Average Error: 36.3 → 32.5
Time: 12.0s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}
↓
\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}
double code(double g, double h, double a) {
	return (cbrt(((1.0 / (2.0 * a)) * (-g + sqrt(((g * g) - (h * h)))))) + cbrt(((1.0 / (2.0 * a)) * (-g - sqrt(((g * g) - (h * h)))))));
}
↓
double code(double g, double h, double a) {
	return ((cbrt((-g + sqrt(((g * g) - (h * h))))) * cbrt((1.0 / (2.0 * a)))) + (cbrt((-g - sqrt(((g * g) - (h * h))))) * cbrt((1.0 / (2.0 * a)))));
}

Error

Bits error versus g

Bits error versus h

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 36.3

    \[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
  2. Using strategy rm

  3. Applied *-commutative36.3

    \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\color{blue}{\left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{1}{2 \cdot a}}}\]

  4. Applied cbrt-prod34.2

    \[\leadsto \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \color{blue}{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]
  5. Using strategy rm

  6. Applied *-commutative34.2

    \[\leadsto \sqrt[3]{\color{blue}{\left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right) \cdot \frac{1}{2 \cdot a}}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

  7. Applied cbrt-prod32.5

    \[\leadsto \color{blue}{\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

  8. Final simplification32.5

    \[\leadsto \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}} + \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}\]

Reproduce

herbie shell --seed 2020066 +o rules:numerics
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))