Average Error: 1.9 → 1.9
Time: 4.8s
Precision: binary64
\[\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}\]
↓
\[{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot \frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{\left(\sqrt[3]{k}\right)}^{m}}}\]
\frac{a \cdot {k}^{m}}{\left(1 + 10 \cdot k\right) + k \cdot k}
↓
{\left(\sqrt[3]{k} \cdot \sqrt[3]{k}\right)}^{m} \cdot \frac{a}{\frac{1 + k \cdot \left(k + 10\right)}{{\left(\sqrt[3]{k}\right)}^{m}}}
(FPCore (a k m)
 :precision binary64
 (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))
↓
(FPCore (a k m)
 :precision binary64
 (*
  (pow (* (cbrt k) (cbrt k)) m)
  (/ a (/ (+ 1.0 (* k (+ k 10.0))) (pow (cbrt k) m)))))
double code(double a, double k, double m) {
	return (((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) pow(((double) (((double) cbrt(k)) * ((double) cbrt(k)))), m)) * (a / (((double) (1.0 + ((double) (k * ((double) (k + 10.0)))))) / ((double) pow(((double) cbrt(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 1.9

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

  3. Applied associate-/l*_binary641.9

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

  4. Simplified1.8

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

  6. Applied add-cube-cbrt_binary641.8

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

  7. Applied unpow-prod-down_binary641.9

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

  8. Applied *-un-lft-identity_binary641.9

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

  9. Applied times-frac_binary641.9

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

  10. Applied *-un-lft-identity_binary641.9

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

  11. Applied times-frac_binary641.9

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

  12. Simplified1.9

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

  13. Final simplification1.9

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

Reproduce

herbie shell --seed 2020205 
(FPCore (a k m)
  :name "Falkner and Boettcher, Appendix A"
  :precision binary64
  (/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k))))