Average Error: 2.1 → 2.0
Time: 20.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{k}^{m} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
{k}^{m} \cdot \frac{a}{1 + \left(k + 10\right) \cdot k}
double f(double a, double k, double m) {
        double r5141010 = a;
        double r5141011 = k;
        double r5141012 = m;
        double r5141013 = pow(r5141011, r5141012);
        double r5141014 = r5141010 * r5141013;
        double r5141015 = 1.0;
        double r5141016 = 10.0;
        double r5141017 = r5141016 * r5141011;
        double r5141018 = r5141015 + r5141017;
        double r5141019 = r5141011 * r5141011;
        double r5141020 = r5141018 + r5141019;
        double r5141021 = r5141014 / r5141020;
        return r5141021;
}
↓
double f(double a, double k, double m) {
        double r5141022 = k;
        double r5141023 = m;
        double r5141024 = pow(r5141022, r5141023);
        double r5141025 = a;
        double r5141026 = 1.0;
        double r5141027 = 10.0;
        double r5141028 = r5141022 + r5141027;
        double r5141029 = r5141028 * r5141022;
        double r5141030 = r5141026 + r5141029;
        double r5141031 = r5141025 / r5141030;
        double r5141032 = r5141024 * r5141031;
        return r5141032;
}

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 2.1

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

  2. Simplified2.0

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

  4. Applied *-un-lft-identity2.0

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

  5. Applied associate-*r*2.0

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

  6. Simplified2.0

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

  7. Final simplification2.0

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

Reproduce

herbie shell --seed 2019132 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))