Average Error: 2.3 → 2.2
Time: 7.3s
Precision: 64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[\frac{a}{-\left(k \cdot \left(10 + k\right) + 1\right)} \cdot \left(-{k}^{m}\right)\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\frac{a}{-\left(k \cdot \left(10 + k\right) + 1\right)} \cdot \left(-{k}^{m}\right)
double code(double a, double k, double m) {
	return ((double) (((double) (a * ((double) pow(k, m)))) / ((double) (((double) (1.0 + ((double) (10.0 * k)))) + ((double) (k * k))))));
}
↓
double code(double a, double k, double m) {
	return ((double) (((double) (a / ((double) -(((double) (((double) (k * ((double) (10.0 + k)))) + 1.0)))))) * ((double) -(((double) pow(k, m))))));
}

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 2.3

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

  2. Simplified2.2

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

  4. Applied clear-num2.2

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

  5. Applied associate-*l/2.2

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

  6. Simplified2.2

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

  8. Applied frac-2neg2.2

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

  9. Applied associate-/r/2.2

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

  10. Final simplification2.2

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

Reproduce

herbie shell --seed 2020114 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1 (* 10 k)) (* k k))))