Average Error: 2.1 → 2.1
Time: 3.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{k \cdot \left(10 + k\right) + 1}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m} \cdot a}{k \cdot \left(10 + k\right) + 1}
double f(double a, double k, double m) {
        double r244436 = a;
        double r244437 = k;
        double r244438 = m;
        double r244439 = pow(r244437, r244438);
        double r244440 = r244436 * r244439;
        double r244441 = 1.0;
        double r244442 = 10.0;
        double r244443 = r244442 * r244437;
        double r244444 = r244441 + r244443;
        double r244445 = r244437 * r244437;
        double r244446 = r244444 + r244445;
        double r244447 = r244440 / r244446;
        return r244447;
}
↓
double f(double a, double k, double m) {
        double r244448 = k;
        double r244449 = m;
        double r244450 = pow(r244448, r244449);
        double r244451 = a;
        double r244452 = r244450 * r244451;
        double r244453 = 10.0;
        double r244454 = r244453 + r244448;
        double r244455 = r244448 * r244454;
        double r244456 = 1.0;
        double r244457 = r244455 + r244456;
        double r244458 = r244452 / r244457;
        return r244458;
}

Error

Bits error versus a

Bits error versus k

Bits error versus m

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 2.1

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

  2. Simplified2.1

    \[\leadsto \color{blue}{\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a}\]
  3. Using strategy rm

  4. Applied associate-*l/2.1

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

  5. Final simplification2.1

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

Reproduce

herbie shell --seed 2019353 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))