Average Error: 2.0 → 0.2
Time: 5.5m
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{{k}^{m}}{\frac{1}{a} + \left(10 + k\right) \cdot \frac{k}{a}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{{k}^{m}}{\frac{1}{a} + \left(10 + k\right) \cdot \frac{k}{a}}
double f(double a, double k, double m) {
        double r89066317 = a;
        double r89066318 = k;
        double r89066319 = m;
        double r89066320 = pow(r89066318, r89066319);
        double r89066321 = r89066317 * r89066320;
        double r89066322 = 1.0;
        double r89066323 = 10.0;
        double r89066324 = r89066323 * r89066318;
        double r89066325 = r89066322 + r89066324;
        double r89066326 = r89066318 * r89066318;
        double r89066327 = r89066325 + r89066326;
        double r89066328 = r89066321 / r89066327;
        return r89066328;
}
↓
double f(double a, double k, double m) {
        double r89066329 = k;
        double r89066330 = m;
        double r89066331 = pow(r89066329, r89066330);
        double r89066332 = 1.0;
        double r89066333 = a;
        double r89066334 = r89066332 / r89066333;
        double r89066335 = 10.0;
        double r89066336 = r89066335 + r89066329;
        double r89066337 = r89066329 / r89066333;
        double r89066338 = r89066336 * r89066337;
        double r89066339 = r89066334 + r89066338;
        double r89066340 = r89066331 / r89066339;
        return r89066340;
}

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

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

  4. Applied add-sqr-sqrt2.0

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

  5. Applied associate-/r*2.0

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

  7. Applied *-un-lft-identity2.0

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

  8. Applied times-frac2.0

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

  9. Applied associate-/l*2.1

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

  10. Simplified2.1

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

  11. Taylor expanded around -inf 4.0

    \[\leadsto \frac{\frac{{k}^{m}}{1}}{\color{blue}{\frac{1}{a} + \left(10 \cdot \frac{k}{a} + \frac{{k}^{2}}{a}\right)}}\]

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))