Average Error: 35.6 → 32.0
Time: 7.7s
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 r153173 = 1.0;
        double r153174 = 2.0;
        double r153175 = a;
        double r153176 = r153174 * r153175;
        double r153177 = r153173 / r153176;
        double r153178 = g;
        double r153179 = -r153178;
        double r153180 = r153178 * r153178;
        double r153181 = h;
        double r153182 = r153181 * r153181;
        double r153183 = r153180 - r153182;
        double r153184 = sqrt(r153183);
        double r153185 = r153179 + r153184;
        double r153186 = r153177 * r153185;
        double r153187 = cbrt(r153186);
        double r153188 = r153179 - r153184;
        double r153189 = r153177 * r153188;
        double r153190 = cbrt(r153189);
        double r153191 = r153187 + r153190;
        return r153191;
}
↓
double f(double g, double h, double a) {
        double r153192 = 1.0;
        double r153193 = g;
        double r153194 = -r153193;
        double r153195 = r153193 * r153193;
        double r153196 = h;
        double r153197 = r153196 * r153196;
        double r153198 = r153195 - r153197;
        double r153199 = sqrt(r153198);
        double r153200 = r153194 + r153199;
        double r153201 = r153192 * r153200;
        double r153202 = cbrt(r153201);
        double r153203 = 2.0;
        double r153204 = a;
        double r153205 = r153203 * r153204;
        double r153206 = cbrt(r153205);
        double r153207 = r153202 / r153206;
        double r153208 = r153194 - r153199;
        double r153209 = r153192 * r153208;
        double r153210 = cbrt(r153209);
        double r153211 = r153210 / r153206;
        double r153212 = r153207 + r153211;
        return r153212;
}

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 35.6

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

  3. Applied associate-*l/35.6

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

  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. Using strategy rm

  6. Applied associate-*l/33.7

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

  7. Applied cbrt-div32.0

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

  8. Final simplification32.0

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

Reproduce

herbie shell --seed 2020056 
(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))))))))