Average Error: 2.0 → 2.0
Time: 10.9s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(\frac{a}{k \cdot \left(10 + k\right) + 1} \cdot {\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m}\right) \cdot {\left(\sqrt[3]{k}\right)}^{m}
double f(double a, double k, double m) {
        double r345478 = a;
        double r345479 = k;
        double r345480 = m;
        double r345481 = pow(r345479, r345480);
        double r345482 = r345478 * r345481;
        double r345483 = 1.0;
        double r345484 = 10.0;
        double r345485 = r345484 * r345479;
        double r345486 = r345483 + r345485;
        double r345487 = r345479 * r345479;
        double r345488 = r345486 + r345487;
        double r345489 = r345482 / r345488;
        return r345489;
}
↓
double f(double a, double k, double m) {
        double r345490 = a;
        double r345491 = k;
        double r345492 = 10.0;
        double r345493 = r345492 + r345491;
        double r345494 = r345491 * r345493;
        double r345495 = 1.0;
        double r345496 = r345494 + r345495;
        double r345497 = r345490 / r345496;
        double r345498 = cbrt(r345491);
        double r345499 = r345498 * r345498;
        double r345500 = m;
        double r345501 = pow(r345499, r345500);
        double r345502 = r345497 * r345501;
        double r345503 = pow(r345498, r345500);
        double r345504 = r345502 * r345503;
        return r345504;
}

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. Simplified2.0

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

  4. Applied add-cube-cbrt2.0

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

  5. Applied unpow-prod-down2.0

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

  6. Applied associate-*r*2.0

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

  7. Final simplification2.0

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))