Average Error: 15.3 → 0.8
Time: 8.5s
Precision: binary64
Cost: 13120
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}
(FPCore (g a) :precision binary64 (cbrt (/ g (* 2.0 a))))
↓
(FPCore (g a) :precision binary64 (/ (cbrt g) (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) / 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
Error0.9
Cost13248
\[\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}\]
Alternative 2
Error0.9
Cost13248
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}\]
Alternative 3
Error0.9
Cost13376
\[\frac{\frac{1}{\sqrt[3]{2 \cdot a}}}{\frac{1}{\sqrt[3]{g}}}\]
Alternative 4
Error1.2
Cost38976
\[\frac{\sqrt[3]{\sqrt[3]{g} \cdot \sqrt[3]{g}}}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{\sqrt[3]{g}}}}\]
Alternative 5
Error1.5
Cost45504
\[\frac{1}{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{\sqrt[3]{g}} \cdot \left(\sqrt[3]{\sqrt[3]{g}} \cdot \sqrt[3]{\sqrt[3]{g}}\right)}}\]
Alternative 6
Error1.6
Cost58688
\[\sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \cdot \left(\sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\right)\]
Alternative 7
Error1.6
Cost78272
\[\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{\sqrt[3]{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}} \cdot \sqrt[3]{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}} \cdot \frac{\sqrt[3]{1}}{\sqrt[3]{\frac{\sqrt[3]{2 \cdot a}}{\sqrt[3]{g}}}}\]

Error

Derivation

  1. Initial program 15.3

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

  3. Applied cbrt-div_binary64_31790.8

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

  4. Simplified0.8

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

  5. Final simplification0.8

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

Reproduce

herbie shell --seed 2021043 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2.0 a))))