Average Error: 36.3 → 32.7
Time: 58.3s
Precision: 64
\[\sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1.0}{a \cdot 2.0}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1.0}{a \cdot 2.0}}\]
\sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}
↓
\sqrt[3]{\frac{1.0}{a \cdot 2.0}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1.0}{a \cdot 2.0}}
double f(double g, double h, double a) {
        double r5979323 = 1.0;
        double r5979324 = 2.0;
        double r5979325 = a;
        double r5979326 = r5979324 * r5979325;
        double r5979327 = r5979323 / r5979326;
        double r5979328 = g;
        double r5979329 = -r5979328;
        double r5979330 = r5979328 * r5979328;
        double r5979331 = h;
        double r5979332 = r5979331 * r5979331;
        double r5979333 = r5979330 - r5979332;
        double r5979334 = sqrt(r5979333);
        double r5979335 = r5979329 + r5979334;
        double r5979336 = r5979327 * r5979335;
        double r5979337 = cbrt(r5979336);
        double r5979338 = r5979329 - r5979334;
        double r5979339 = r5979327 * r5979338;
        double r5979340 = cbrt(r5979339);
        double r5979341 = r5979337 + r5979340;
        return r5979341;
}
↓
double f(double g, double h, double a) {
        double r5979342 = 1.0;
        double r5979343 = a;
        double r5979344 = 2.0;
        double r5979345 = r5979343 * r5979344;
        double r5979346 = r5979342 / r5979345;
        double r5979347 = cbrt(r5979346);
        double r5979348 = g;
        double r5979349 = -r5979348;
        double r5979350 = r5979348 * r5979348;
        double r5979351 = h;
        double r5979352 = r5979351 * r5979351;
        double r5979353 = r5979350 - r5979352;
        double r5979354 = sqrt(r5979353);
        double r5979355 = r5979349 - r5979354;
        double r5979356 = cbrt(r5979355);
        double r5979357 = r5979347 * r5979356;
        double r5979358 = r5979349 + r5979354;
        double r5979359 = cbrt(r5979358);
        double r5979360 = r5979359 * r5979347;
        double r5979361 = r5979357 + r5979360;
        return r5979361;
}

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 36.3

    \[\sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
  2. Using strategy rm

  3. Applied cbrt-prod34.6

    \[\leadsto \color{blue}{\sqrt[3]{\frac{1.0}{2.0 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}}} + \sqrt[3]{\frac{1.0}{2.0 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
  4. Using strategy rm

  5. Applied cbrt-prod32.7

    \[\leadsto \sqrt[3]{\frac{1.0}{2.0 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \color{blue}{\sqrt[3]{\frac{1.0}{2.0 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}\]

  6. Final simplification32.7

    \[\leadsto \sqrt[3]{\frac{1.0}{a \cdot 2.0}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1.0}{a \cdot 2.0}}\]

Reproduce

herbie shell --seed 2019165 
(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))))))))