Average Error: 2.2 → 2.2
Time: 3.6s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
double f(double a, double k, double m) {
        double r374514 = a;
        double r374515 = k;
        double r374516 = m;
        double r374517 = pow(r374515, r374516);
        double r374518 = r374514 * r374517;
        double r374519 = 1.0;
        double r374520 = 10.0;
        double r374521 = r374520 * r374515;
        double r374522 = r374519 + r374521;
        double r374523 = r374515 * r374515;
        double r374524 = r374522 + r374523;
        double r374525 = r374518 / r374524;
        return r374525;
}
↓
double f(double a, double k, double m) {
        double r374526 = a;
        double r374527 = k;
        double r374528 = m;
        double r374529 = pow(r374527, r374528);
        double r374530 = r374526 * r374529;
        double r374531 = 1.0;
        double r374532 = 10.0;
        double r374533 = r374532 * r374527;
        double r374534 = r374531 + r374533;
        double r374535 = r374527 * r374527;
        double r374536 = r374534 + r374535;
        double r374537 = r374530 / r374536;
        return r374537;
}

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 2.2

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

  2. Final simplification2.2

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))