Average Error: 2.3 → 2.3
Time: 6.0s
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 r251393 = a;
        double r251394 = k;
        double r251395 = m;
        double r251396 = pow(r251394, r251395);
        double r251397 = r251393 * r251396;
        double r251398 = 1.0;
        double r251399 = 10.0;
        double r251400 = r251399 * r251394;
        double r251401 = r251398 + r251400;
        double r251402 = r251394 * r251394;
        double r251403 = r251401 + r251402;
        double r251404 = r251397 / r251403;
        return r251404;
}
↓
double f(double a, double k, double m) {
        double r251405 = k;
        double r251406 = m;
        double r251407 = pow(r251405, r251406);
        double r251408 = a;
        double r251409 = r251407 * r251408;
        double r251410 = 10.0;
        double r251411 = r251410 + r251405;
        double r251412 = r251405 * r251411;
        double r251413 = 1.0;
        double r251414 = r251412 + r251413;
        double r251415 = r251409 / r251414;
        return r251415;
}

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 2.3

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

  2. Simplified2.3

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

  4. Applied associate-*l/2.3

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

  5. Final simplification2.3

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

Reproduce

herbie shell --seed 2020057 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))