Average Error: 2.1 → 2.0
Time: 4.0s
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 r273513 = a;
        double r273514 = k;
        double r273515 = m;
        double r273516 = pow(r273514, r273515);
        double r273517 = r273513 * r273516;
        double r273518 = 1.0;
        double r273519 = 10.0;
        double r273520 = r273519 * r273514;
        double r273521 = r273518 + r273520;
        double r273522 = r273514 * r273514;
        double r273523 = r273521 + r273522;
        double r273524 = r273517 / r273523;
        return r273524;
}
↓
double f(double a, double k, double m) {
        double r273525 = a;
        double r273526 = k;
        double r273527 = m;
        double r273528 = pow(r273526, r273527);
        double r273529 = r273525 * r273528;
        double r273530 = 1.0;
        double r273531 = 10.0;
        double r273532 = r273531 + r273526;
        double r273533 = r273526 * r273532;
        double r273534 = r273530 + r273533;
        double r273535 = r273529 / r273534;
        return r273535;
}

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. Using strategy rm

  3. Applied associate-+l+2.1

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

  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 2020021 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))