Average Error: 36.4 → 32.5
Time: 8.5s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\]
\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]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} + \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 r154406 = 1.0;
        double r154407 = 2.0;
        double r154408 = a;
        double r154409 = r154407 * r154408;
        double r154410 = r154406 / r154409;
        double r154411 = g;
        double r154412 = -r154411;
        double r154413 = r154411 * r154411;
        double r154414 = h;
        double r154415 = r154414 * r154414;
        double r154416 = r154413 - r154415;
        double r154417 = sqrt(r154416);
        double r154418 = r154412 + r154417;
        double r154419 = r154410 * r154418;
        double r154420 = cbrt(r154419);
        double r154421 = r154412 - r154417;
        double r154422 = r154410 * r154421;
        double r154423 = cbrt(r154422);
        double r154424 = r154420 + r154423;
        return r154424;
}
↓
double f(double g, double h, double a) {
        double r154425 = 1.0;
        double r154426 = 2.0;
        double r154427 = a;
        double r154428 = r154426 * r154427;
        double r154429 = r154425 / r154428;
        double r154430 = cbrt(r154429);
        double r154431 = g;
        double r154432 = -r154431;
        double r154433 = r154431 * r154431;
        double r154434 = h;
        double r154435 = r154434 * r154434;
        double r154436 = r154433 - r154435;
        double r154437 = sqrt(r154436);
        double r154438 = r154432 + r154437;
        double r154439 = cbrt(r154438);
        double r154440 = r154430 * r154439;
        double r154441 = r154432 - r154437;
        double r154442 = cbrt(r154441);
        double r154443 = r154430 * r154442;
        double r154444 = r154440 + r154443;
        return r154444;
}

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 36.4

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

  3. Applied cbrt-prod34.2

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

  5. Applied cbrt-prod32.5

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

  6. Final simplification32.5

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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))))))))