Average Error: 15.4 → 0.8
Time: 5.1s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}} \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}

(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (* (cbrt g) (/ 1.0 (cbrt (* 2.0 a)))))
double code(double g, double a) {
	return cbrt(g / (2.0 * a));
}
↓
double code(double g, double a) {
	return cbrt(g) * (1.0 / cbrt(2.0 * a));
}

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 15.4

    \[\sqrt[3]{\frac{g}{2 \cdot a}} \]

  2. Applied cbrt-div_binary640.8

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

  3. Applied div-inv_binary640.8

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

  4. Applied *-un-lft-identity_binary640.8

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

  5. Applied add-cube-cbrt_binary640.8

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

  6. Applied times-frac_binary640.8

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

  7. Applied associate-*r*_binary640.8

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

  8. Simplified0.8

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

  9. Final simplification0.8

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

Reproduce

herbie shell --seed 2022067 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))