Average Error: 36.6 → 33.0
Time: 16.1s
Precision: 64
\[\sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) + \sqrt{g \cdot g - h \cdot h}\right)} + \sqrt[3]{\frac{1}{2 \cdot a} \cdot \left(\left(-g\right) - \sqrt{g \cdot g - h \cdot h}\right)}\]
↓
\[\sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\sqrt{g \cdot g - h \cdot h} - g} + \sqrt[3]{\frac{1}{2 \cdot a}} \cdot \sqrt[3]{\left(-g\right) - \sqrt{g \cdot g - h \cdot h}}\]
\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]{\sqrt{g \cdot g - h \cdot h} - g} + \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 r182485 = 1.0;
        double r182486 = 2.0;
        double r182487 = a;
        double r182488 = r182486 * r182487;
        double r182489 = r182485 / r182488;
        double r182490 = g;
        double r182491 = -r182490;
        double r182492 = r182490 * r182490;
        double r182493 = h;
        double r182494 = r182493 * r182493;
        double r182495 = r182492 - r182494;
        double r182496 = sqrt(r182495);
        double r182497 = r182491 + r182496;
        double r182498 = r182489 * r182497;
        double r182499 = cbrt(r182498);
        double r182500 = r182491 - r182496;
        double r182501 = r182489 * r182500;
        double r182502 = cbrt(r182501);
        double r182503 = r182499 + r182502;
        return r182503;
}
↓
double f(double g, double h, double a) {
        double r182504 = 1.0;
        double r182505 = 2.0;
        double r182506 = a;
        double r182507 = r182505 * r182506;
        double r182508 = r182504 / r182507;
        double r182509 = cbrt(r182508);
        double r182510 = g;
        double r182511 = r182510 * r182510;
        double r182512 = h;
        double r182513 = r182512 * r182512;
        double r182514 = r182511 - r182513;
        double r182515 = sqrt(r182514);
        double r182516 = r182515 - r182510;
        double r182517 = cbrt(r182516);
        double r182518 = r182509 * r182517;
        double r182519 = -r182510;
        double r182520 = r182519 - r182515;
        double r182521 = cbrt(r182520);
        double r182522 = r182509 * r182521;
        double r182523 = r182518 + r182522;
        return r182523;
}

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. Using strategy rm

  3. Applied cbrt-prod34.7

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

  4. Simplified34.7

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

  6. Applied cbrt-prod33.0

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

  7. Final simplification33.0

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

Reproduce

herbie shell --seed 2020047 
(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))))))))