Average Error: 2.0 → 2.0
Time: 24.4s
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 r9037342 = a;
        double r9037343 = k;
        double r9037344 = m;
        double r9037345 = pow(r9037343, r9037344);
        double r9037346 = r9037342 * r9037345;
        double r9037347 = 1.0;
        double r9037348 = 10.0;
        double r9037349 = r9037348 * r9037343;
        double r9037350 = r9037347 + r9037349;
        double r9037351 = r9037343 * r9037343;
        double r9037352 = r9037350 + r9037351;
        double r9037353 = r9037346 / r9037352;
        return r9037353;
}
↓
double f(double a, double k, double m) {
        double r9037354 = a;
        double r9037355 = 1.0;
        double r9037356 = k;
        double r9037357 = 10.0;
        double r9037358 = r9037356 + r9037357;
        double r9037359 = r9037358 * r9037356;
        double r9037360 = r9037355 + r9037359;
        double r9037361 = r9037354 / r9037360;
        double r9037362 = m;
        double r9037363 = pow(r9037356, r9037362);
        double r9037364 = r9037355 / r9037363;
        double r9037365 = r9037361 / r9037364;
        return r9037365;
}

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))))