Average Error: 2.0 → 2.0
Time: 17.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{k}^{m} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
{k}^{m} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}
double f(double a, double k, double m) {
        double r8083522 = a;
        double r8083523 = k;
        double r8083524 = m;
        double r8083525 = pow(r8083523, r8083524);
        double r8083526 = r8083522 * r8083525;
        double r8083527 = 1.0;
        double r8083528 = 10.0;
        double r8083529 = r8083528 * r8083523;
        double r8083530 = r8083527 + r8083529;
        double r8083531 = r8083523 * r8083523;
        double r8083532 = r8083530 + r8083531;
        double r8083533 = r8083526 / r8083532;
        return r8083533;
}
↓
double f(double a, double k, double m) {
        double r8083534 = k;
        double r8083535 = m;
        double r8083536 = pow(r8083534, r8083535);
        double r8083537 = a;
        double r8083538 = 1.0;
        double r8083539 = 10.0;
        double r8083540 = r8083534 + r8083539;
        double r8083541 = r8083540 * r8083534;
        double r8083542 = r8083538 + r8083541;
        double r8083543 = r8083537 / r8083542;
        double r8083544 = r8083536 * r8083543;
        return r8083544;
}

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 2.0

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

  2. Simplified2.0

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

  3. Final simplification2.0

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

Reproduce

herbie shell --seed 2019135 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))