Average Error: 35.3 → 31.4
Time: 29.8s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + g\right) \cdot \frac{-1}{2}}}{\sqrt[3]{a}}\]
\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]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(\sqrt{g \cdot g - h \cdot h} + g\right) \cdot \frac{-1}{2}}}{\sqrt[3]{a}}
double f(double g, double h, double a) {
        double r4606072 = 1.0;
        double r4606073 = 2.0;
        double r4606074 = a;
        double r4606075 = r4606073 * r4606074;
        double r4606076 = r4606072 / r4606075;
        double r4606077 = g;
        double r4606078 = -r4606077;
        double r4606079 = r4606077 * r4606077;
        double r4606080 = h;
        double r4606081 = r4606080 * r4606080;
        double r4606082 = r4606079 - r4606081;
        double r4606083 = sqrt(r4606082);
        double r4606084 = r4606078 + r4606083;
        double r4606085 = r4606076 * r4606084;
        double r4606086 = cbrt(r4606085);
        double r4606087 = r4606078 - r4606083;
        double r4606088 = r4606076 * r4606087;
        double r4606089 = cbrt(r4606088);
        double r4606090 = r4606086 + r4606089;
        return r4606090;
}
↓
double f(double g, double h, double a) {
        double r4606091 = g;
        double r4606092 = r4606091 * r4606091;
        double r4606093 = h;
        double r4606094 = r4606093 * r4606093;
        double r4606095 = r4606092 - r4606094;
        double r4606096 = sqrt(r4606095);
        double r4606097 = r4606096 - r4606091;
        double r4606098 = cbrt(r4606097);
        double r4606099 = 1.0;
        double r4606100 = a;
        double r4606101 = 2.0;
        double r4606102 = r4606100 * r4606101;
        double r4606103 = r4606099 / r4606102;
        double r4606104 = cbrt(r4606103);
        double r4606105 = r4606098 * r4606104;
        double r4606106 = r4606096 + r4606091;
        double r4606107 = -0.5;
        double r4606108 = r4606106 * r4606107;
        double r4606109 = cbrt(r4606108);
        double r4606110 = cbrt(r4606100);
        double r4606111 = r4606109 / r4606110;
        double r4606112 = r4606105 + r4606111;
        return r4606112;
}

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 35.3

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

  2. Simplified35.2

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

  4. Applied associate-*r/35.2

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

  5. Applied cbrt-div33.2

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

  7. Applied div-inv33.2

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

  8. Applied cbrt-prod31.4

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

  9. Final simplification31.4

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

Reproduce

herbie shell --seed 2019152 
(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))))))))