Average Error: 1.9 → 1.9
Time: 4.5s
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 r269193 = a;
        double r269194 = k;
        double r269195 = m;
        double r269196 = pow(r269194, r269195);
        double r269197 = r269193 * r269196;
        double r269198 = 1.0;
        double r269199 = 10.0;
        double r269200 = r269199 * r269194;
        double r269201 = r269198 + r269200;
        double r269202 = r269194 * r269194;
        double r269203 = r269201 + r269202;
        double r269204 = r269197 / r269203;
        return r269204;
}
↓
double f(double a, double k, double m) {
        double r269205 = a;
        double r269206 = k;
        double r269207 = m;
        double r269208 = 2.0;
        double r269209 = r269207 / r269208;
        double r269210 = pow(r269206, r269209);
        double r269211 = r269205 * r269210;
        double r269212 = r269211 * r269210;
        double r269213 = 1.0;
        double r269214 = 10.0;
        double r269215 = r269214 + r269206;
        double r269216 = r269206 * r269215;
        double r269217 = r269213 + r269216;
        double r269218 = r269212 / r269217;
        return r269218;
}

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. Using strategy rm

  3. Applied associate-+l+1.9

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

  4. Simplified1.9

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

  6. Applied sqr-pow1.9

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

  7. Applied associate-*r*1.9

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

  8. Final simplification1.9

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

Reproduce

herbie shell --seed 2020081 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))