Average Error: 2.3 → 2.3
Time: 46.7s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left({k}^{m} \cdot a\right) \cdot \frac{1}{1 + \left(k + 10\right) \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left({k}^{m} \cdot a\right) \cdot \frac{1}{1 + \left(k + 10\right) \cdot k}
double f(double a, double k, double m) {
        double r2928266 = a;
        double r2928267 = k;
        double r2928268 = m;
        double r2928269 = pow(r2928267, r2928268);
        double r2928270 = r2928266 * r2928269;
        double r2928271 = 1.0;
        double r2928272 = 10.0;
        double r2928273 = r2928272 * r2928267;
        double r2928274 = r2928271 + r2928273;
        double r2928275 = r2928267 * r2928267;
        double r2928276 = r2928274 + r2928275;
        double r2928277 = r2928270 / r2928276;
        return r2928277;
}
↓
double f(double a, double k, double m) {
        double r2928278 = k;
        double r2928279 = m;
        double r2928280 = pow(r2928278, r2928279);
        double r2928281 = a;
        double r2928282 = r2928280 * r2928281;
        double r2928283 = 1.0;
        double r2928284 = 10.0;
        double r2928285 = r2928278 + r2928284;
        double r2928286 = r2928285 * r2928278;
        double r2928287 = r2928283 + r2928286;
        double r2928288 = r2928283 / r2928287;
        double r2928289 = r2928282 * r2928288;
        return r2928289;
}

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 2.3

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

  2. Simplified2.3

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

  4. Applied div-inv2.3

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

  5. Final simplification2.3

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

Reproduce

herbie shell --seed 2019144 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))