Average Error: 2.0 → 2.0
Time: 7.1s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a \cdot {k}^{m}}{1 + k \cdot \left(10 + k\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a \cdot {k}^{m}}{1 + k \cdot \left(10 + k\right)}
double f(double a, double k, double m) {
        double r233415 = a;
        double r233416 = k;
        double r233417 = m;
        double r233418 = pow(r233416, r233417);
        double r233419 = r233415 * r233418;
        double r233420 = 1.0;
        double r233421 = 10.0;
        double r233422 = r233421 * r233416;
        double r233423 = r233420 + r233422;
        double r233424 = r233416 * r233416;
        double r233425 = r233423 + r233424;
        double r233426 = r233419 / r233425;
        return r233426;
}
↓
double f(double a, double k, double m) {
        double r233427 = a;
        double r233428 = k;
        double r233429 = m;
        double r233430 = pow(r233428, r233429);
        double r233431 = r233427 * r233430;
        double r233432 = 1.0;
        double r233433 = 10.0;
        double r233434 = r233433 + r233428;
        double r233435 = r233428 * r233434;
        double r233436 = r233432 + r233435;
        double r233437 = r233431 / r233436;
        return r233437;
}

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. Using strategy rm

  3. Applied associate-+l+2.0

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

  4. Simplified2.0

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

  5. Final simplification2.0

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

Reproduce

herbie shell --seed 2019356 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))