = r50701536 + r50701537;
        double r50701539 = r50701532 / r50701538;
        return r50701539;
}

↓

double f(double a, double k, double m) {
        double r50701540 = k;
        double r50701541 = m;
        double r50701542 = pow(r50701540, r50701541);
        double r50701543 = 1.0;
        double r50701544 = a;
        double r50701545 = r50701543 / r50701544;
        double r50701546 = r50701540 / r50701544;
        double r50701547 = 10.0;
        double r50701548 = r50701547 + r50701540;
        double r50701549 = r50701546 * r50701548;
        double r50701550 = r50701545 + r50701549;
        double r50701551 = r50701542 / r50701550;
        return r50701551;
}

\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}

↓

\frac{{k}^{m}}{\frac{1}{a} + \frac{k}{a} \cdot \left(10 + k\right)}

Derivation

Initial program 1.9
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
Simplified1.9
\[\leadsto \color{blue}{\frac{{k}^{m} \cdot a}{k \cdot \left(k + 10\right) + 1}}\]
Using strategy rm
Applied associate-/l*2.0
\[\leadsto \color{blue}{\frac{{k}^{m}}{\frac{k \cdot \left(k + 10\right) + 1}{a}}}\]
Taylor expanded around inf 3.7
\[\leadsto \frac{{k}^{m}}{\color{blue}{\frac{1}{a} + \left(10 \cdot \frac{k}{a} + \frac{{k}^{2}}{a}\right)}}\]
Simplified0.2
\[\leadsto \frac{{k}^{m}}{\color{blue}{\left(10 + k\right) \cdot \frac{k}{a} + \frac{1}{a}}}\]
Final simplification0.2
\[\leadsto \frac{{k}^{m}}{\frac{1}{a} + \frac{k}{a} \cdot \left(10 + k\right)}\]

Reproduce

herbie shell --seed 2019101 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))

Error

Derivation

Reproduce