Average Error: 35.9 → 32.1
Time: 7.8s
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 r167446 = 1.0;
        double r167447 = 2.0;
        double r167448 = a;
        double r167449 = r167447 * r167448;
        double r167450 = r167446 / r167449;
        double r167451 = g;
        double r167452 = -r167451;
        double r167453 = r167451 * r167451;
        double r167454 = h;
        double r167455 = r167454 * r167454;
        double r167456 = r167453 - r167455;
        double r167457 = sqrt(r167456);
        double r167458 = r167452 + r167457;
        double r167459 = r167450 * r167458;
        double r167460 = cbrt(r167459);
        double r167461 = r167452 - r167457;
        double r167462 = r167450 * r167461;
        double r167463 = cbrt(r167462);
        double r167464 = r167460 + r167463;
        return r167464;
}
↓
double f(double g, double h, double a) {
        double r167465 = 1.0;
        double r167466 = 2.0;
        double r167467 = a;
        double r167468 = r167466 * r167467;
        double r167469 = r167465 / r167468;
        double r167470 = cbrt(r167469);
        double r167471 = g;
        double r167472 = -r167471;
        double r167473 = r167471 * r167471;
        double r167474 = h;
        double r167475 = r167474 * r167474;
        double r167476 = r167473 - r167475;
        double r167477 = sqrt(r167476);
        double r167478 = r167472 + r167477;
        double r167479 = cbrt(r167478);
        double r167480 = r167470 * r167479;
        double r167481 = r167472 - r167477;
        double r167482 = cbrt(r167481);
        double r167483 = r167470 * r167482;
        double r167484 = r167480 + r167483;
        return r167484;
}

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 35.9

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

  3. Applied cbrt-prod33.8

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

  5. Applied cbrt-prod32.1

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

  6. Final simplification32.1

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

Reproduce

herbie shell --seed 2020059 
(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))))))))