Average Error: 15.7 → 0.8
Time: 7.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{\frac{g}{2}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{\frac{g}{2}}}{\sqrt[3]{a}}
double code(double g, double a) {
	return cbrt((g / (2.0 * a)));
}
↓
double code(double g, double a) {
	return (cbrt((g / 2.0)) / cbrt(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 15.7

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

  3. Applied associate-/r*15.7

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

  4. Applied cbrt-div0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))