Average Error: 15.4 → 0.8
Time: 3.9s
Precision: binary64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \left(\sqrt[3]{-0.5} \cdot \sqrt[3]{\frac{-1}{a}}\right)
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a)
 :precision binary64
 (* (cbrt g) (* (cbrt -0.5) (cbrt (/ -1.0 a)))))
double code(double g, double a) {
	return ((double) cbrt((g / ((double) (2.0 * a)))));
}
↓
double code(double g, double a) {
	return ((double) (((double) cbrt(g)) * ((double) (((double) cbrt(-0.5)) * ((double) cbrt((-1.0 / a)))))));
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

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Derivation

  1. Initial program Error: 15.4 bits

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

  3. Applied div-invError: 15.4 bits

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

  4. Applied cbrt-prodError: 0.8 bits

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

  5. Taylor expanded around -inf Error: 35.1 bits

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\left(\sqrt[3]{-0.5} \cdot e^{0.3333333333333333 \cdot \left(\log 1 + \log \left(\frac{-1}{a}\right)\right)}\right)}\]

  6. SimplifiedError: 0.8 bits

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

  7. Final simplificationError: 0.8 bits

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

Reproduce

herbie shell --seed 2020205 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))