Average Error: 1.9 → 1.9
Time: 6.5s
Precision: binary64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k} \]
↓
\[\left(a \cdot {k}^{m}\right) \cdot \frac{1}{1 + k \cdot \left(k + 10\right)} \]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
\left(a \cdot {k}^{m}\right) \cdot \frac{1}{1 + k \cdot \left(k + 10\right)}

(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
↓
(FPCore (a k m)
 :precision binary64
 (* (* a (pow k m)) (/ 1.0 (+ 1.0 (* k (+ k 10.0))))))
double code(double a, double k, double m) {
	return (a * pow(k, m)) / ((1.0 + (10.0 * k)) + (k * k));
}
↓
double code(double a, double k, double m) {
	return (a * pow(k, m)) * (1.0 / (1.0 + (k * (k + 10.0))));
}

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 1.9

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

  2. Simplified1.9

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

  4. Applied distribute-rgt-in_binary641.9

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

  5. Simplified1.9

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

  7. Applied div-inv_binary641.9

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

  8. Simplified1.9

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

  9. Final simplification1.9

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

Reproduce

herbie shell --seed 2021206 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))