Average Error: 2.0 → 2.0
Time: 11.6s
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 r355620 = a;
        double r355621 = k;
        double r355622 = m;
        double r355623 = pow(r355621, r355622);
        double r355624 = r355620 * r355623;
        double r355625 = 1.0;
        double r355626 = 10.0;
        double r355627 = r355626 * r355621;
        double r355628 = r355625 + r355627;
        double r355629 = r355621 * r355621;
        double r355630 = r355628 + r355629;
        double r355631 = r355624 / r355630;
        return r355631;
}
↓
double f(double a, double k, double m) {
        double r355632 = a;
        double r355633 = k;
        double r355634 = 10.0;
        double r355635 = r355634 + r355633;
        double r355636 = r355633 * r355635;
        double r355637 = 1.0;
        double r355638 = r355636 + r355637;
        double r355639 = r355632 / r355638;
        double r355640 = m;
        double r355641 = 2.0;
        double r355642 = r355640 / r355641;
        double r355643 = pow(r355633, r355642);
        double r355644 = r355639 * r355643;
        double r355645 = r355644 * r355643;
        return r355645;
}

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))))