Average Error: 34.7 → 31.1
Time: 22.3s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \cdot \sqrt[3]{\frac{1}{a \cdot 2}} + \frac{\sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}}{\sqrt[3]{a \cdot 2}}\]
\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]{\left(-g\right) + \sqrt{g \cdot g - h \cdot h}} \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 r2510375 = 1.0;
        double r2510376 = 2.0;
        double r2510377 = a;
        double r2510378 = r2510376 * r2510377;
        double r2510379 = r2510375 / r2510378;
        double r2510380 = g;
        double r2510381 = -r2510380;
        double r2510382 = r2510380 * r2510380;
        double r2510383 = h;
        double r2510384 = r2510383 * r2510383;
        double r2510385 = r2510382 - r2510384;
        double r2510386 = sqrt(r2510385);
        double r2510387 = r2510381 + r2510386;
        double r2510388 = r2510379 * r2510387;
        double r2510389 = cbrt(r2510388);
        double r2510390 = r2510381 - r2510386;
        double r2510391 = r2510379 * r2510390;
        double r2510392 = cbrt(r2510391);
        double r2510393 = r2510389 + r2510392;
        return r2510393;
}
↓
double f(double g, double h, double a) {
        double r2510394 = g;
        double r2510395 = -r2510394;
        double r2510396 = r2510394 * r2510394;
        double r2510397 = h;
        double r2510398 = r2510397 * r2510397;
        double r2510399 = r2510396 - r2510398;
        double r2510400 = sqrt(r2510399);
        double r2510401 = r2510395 + r2510400;
        double r2510402 = cbrt(r2510401);
        double r2510403 = 1.0;
        double r2510404 = a;
        double r2510405 = 2.0;
        double r2510406 = r2510404 * r2510405;
        double r2510407 = r2510403 / r2510406;
        double r2510408 = cbrt(r2510407);
        double r2510409 = r2510402 * r2510408;
        double r2510410 = r2510395 - r2510400;
        double r2510411 = cbrt(r2510410);
        double r2510412 = cbrt(r2510406);
        double r2510413 = r2510411 / r2510412;
        double r2510414 = r2510409 + r2510413;
        return r2510414;
}

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 34.7

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

  3. Applied associate-*l/34.7

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

  4. Applied cbrt-div32.9

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

  6. Applied cbrt-prod31.1

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

  7. Final simplification31.1

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

Reproduce

herbie shell --seed 2019153 
(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))))))))