Average Error: 1.9 → 1.9
Time: 6.0s
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 r295442 = a;
        double r295443 = k;
        double r295444 = m;
        double r295445 = pow(r295443, r295444);
        double r295446 = r295442 * r295445;
        double r295447 = 1.0;
        double r295448 = 10.0;
        double r295449 = r295448 * r295443;
        double r295450 = r295447 + r295449;
        double r295451 = r295443 * r295443;
        double r295452 = r295450 + r295451;
        double r295453 = r295446 / r295452;
        return r295453;
}
↓
double f(double a, double k, double m) {
        double r295454 = k;
        double r295455 = m;
        double r295456 = pow(r295454, r295455);
        double r295457 = 10.0;
        double r295458 = r295457 + r295454;
        double r295459 = r295454 * r295458;
        double r295460 = 1.0;
        double r295461 = r295459 + r295460;
        double r295462 = r295456 / r295461;
        double r295463 = a;
        double r295464 = r295462 * r295463;
        return r295464;
}

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 2019322 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))