Average Error: 34.7 → 31.1
Time: 23.8s
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 r3717413 = 1.0;
        double r3717414 = 2.0;
        double r3717415 = a;
        double r3717416 = r3717414 * r3717415;
        double r3717417 = r3717413 / r3717416;
        double r3717418 = g;
        double r3717419 = -r3717418;
        double r3717420 = r3717418 * r3717418;
        double r3717421 = h;
        double r3717422 = r3717421 * r3717421;
        double r3717423 = r3717420 - r3717422;
        double r3717424 = sqrt(r3717423);
        double r3717425 = r3717419 + r3717424;
        double r3717426 = r3717417 * r3717425;
        double r3717427 = cbrt(r3717426);
        double r3717428 = r3717419 - r3717424;
        double r3717429 = r3717417 * r3717428;
        double r3717430 = cbrt(r3717429);
        double r3717431 = r3717427 + r3717430;
        return r3717431;
}
↓
double f(double g, double h, double a) {
        double r3717432 = g;
        double r3717433 = -r3717432;
        double r3717434 = r3717432 * r3717432;
        double r3717435 = h;
        double r3717436 = r3717435 * r3717435;
        double r3717437 = r3717434 - r3717436;
        double r3717438 = sqrt(r3717437);
        double r3717439 = r3717433 + r3717438;
        double r3717440 = cbrt(r3717439);
        double r3717441 = 1.0;
        double r3717442 = a;
        double r3717443 = 2.0;
        double r3717444 = r3717442 * r3717443;
        double r3717445 = r3717441 / r3717444;
        double r3717446 = cbrt(r3717445);
        double r3717447 = r3717440 * r3717446;
        double r3717448 = r3717433 - r3717438;
        double r3717449 = cbrt(r3717448);
        double r3717450 = cbrt(r3717444);
        double r3717451 = r3717449 / r3717450;
        double r3717452 = r3717447 + r3717451;
        return r3717452;
}

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 +o rules:numerics
(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))))))))