Average Error: 35.9 → 32.1
Time: 33.0s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \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 \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}
double f(double g, double h, double a) {
        double r106048 = 1.0;
        double r106049 = 2.0;
        double r106050 = a;
        double r106051 = r106049 * r106050;
        double r106052 = r106048 / r106051;
        double r106053 = g;
        double r106054 = -r106053;
        double r106055 = r106053 * r106053;
        double r106056 = h;
        double r106057 = r106056 * r106056;
        double r106058 = r106055 - r106057;
        double r106059 = sqrt(r106058);
        double r106060 = r106054 + r106059;
        double r106061 = r106052 * r106060;
        double r106062 = cbrt(r106061);
        double r106063 = r106054 - r106059;
        double r106064 = r106052 * r106063;
        double r106065 = cbrt(r106064);
        double r106066 = r106062 + r106065;
        return r106066;
}
↓
double f(double g, double h, double a) {
        double r106067 = 1.0;
        double r106068 = 2.0;
        double r106069 = a;
        double r106070 = r106068 * r106069;
        double r106071 = r106067 / r106070;
        double r106072 = cbrt(r106071);
        double r106073 = g;
        double r106074 = r106073 * r106073;
        double r106075 = h;
        double r106076 = r106075 * r106075;
        double r106077 = r106074 - r106076;
        double r106078 = sqrt(r106077);
        double r106079 = r106078 - r106073;
        double r106080 = cbrt(r106079);
        double r106081 = r106072 * r106080;
        double r106082 = -r106073;
        double r106083 = r106082 - r106078;
        double r106084 = cbrt(r106083);
        double r106085 = r106072 * r106084;
        double r106086 = r106081 + r106085;
        return r106086;
}

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 35.9

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

  2. Simplified35.9

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

  4. Applied cbrt-prod33.9

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

  6. Applied cbrt-prod32.1

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

  7. Final simplification32.1

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

Reproduce

herbie shell --seed 2019199 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1.0 (* 2.0 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))