Average Error: 2.0 → 2.0
Time: 5.7s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}}{1 + k \cdot \left(10 + k\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}}{1 + k \cdot \left(10 + k\right)}
double f(double a, double k, double m) {
        double r297680 = a;
        double r297681 = k;
        double r297682 = m;
        double r297683 = pow(r297681, r297682);
        double r297684 = r297680 * r297683;
        double r297685 = 1.0;
        double r297686 = 10.0;
        double r297687 = r297686 * r297681;
        double r297688 = r297685 + r297687;
        double r297689 = r297681 * r297681;
        double r297690 = r297688 + r297689;
        double r297691 = r297684 / r297690;
        return r297691;
}
↓
double f(double a, double k, double m) {
        double r297692 = a;
        double r297693 = k;
        double r297694 = m;
        double r297695 = 2.0;
        double r297696 = r297694 / r297695;
        double r297697 = pow(r297693, r297696);
        double r297698 = r297692 * r297697;
        double r297699 = r297698 * r297697;
        double r297700 = 1.0;
        double r297701 = 10.0;
        double r297702 = r297701 + r297693;
        double r297703 = r297693 * r297702;
        double r297704 = r297700 + r297703;
        double r297705 = r297699 / r297704;
        return r297705;
}

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 associate-+l+2.0

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

  4. Simplified2.0

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

  6. Applied sqr-pow2.0

    \[\leadsto \frac{a \cdot \color{blue}{\left({k}^{\left(\frac{m}{2}\right)} \cdot {k}^{\left(\frac{m}{2}\right)}\right)}}{1 + k \cdot \left(10 + k\right)}\]

  7. Applied associate-*r*2.0

    \[\leadsto \frac{\color{blue}{\left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}}}{1 + k \cdot \left(10 + k\right)}\]

  8. Final simplification2.0

    \[\leadsto \frac{\left(a \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}}{1 + k \cdot \left(10 + k\right)}\]

Reproduce

herbie shell --seed 2020047 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))