Average Error: 1.9 → 1.9
Time: 1.8m
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\sqrt{{k}^{m}} \cdot \left(\sqrt{{k}^{m}} \cdot a\right)}{1 + k \cdot \left(k + 10\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\sqrt{{k}^{m}} \cdot \left(\sqrt{{k}^{m}} \cdot a\right)}{1 + k \cdot \left(k + 10\right)}
double f(double a, double k, double m) {
        double r67139018 = a;
        double r67139019 = k;
        double r67139020 = m;
        double r67139021 = pow(r67139019, r67139020);
        double r67139022 = r67139018 * r67139021;
        double r67139023 = 1.0;
        double r67139024 = 10.0;
        double r67139025 = r67139024 * r67139019;
        double r67139026 = r67139023 + r67139025;
        double r67139027 = r67139019 * r67139019;
        double r67139028 = r67139026 + r67139027;
        double r67139029 = r67139022 / r67139028;
        return r67139029;
}
↓
double f(double a, double k, double m) {
        double r67139030 = k;
        double r67139031 = m;
        double r67139032 = pow(r67139030, r67139031);
        double r67139033 = sqrt(r67139032);
        double r67139034 = a;
        double r67139035 = r67139033 * r67139034;
        double r67139036 = r67139033 * r67139035;
        double r67139037 = 1.0;
        double r67139038 = 10.0;
        double r67139039 = r67139030 + r67139038;
        double r67139040 = r67139030 * r67139039;
        double r67139041 = r67139037 + r67139040;
        double r67139042 = r67139036 / r67139041;
        return r67139042;
}

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. Simplified1.8

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

  4. Applied add-sqr-sqrt1.9

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

  5. Applied associate-*l*1.9

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

  6. Final simplification1.9

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

Reproduce

herbie shell --seed 2019121 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))