Average Error: 36.2 → 32.3
Time: 24.0s
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 r129016 = 1.0;
        double r129017 = 2.0;
        double r129018 = a;
        double r129019 = r129017 * r129018;
        double r129020 = r129016 / r129019;
        double r129021 = g;
        double r129022 = -r129021;
        double r129023 = r129021 * r129021;
        double r129024 = h;
        double r129025 = r129024 * r129024;
        double r129026 = r129023 - r129025;
        double r129027 = sqrt(r129026);
        double r129028 = r129022 + r129027;
        double r129029 = r129020 * r129028;
        double r129030 = cbrt(r129029);
        double r129031 = r129022 - r129027;
        double r129032 = r129020 * r129031;
        double r129033 = cbrt(r129032);
        double r129034 = r129030 + r129033;
        return r129034;
}
↓
double f(double g, double h, double a) {
        double r129035 = 1.0;
        double r129036 = 2.0;
        double r129037 = a;
        double r129038 = r129036 * r129037;
        double r129039 = r129035 / r129038;
        double r129040 = cbrt(r129039);
        double r129041 = g;
        double r129042 = r129041 * r129041;
        double r129043 = h;
        double r129044 = r129043 * r129043;
        double r129045 = r129042 - r129044;
        double r129046 = sqrt(r129045);
        double r129047 = r129046 - r129041;
        double r129048 = cbrt(r129047);
        double r129049 = r129040 * r129048;
        double r129050 = -r129041;
        double r129051 = r129050 - r129046;
        double r129052 = cbrt(r129051);
        double r129053 = r129040 * r129052;
        double r129054 = r129049 + r129053;
        return r129054;
}

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 36.2

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

  3. Applied cbrt-prod34.1

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

  4. Simplified34.1

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

  6. Applied cbrt-prod32.3

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

  7. Final simplification32.3

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

Reproduce

herbie shell --seed 2019195 
(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))))))))