Average Error: 2.1 → 2.0
Time: 11.4s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[a \cdot \frac{{k}^{m}}{1 + k \cdot \left(10 + k\right)}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
a \cdot \frac{{k}^{m}}{1 + k \cdot \left(10 + k\right)}
double f(double a, double k, double m) {
        double r251637 = a;
        double r251638 = k;
        double r251639 = m;
        double r251640 = pow(r251638, r251639);
        double r251641 = r251637 * r251640;
        double r251642 = 1.0;
        double r251643 = 10.0;
        double r251644 = r251643 * r251638;
        double r251645 = r251642 + r251644;
        double r251646 = r251638 * r251638;
        double r251647 = r251645 + r251646;
        double r251648 = r251641 / r251647;
        return r251648;
}
↓
double f(double a, double k, double m) {
        double r251649 = a;
        double r251650 = k;
        double r251651 = m;
        double r251652 = pow(r251650, r251651);
        double r251653 = 1.0;
        double r251654 = 10.0;
        double r251655 = r251654 + r251650;
        double r251656 = r251650 * r251655;
        double r251657 = r251653 + r251656;
        double r251658 = r251652 / r251657;
        double r251659 = r251649 * r251658;
        return r251659;
}

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 *-un-lft-identity2.1

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  6. Simplified2.0

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

  7. Final simplification2.0

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

Reproduce

herbie shell --seed 2019208 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))