Average Error: 35.9 → 32.2
Time: 29.0s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\frac{\sqrt[3]{1 \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}}{\sqrt[3]{2 \cdot a}} + \frac{\sqrt[3]{1 \cdot \left(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right)}}{\sqrt[3]{2 \cdot a}}\]
\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(\sqrt{g \cdot g - h \cdot h} + \left(-g\right)\right)}}{\sqrt[3]{2 \cdot a}}
double f(double g, double h, double a) {
        double r5363437 = 1.0;
        double r5363438 = 2.0;
        double r5363439 = a;
        double r5363440 = r5363438 * r5363439;
        double r5363441 = r5363437 / r5363440;
        double r5363442 = g;
        double r5363443 = -r5363442;
        double r5363444 = r5363442 * r5363442;
        double r5363445 = h;
        double r5363446 = r5363445 * r5363445;
        double r5363447 = r5363444 - r5363446;
        double r5363448 = sqrt(r5363447);
        double r5363449 = r5363443 + r5363448;
        double r5363450 = r5363441 * r5363449;
        double r5363451 = cbrt(r5363450);
        double r5363452 = r5363443 - r5363448;
        double r5363453 = r5363441 * r5363452;
        double r5363454 = cbrt(r5363453);
        double r5363455 = r5363451 + r5363454;
        return r5363455;
}
↓
double f(double g, double h, double a) {
        double r5363456 = 1.0;
        double r5363457 = g;
        double r5363458 = -r5363457;
        double r5363459 = r5363457 * r5363457;
        double r5363460 = h;
        double r5363461 = r5363460 * r5363460;
        double r5363462 = r5363459 - r5363461;
        double r5363463 = sqrt(r5363462);
        double r5363464 = r5363458 - r5363463;
        double r5363465 = r5363456 * r5363464;
        double r5363466 = cbrt(r5363465);
        double r5363467 = 2.0;
        double r5363468 = a;
        double r5363469 = r5363467 * r5363468;
        double r5363470 = cbrt(r5363469);
        double r5363471 = r5363466 / r5363470;
        double r5363472 = r5363463 + r5363458;
        double r5363473 = r5363456 * r5363472;
        double r5363474 = cbrt(r5363473);
        double r5363475 = r5363474 / r5363470;
        double r5363476 = r5363471 + r5363475;
        return r5363476;
}

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 associate-*l/35.9

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

  4. Applied cbrt-div33.9

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

  6. Applied associate-*l/33.9

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

  7. Applied cbrt-div32.2

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

  8. Final simplification32.2

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

Reproduce

herbie shell --seed 2019170 
(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))))))))