Average Error: 2.1 → 2.1
Time: 3.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{k}^{m} \cdot \frac{a}{k \cdot \left(10 + k\right) + 1}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
{k}^{m} \cdot \frac{a}{k \cdot \left(10 + k\right) + 1}
double f(double a, double k, double m) {
        double r171459 = a;
        double r171460 = k;
        double r171461 = m;
        double r171462 = pow(r171460, r171461);
        double r171463 = r171459 * r171462;
        double r171464 = 1.0;
        double r171465 = 10.0;
        double r171466 = r171465 * r171460;
        double r171467 = r171464 + r171466;
        double r171468 = r171460 * r171460;
        double r171469 = r171467 + r171468;
        double r171470 = r171463 / r171469;
        return r171470;
}
↓
double f(double a, double k, double m) {
        double r171471 = k;
        double r171472 = m;
        double r171473 = pow(r171471, r171472);
        double r171474 = a;
        double r171475 = 10.0;
        double r171476 = r171475 + r171471;
        double r171477 = r171471 * r171476;
        double r171478 = 1.0;
        double r171479 = r171477 + r171478;
        double r171480 = r171474 / r171479;
        double r171481 = r171473 * r171480;
        return r171481;
}

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 div-inv2.1

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

  5. Applied associate-*l*2.1

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

  6. Simplified2.1

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

  7. Final simplification2.1

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

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))))