Average Error: 1.9 → 1.9
Time: 5.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m}}{k \cdot \left(10 + k\right) + 1} \cdot a
double f(double a, double k, double m) {
        double r343588 = a;
        double r343589 = k;
        double r343590 = m;
        double r343591 = pow(r343589, r343590);
        double r343592 = r343588 * r343591;
        double r343593 = 1.0;
        double r343594 = 10.0;
        double r343595 = r343594 * r343589;
        double r343596 = r343593 + r343595;
        double r343597 = r343589 * r343589;
        double r343598 = r343596 + r343597;
        double r343599 = r343592 / r343598;
        return r343599;
}
↓
double f(double a, double k, double m) {
        double r343600 = k;
        double r343601 = m;
        double r343602 = pow(r343600, r343601);
        double r343603 = 10.0;
        double r343604 = r343603 + r343600;
        double r343605 = r343600 * r343604;
        double r343606 = 1.0;
        double r343607 = r343605 + r343606;
        double r343608 = r343602 / r343607;
        double r343609 = a;
        double r343610 = r343608 * r343609;
        return r343610;
}

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 1.9

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

  2. Simplified1.9

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

  3. Final simplification1.9

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

Reproduce

herbie shell --seed 2019318 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))