Average Error: 35.3 → 31.5
Time: 28.1s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}\]
\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]{\sqrt{g \cdot g - h \cdot h} - g} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}
double f(double g, double h, double a) {
        double r4757530 = 1.0;
        double r4757531 = 2.0;
        double r4757532 = a;
        double r4757533 = r4757531 * r4757532;
        double r4757534 = r4757530 / r4757533;
        double r4757535 = g;
        double r4757536 = -r4757535;
        double r4757537 = r4757535 * r4757535;
        double r4757538 = h;
        double r4757539 = r4757538 * r4757538;
        double r4757540 = r4757537 - r4757539;
        double r4757541 = sqrt(r4757540);
        double r4757542 = r4757536 + r4757541;
        double r4757543 = r4757534 * r4757542;
        double r4757544 = cbrt(r4757543);
        double r4757545 = r4757536 - r4757541;
        double r4757546 = r4757534 * r4757545;
        double r4757547 = cbrt(r4757546);
        double r4757548 = r4757544 + r4757547;
        return r4757548;
}
↓
double f(double g, double h, double a) {
        double r4757549 = g;
        double r4757550 = r4757549 * r4757549;
        double r4757551 = h;
        double r4757552 = r4757551 * r4757551;
        double r4757553 = r4757550 - r4757552;
        double r4757554 = sqrt(r4757553);
        double r4757555 = r4757554 - r4757549;
        double r4757556 = cbrt(r4757555);
        double r4757557 = 1.0;
        double r4757558 = a;
        double r4757559 = 2.0;
        double r4757560 = r4757558 * r4757559;
        double r4757561 = r4757557 / r4757560;
        double r4757562 = cbrt(r4757561);
        double r4757563 = r4757556 * r4757562;
        double r4757564 = -r4757549;
        double r4757565 = r4757564 - r4757554;
        double r4757566 = cbrt(r4757565);
        double r4757567 = cbrt(r4757560);
        double r4757568 = r4757566 / r4757567;
        double r4757569 = r4757563 + r4757568;
        return r4757569;
}

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 35.3

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

  2. Simplified35.3

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

  4. Applied div-inv35.3

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

  5. Applied cbrt-prod33.3

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

  7. Applied cbrt-div31.5

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

  8. Final simplification31.5

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

Reproduce

herbie shell --seed 2019135 
(FPCore (g h a)
  :name "2-ancestry mixing, positive discriminant"
  (+ (cbrt (* (/ 1 (* 2 a)) (+ (- g) (sqrt (- (* g g) (* h h)))))) (cbrt (* (/ 1 (* 2 a)) (- (- g) (sqrt (- (* g g) (* h h))))))))