Average Error: 35.8 → 32.3
Time: 9.4s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}
↓
\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}
double f(double g, double h, double a) {
        double r170035 = 1.0;
        double r170036 = 2.0;
        double r170037 = a;
        double r170038 = r170036 * r170037;
        double r170039 = r170035 / r170038;
        double r170040 = g;
        double r170041 = -r170040;
        double r170042 = r170040 * r170040;
        double r170043 = h;
        double r170044 = r170043 * r170043;
        double r170045 = r170042 - r170044;
        double r170046 = sqrt(r170045);
        double r170047 = r170041 + r170046;
        double r170048 = r170039 * r170047;
        double r170049 = cbrt(r170048);
        double r170050 = r170041 - r170046;
        double r170051 = r170039 * r170050;
        double r170052 = cbrt(r170051);
        double r170053 = r170049 + r170052;
        return r170053;
}
↓
double f(double g, double h, double a) {
        double r170054 = 1.0;
        double r170055 = g;
        double r170056 = -r170055;
        double r170057 = r170055 * r170055;
        double r170058 = h;
        double r170059 = r170058 * r170058;
        double r170060 = r170057 - r170059;
        double r170061 = sqrt(r170060);
        double r170062 = r170056 + r170061;
        double r170063 = r170054 * r170062;
        double r170064 = cbrt(r170063);
        double r170065 = 2.0;
        double r170066 = a;
        double r170067 = r170065 * r170066;
        double r170068 = cbrt(r170067);
        double r170069 = r170064 / r170068;
        double r170070 = r170056 - r170061;
        double r170071 = r170054 * r170070;
        double r170072 = cbrt(r170071);
        double r170073 = r170072 / r170068;
        double r170074 = r170069 + r170073;
        return r170074;
}

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 35.8

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

  3. Applied associate-*l/35.8

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

  4. Applied cbrt-div34.0

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

  6. Applied associate-*l/34.0

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

  7. Applied cbrt-div32.3

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

  8. Final simplification32.3

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

Reproduce

herbie shell --seed 2020033 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  :precision binary64
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))