Average Error: 1.9 → 1.8
Time: 17.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a \cdot {k}^{m}}{k \cdot \left(10 + k\right) + 1}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a \cdot {k}^{m}}{k \cdot \left(10 + k\right) + 1}
double f(double a, double k, double m) {
        double r290726 = a;
        double r290727 = k;
        double r290728 = m;
        double r290729 = pow(r290727, r290728);
        double r290730 = r290726 * r290729;
        double r290731 = 1.0;
        double r290732 = 10.0;
        double r290733 = r290732 * r290727;
        double r290734 = r290731 + r290733;
        double r290735 = r290727 * r290727;
        double r290736 = r290734 + r290735;
        double r290737 = r290730 / r290736;
        return r290737;
}
↓
double f(double a, double k, double m) {
        double r290738 = a;
        double r290739 = k;
        double r290740 = m;
        double r290741 = pow(r290739, r290740);
        double r290742 = r290738 * r290741;
        double r290743 = 10.0;
        double r290744 = r290743 + r290739;
        double r290745 = r290739 * r290744;
        double r290746 = 1.0;
        double r290747 = r290745 + r290746;
        double r290748 = r290742 / r290747;
        return r290748;
}

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. Using strategy rm

  4. Applied add-sqr-sqrt1.9

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

  5. Applied associate-/r*1.9

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

  6. Final simplification1.8

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

Reproduce

herbie shell --seed 2019303 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))