Average Error: 2.0 → 2.0
Time: 22.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{a}{1 + \left(k + 10\right) \cdot k}}{\frac{1}{{k}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\frac{a}{1 + \left(k + 10\right) \cdot k}}{\frac{1}{{k}^{m}}}
double f(double a, double k, double m) {
        double r9797253 = a;
        double r9797254 = k;
        double r9797255 = m;
        double r9797256 = pow(r9797254, r9797255);
        double r9797257 = r9797253 * r9797256;
        double r9797258 = 1.0;
        double r9797259 = 10.0;
        double r9797260 = r9797259 * r9797254;
        double r9797261 = r9797258 + r9797260;
        double r9797262 = r9797254 * r9797254;
        double r9797263 = r9797261 + r9797262;
        double r9797264 = r9797257 / r9797263;
        return r9797264;
}
↓
double f(double a, double k, double m) {
        double r9797265 = a;
        double r9797266 = 1.0;
        double r9797267 = k;
        double r9797268 = 10.0;
        double r9797269 = r9797267 + r9797268;
        double r9797270 = r9797269 * r9797267;
        double r9797271 = r9797266 + r9797270;
        double r9797272 = r9797265 / r9797271;
        double r9797273 = m;
        double r9797274 = pow(r9797267, r9797273);
        double r9797275 = r9797266 / r9797274;
        double r9797276 = r9797272 / r9797275;
        return r9797276;
}

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

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

  4. Applied div-inv2.0

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

  5. Applied associate-/r*2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2019162 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))