Average Error: 1.8 → 1.8
Time: 4.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{k \cdot 10 + \left({k}^{2} + 1\right)} \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m}}{k \cdot 10 + \left({k}^{2} + 1\right)} \cdot a
double f(double a, double k, double m) {
        double r231700 = a;
        double r231701 = k;
        double r231702 = m;
        double r231703 = pow(r231701, r231702);
        double r231704 = r231700 * r231703;
        double r231705 = 1.0;
        double r231706 = 10.0;
        double r231707 = r231706 * r231701;
        double r231708 = r231705 + r231707;
        double r231709 = r231701 * r231701;
        double r231710 = r231708 + r231709;
        double r231711 = r231704 / r231710;
        return r231711;
}
↓
double f(double a, double k, double m) {
        double r231712 = k;
        double r231713 = m;
        double r231714 = pow(r231712, r231713);
        double r231715 = 10.0;
        double r231716 = r231712 * r231715;
        double r231717 = 2.0;
        double r231718 = pow(r231712, r231717);
        double r231719 = 1.0;
        double r231720 = r231718 + r231719;
        double r231721 = r231716 + r231720;
        double r231722 = r231714 / r231721;
        double r231723 = a;
        double r231724 = r231722 * r231723;
        return r231724;
}

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 1.8

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

  2. Simplified1.8

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

  4. Applied distribute-lft-in1.8

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

  5. Applied associate-+l+1.8

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

  6. Simplified1.8

    \[\leadsto \frac{{k}^{m}}{k \cdot 10 + \color{blue}{\left({k}^{2} + 1\right)}} \cdot a\]

  7. Final simplification1.8

    \[\leadsto \frac{{k}^{m}}{k \cdot 10 + \left({k}^{2} + 1\right)} \cdot a\]

Reproduce

herbie shell --seed 2020089 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))