Average Error: 15.3 → 0.9
Time: 5.3s
Precision: binary64
Cost: 13248
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}\]
\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

Alternatives

Alternative 1
Error0.8
Cost13120
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
Alternative 2
Error0.8
Cost13120
\[\sqrt[3]{g} \cdot \sqrt[3]{\frac{0.5}{a}}\]
Alternative 3
Error15.3
Cost6848
\[\frac{1}{\sqrt[3]{\frac{2 \cdot a}{g}}}\]
Alternative 4
Error15.3
Cost6720
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
Alternative 5
Error61.1
Cost64
\[1\]

Error

Derivation

  1. Initial program 15.3

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

  3. Applied cbrt-div_binary64_52250.8

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

  5. Applied div-inv_binary64_51900.9

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

  6. Simplified0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2021044 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))