Average Error: 15.5 → 0.9
Time: 2.5s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}} \]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}} \]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}

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

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 15.5

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

  3. Applied cbrt-div_binary640.9

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

  4. Simplified0.9

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

  6. Applied *-un-lft-identity_binary640.9

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

  7. Applied associate-/r*_binary640.9

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

  8. Final simplification0.9

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

Reproduce

herbie shell --seed 2021204 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))