Average Error: 2.0 → 2.0
Time: 23.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{\frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{\frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}
double f(double a, double k, double m) {
        double r15900596 = a;
        double r15900597 = k;
        double r15900598 = m;
        double r15900599 = pow(r15900597, r15900598);
        double r15900600 = r15900596 * r15900599;
        double r15900601 = 1.0;
        double r15900602 = 10.0;
        double r15900603 = r15900602 * r15900597;
        double r15900604 = r15900601 + r15900603;
        double r15900605 = r15900597 * r15900597;
        double r15900606 = r15900604 + r15900605;
        double r15900607 = r15900600 / r15900606;
        return r15900607;
}
↓
double f(double a, double k, double m) {
        double r15900608 = a;
        double r15900609 = k;
        double r15900610 = cbrt(r15900609);
        double r15900611 = r15900610 * r15900610;
        double r15900612 = m;
        double r15900613 = pow(r15900611, r15900612);
        double r15900614 = r15900608 * r15900613;
        double r15900615 = pow(r15900610, r15900612);
        double r15900616 = r15900614 * r15900615;
        double r15900617 = 1.0;
        double r15900618 = 10.0;
        double r15900619 = r15900618 * r15900609;
        double r15900620 = r15900617 + r15900619;
        double r15900621 = r15900609 * r15900609;
        double r15900622 = r15900620 + r15900621;
        double r15900623 = sqrt(r15900622);
        double r15900624 = r15900616 / r15900623;
        double r15900625 = r15900624 / r15900623;
        return r15900625;
}

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 add-cube-cbrt2.0

    \[\leadsto \frac{a \cdot {\color{blue}{\left(\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right) \cdot \sqrt[3]{k}\right)}}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  4. Applied unpow-prod-down2.0

    \[\leadsto \frac{a \cdot \color{blue}{\left({\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot {\left(\sqrt[3]{k}\right)}^{m}\right)}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]

  5. Applied associate-*r*2.0

    \[\leadsto \frac{\color{blue}{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
  6. Using strategy rm

  7. Applied add-sqr-sqrt2.0

    \[\leadsto \frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\color{blue}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k} \cdot \sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}\]

  8. Applied associate-/r*2.0

    \[\leadsto \color{blue}{\frac{\frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}\]

  9. Final simplification2.0

    \[\leadsto \frac{\frac{\left(a \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}}{\sqrt{\left(1 + 10 \cdot k\right) + k \cdot k}}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))