Average Error: 35.5 → 31.9
Time: 35.6s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}\]
\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]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r19975031 = 1.0;
        double r19975032 = 2.0;
        double r19975033 = a;
        double r19975034 = r19975032 * r19975033;
        double r19975035 = r19975031 / r19975034;
        double r19975036 = g;
        double r19975037 = -r19975036;
        double r19975038 = r19975036 * r19975036;
        double r19975039 = h;
        double r19975040 = r19975039 * r19975039;
        double r19975041 = r19975038 - r19975040;
        double r19975042 = sqrt(r19975041);
        double r19975043 = r19975037 + r19975042;
        double r19975044 = r19975035 * r19975043;
        double r19975045 = cbrt(r19975044);
        double r19975046 = r19975037 - r19975042;
        double r19975047 = r19975035 * r19975046;
        double r19975048 = cbrt(r19975047);
        double r19975049 = r19975045 + r19975048;
        return r19975049;
}
↓
double f(double g, double h, double a) {
        double r19975050 = g;
        double r19975051 = -r19975050;
        double r19975052 = r19975050 * r19975050;
        double r19975053 = h;
        double r19975054 = r19975053 * r19975053;
        double r19975055 = r19975052 - r19975054;
        double r19975056 = sqrt(r19975055);
        double r19975057 = r19975051 - r19975056;
        double r19975058 = cbrt(r19975057);
        double r19975059 = 1.0;
        double r19975060 = a;
        double r19975061 = 2.0;
        double r19975062 = r19975060 * r19975061;
        double r19975063 = r19975059 / r19975062;
        double r19975064 = cbrt(r19975063);
        double r19975065 = r19975058 * r19975064;
        double r19975066 = r19975056 - r19975050;
        double r19975067 = cbrt(r19975066);
        double r19975068 = cbrt(r19975062);
        double r19975069 = r19975067 / r19975068;
        double r19975070 = r19975065 + r19975069;
        return r19975070;
}

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 35.5

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

  3. Applied associate-*l/35.5

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

  4. Applied cbrt-div33.7

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

  5. Simplified33.7

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

  7. Applied cbrt-prod31.9

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

  8. Final simplification31.9

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

Reproduce

herbie shell --seed 2019104 
(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))))))))