Average Error: 2.1 → 2.1
Time: 11.8s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{\sqrt{1 + k \cdot \left(10 + k\right)}} \cdot \frac{{k}^{m}}{\sqrt{1 + k \cdot \left(10 + k\right)}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{\sqrt{1 + k \cdot \left(10 + k\right)}} \cdot \frac{{k}^{m}}{\sqrt{1 + k \cdot \left(10 + k\right)}}
double f(double a, double k, double m) {
        double r325588 = a;
        double r325589 = k;
        double r325590 = m;
        double r325591 = pow(r325589, r325590);
        double r325592 = r325588 * r325591;
        double r325593 = 1.0;
        double r325594 = 10.0;
        double r325595 = r325594 * r325589;
        double r325596 = r325593 + r325595;
        double r325597 = r325589 * r325589;
        double r325598 = r325596 + r325597;
        double r325599 = r325592 / r325598;
        return r325599;
}
↓
double f(double a, double k, double m) {
        double r325600 = a;
        double r325601 = 1.0;
        double r325602 = k;
        double r325603 = 10.0;
        double r325604 = r325603 + r325602;
        double r325605 = r325602 * r325604;
        double r325606 = r325601 + r325605;
        double r325607 = sqrt(r325606);
        double r325608 = r325600 / r325607;
        double r325609 = m;
        double r325610 = pow(r325602, r325609);
        double r325611 = r325610 / r325607;
        double r325612 = r325608 * r325611;
        return r325612;
}

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 add-sqr-sqrt2.1

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

  4. Applied times-frac2.1

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

  5. Simplified2.1

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

  6. Simplified2.1

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

  7. Final simplification2.1

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

Reproduce

herbie shell --seed 2020043 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))