Average Error: 1.9 → 2.0
Time: 20.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{a}{\sqrt{k \cdot \left(10 + k\right) + 1}}}{\frac{\sqrt{k \cdot \left(10 + k\right) + 1}}{{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\frac{a}{\sqrt{k \cdot \left(10 + k\right) + 1}}}{\frac{\sqrt{k \cdot \left(10 + k\right) + 1}}{{k}^{m}}}
double f(double a, double k, double m) {
        double r181724 = a;
        double r181725 = k;
        double r181726 = m;
        double r181727 = pow(r181725, r181726);
        double r181728 = r181724 * r181727;
        double r181729 = 1.0;
        double r181730 = 10.0;
        double r181731 = r181730 * r181725;
        double r181732 = r181729 + r181731;
        double r181733 = r181725 * r181725;
        double r181734 = r181732 + r181733;
        double r181735 = r181728 / r181734;
        return r181735;
}
↓
double f(double a, double k, double m) {
        double r181736 = a;
        double r181737 = k;
        double r181738 = 10.0;
        double r181739 = r181738 + r181737;
        double r181740 = r181737 * r181739;
        double r181741 = 1.0;
        double r181742 = r181740 + r181741;
        double r181743 = sqrt(r181742);
        double r181744 = r181736 / r181743;
        double r181745 = m;
        double r181746 = pow(r181737, r181745);
        double r181747 = r181743 / r181746;
        double r181748 = r181744 / r181747;
        return r181748;
}

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

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

  4. Applied *-un-lft-identity1.9

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

  5. Applied unpow-prod-down1.9

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

  6. Applied add-sqr-sqrt2.0

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

  7. Applied times-frac2.0

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

  8. Applied associate-/r*2.0

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

  9. Simplified2.0

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

  10. Final simplification2.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))