Average Error: 35.2 → 31.6
Time: 22.3s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{a \cdot 2}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}\]
\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]{\frac{1}{a \cdot 2}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}}
double f(double g, double h, double a) {
        double r2591029 = 1.0;
        double r2591030 = 2.0;
        double r2591031 = a;
        double r2591032 = r2591030 * r2591031;
        double r2591033 = r2591029 / r2591032;
        double r2591034 = g;
        double r2591035 = -r2591034;
        double r2591036 = r2591034 * r2591034;
        double r2591037 = h;
        double r2591038 = r2591037 * r2591037;
        double r2591039 = r2591036 - r2591038;
        double r2591040 = sqrt(r2591039);
        double r2591041 = r2591035 + r2591040;
        double r2591042 = r2591033 * r2591041;
        double r2591043 = cbrt(r2591042);
        double r2591044 = r2591035 - r2591040;
        double r2591045 = r2591033 * r2591044;
        double r2591046 = cbrt(r2591045);
        double r2591047 = r2591043 + r2591046;
        return r2591047;
}
↓
double f(double g, double h, double a) {
        double r2591048 = 1.0;
        double r2591049 = a;
        double r2591050 = 2.0;
        double r2591051 = r2591049 * r2591050;
        double r2591052 = r2591048 / r2591051;
        double r2591053 = cbrt(r2591052);
        double r2591054 = g;
        double r2591055 = -r2591054;
        double r2591056 = r2591054 * r2591054;
        double r2591057 = h;
        double r2591058 = r2591057 * r2591057;
        double r2591059 = r2591056 - r2591058;
        double r2591060 = sqrt(r2591059);
        double r2591061 = r2591055 - r2591060;
        double r2591062 = cbrt(r2591061);
        double r2591063 = r2591053 * r2591062;
        double r2591064 = r2591055 + r2591060;
        double r2591065 = cbrt(r2591064);
        double r2591066 = r2591065 * r2591053;
        double r2591067 = r2591063 + r2591066;
        return r2591067;
}

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 35.2

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

  3. Applied cbrt-prod33.3

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

  5. Applied cbrt-prod31.6

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

  6. Final simplification31.6

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

Reproduce

herbie shell --seed 2019128 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))