Average Error: 2.1 → 2.0
Time: 4.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m} \cdot a}{k \cdot \left(10 + k\right) + 1}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m} \cdot a}{k \cdot \left(10 + k\right) + 1}
double f(double a, double k, double m) {
        double r215386 = a;
        double r215387 = k;
        double r215388 = m;
        double r215389 = pow(r215387, r215388);
        double r215390 = r215386 * r215389;
        double r215391 = 1.0;
        double r215392 = 10.0;
        double r215393 = r215392 * r215387;
        double r215394 = r215391 + r215393;
        double r215395 = r215387 * r215387;
        double r215396 = r215394 + r215395;
        double r215397 = r215390 / r215396;
        return r215397;
}
↓
double f(double a, double k, double m) {
        double r215398 = k;
        double r215399 = m;
        double r215400 = pow(r215398, r215399);
        double r215401 = a;
        double r215402 = r215400 * r215401;
        double r215403 = 10.0;
        double r215404 = r215403 + r215398;
        double r215405 = r215398 * r215404;
        double r215406 = 1.0;
        double r215407 = r215405 + r215406;
        double r215408 = r215402 / r215407;
        return r215408;
}

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. Simplified2.1

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

  4. Applied associate-*l/2.0

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

  5. Final simplification2.0

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

Reproduce

herbie shell --seed 2019346 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))