Average Error: 36.6 → 32.8
Time: 20.1s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} + \frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}}\]
\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)}
↓
\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} + \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 r127541 = 1.0;
        double r127542 = 2.0;
        double r127543 = a;
        double r127544 = r127542 * r127543;
        double r127545 = r127541 / r127544;
        double r127546 = g;
        double r127547 = -r127546;
        double r127548 = r127546 * r127546;
        double r127549 = h;
        double r127550 = r127549 * r127549;
        double r127551 = r127548 - r127550;
        double r127552 = sqrt(r127551);
        double r127553 = r127547 + r127552;
        double r127554 = r127545 * r127553;
        double r127555 = cbrt(r127554);
        double r127556 = r127547 - r127552;
        double r127557 = r127545 * r127556;
        double r127558 = cbrt(r127557);
        double r127559 = r127555 + r127558;
        return r127559;
}
↓
double f(double g, double h, double a) {
        double r127560 = 1.0;
        double r127561 = 2.0;
        double r127562 = a;
        double r127563 = r127561 * r127562;
        double r127564 = r127560 / r127563;
        double r127565 = cbrt(r127564);
        double r127566 = g;
        double r127567 = r127566 * r127566;
        double r127568 = h;
        double r127569 = r127568 * r127568;
        double r127570 = r127567 - r127569;
        double r127571 = sqrt(r127570);
        double r127572 = r127571 - r127566;
        double r127573 = cbrt(r127572);
        double r127574 = r127565 * r127573;
        double r127575 = -r127566;
        double r127576 = r127575 - r127571;
        double r127577 = r127560 * r127576;
        double r127578 = cbrt(r127577);
        double r127579 = cbrt(r127563);
        double r127580 = r127578 / r127579;
        double r127581 = r127574 + r127580;
        return r127581;
}

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 36.6

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

  2. Simplified36.6

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

  4. Applied cbrt-prod34.6

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

  6. Applied associate-*l/34.6

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

  7. Applied cbrt-div32.8

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

  8. Final simplification32.8

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

Reproduce

herbie shell --seed 2019351 
(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))))))))