Average Error: 2.0 → 2.0
Time: 6.5s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{{k}^{m}}{\sqrt{k \cdot \left(10 + k\right) + 1}}}{\sqrt{k \cdot \left(10 + k\right) + 1}} \cdot a\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\frac{{k}^{m}}{\sqrt{k \cdot \left(10 + k\right) + 1}}}{\sqrt{k \cdot \left(10 + k\right) + 1}} \cdot a
double f(double a, double k, double m) {
        double r346222 = a;
        double r346223 = k;
        double r346224 = m;
        double r346225 = pow(r346223, r346224);
        double r346226 = r346222 * r346225;
        double r346227 = 1.0;
        double r346228 = 10.0;
        double r346229 = r346228 * r346223;
        double r346230 = r346227 + r346229;
        double r346231 = r346223 * r346223;
        double r346232 = r346230 + r346231;
        double r346233 = r346226 / r346232;
        return r346233;
}
↓
double f(double a, double k, double m) {
        double r346234 = k;
        double r346235 = m;
        double r346236 = pow(r346234, r346235);
        double r346237 = 10.0;
        double r346238 = r346237 + r346234;
        double r346239 = r346234 * r346238;
        double r346240 = 1.0;
        double r346241 = r346239 + r346240;
        double r346242 = sqrt(r346241);
        double r346243 = r346236 / r346242;
        double r346244 = r346243 / r346242;
        double r346245 = a;
        double r346246 = r346244 * r346245;
        return r346246;
}

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

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

  4. Applied add-sqr-sqrt2.0

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

  5. Applied associate-/r*2.0

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

  6. Final simplification2.0

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

Reproduce

herbie shell --seed 2020064 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))