Average Error: 2.0 → 2.1
Time: 19.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{1}{\frac{\frac{k \cdot \left(10 + k\right) + 1}{a}}{{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{1}{\frac{\frac{k \cdot \left(10 + k\right) + 1}{a}}{{k}^{m}}}
double f(double a, double k, double m) {
        double r151907 = a;
        double r151908 = k;
        double r151909 = m;
        double r151910 = pow(r151908, r151909);
        double r151911 = r151907 * r151910;
        double r151912 = 1.0;
        double r151913 = 10.0;
        double r151914 = r151913 * r151908;
        double r151915 = r151912 + r151914;
        double r151916 = r151908 * r151908;
        double r151917 = r151915 + r151916;
        double r151918 = r151911 / r151917;
        return r151918;
}
↓
double f(double a, double k, double m) {
        double r151919 = 1.0;
        double r151920 = k;
        double r151921 = 10.0;
        double r151922 = r151921 + r151920;
        double r151923 = r151920 * r151922;
        double r151924 = 1.0;
        double r151925 = r151923 + r151924;
        double r151926 = a;
        double r151927 = r151925 / r151926;
        double r151928 = m;
        double r151929 = pow(r151920, r151928);
        double r151930 = r151927 / r151929;
        double r151931 = r151919 / r151930;
        return r151931;
}

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. Using strategy rm

  3. Applied clear-num2.1

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

  4. Simplified2.1

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

  5. Final simplification2.1

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

Reproduce

herbie shell --seed 2019209 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))