Average Error: 2.0 → 2.0
Time: 18.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {k}^{\left(\frac{m}{2}\right)}\right) \cdot {k}^{\left(\frac{m}{2}\right)}
double f(double a, double k, double m) {
        double r311648 = a;
        double r311649 = k;
        double r311650 = m;
        double r311651 = pow(r311649, r311650);
        double r311652 = r311648 * r311651;
        double r311653 = 1.0;
        double r311654 = 10.0;
        double r311655 = r311654 * r311649;
        double r311656 = r311653 + r311655;
        double r311657 = r311649 * r311649;
        double r311658 = r311656 + r311657;
        double r311659 = r311652 / r311658;
        return r311659;
}
↓
double f(double a, double k, double m) {
        double r311660 = a;
        double r311661 = k;
        double r311662 = 10.0;
        double r311663 = r311662 + r311661;
        double r311664 = r311661 * r311663;
        double r311665 = 1.0;
        double r311666 = r311664 + r311665;
        double r311667 = r311660 / r311666;
        double r311668 = m;
        double r311669 = 2.0;
        double r311670 = r311668 / r311669;
        double r311671 = pow(r311661, r311670);
        double r311672 = r311667 * r311671;
        double r311673 = r311672 * r311671;
        return r311673;
}

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. Simplified2.0

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

  4. Applied sqr-pow2.0

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

  5. Applied associate-*r*2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))