Average Error: 15.9 → 0.8
Time: 3.4s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (/ 1.0 (/ (cbrt a) (cbrt (* 0.5 g)))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return 1.0 / (cbrt(a) / cbrt(0.5 * g));
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.9

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied div-inv_binary64_142215.9

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\]

  4. Applied cbrt-prod_binary64_14530.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{0.5}{a}}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity_binary64_14250.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{\color{blue}{1 \cdot a}}}\]

  8. Applied add-sqr-sqrt_binary64_14460.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\frac{\color{blue}{\sqrt{0.5} \cdot \sqrt{0.5}}}{1 \cdot a}}\]

  9. Applied times-frac_binary64_14310.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{\sqrt{0.5}}{1} \cdot \frac{\sqrt{0.5}}{a}}}\]

  10. Applied cbrt-prod_binary64_14530.9

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{\frac{\sqrt{0.5}}{1}} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\right)}\]

  11. Applied associate-*r*_binary64_13670.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{1}}\right) \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}}\]

  12. Simplified0.9

    \[\leadsto \color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right)} \cdot \sqrt[3]{\frac{\sqrt{0.5}}{a}}\]
  13. Using strategy rm

  14. Applied cbrt-div_binary64_14541.1

    \[\leadsto \left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right) \cdot \color{blue}{\frac{\sqrt[3]{\sqrt{0.5}}}{\sqrt[3]{a}}}\]

  15. Applied associate-*r/_binary64_13691.1

    \[\leadsto \color{blue}{\frac{\left(\sqrt[3]{g} \cdot \sqrt[3]{\sqrt{0.5}}\right) \cdot \sqrt[3]{\sqrt{0.5}}}{\sqrt[3]{a}}}\]

  16. Simplified0.8

    \[\leadsto \frac{\color{blue}{\sqrt[3]{0.5 \cdot g}}}{\sqrt[3]{a}}\]
  17. Using strategy rm

  18. Applied clear-num_binary64_14240.8

    \[\leadsto \color{blue}{\frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}}\]

  19. Final simplification0.8

    \[\leadsto \frac{1}{\frac{\sqrt[3]{a}}{\sqrt[3]{0.5 \cdot g}}}\]

Reproduce

herbie shell --seed 2020280 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))