Average Error: 15.4 → 0.9
Time: 14.8s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot g\right) \cdot \sqrt[3]{\frac{1}{2}}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{\frac{1}{a}} \cdot \sqrt[3]{\left(\left(\sqrt[3]{\frac{1}{2}} \cdot \sqrt[3]{\frac{1}{2}}\right) \cdot g\right) \cdot \sqrt[3]{\frac{1}{2}}}
double f(double g, double a) {
        double r4952951 = g;
        double r4952952 = 2.0;
        double r4952953 = a;
        double r4952954 = r4952952 * r4952953;
        double r4952955 = r4952951 / r4952954;
        double r4952956 = cbrt(r4952955);
        return r4952956;
}
↓
double f(double g, double a) {
        double r4952957 = 1.0;
        double r4952958 = a;
        double r4952959 = r4952957 / r4952958;
        double r4952960 = cbrt(r4952959);
        double r4952961 = 0.5;
        double r4952962 = cbrt(r4952961);
        double r4952963 = r4952962 * r4952962;
        double r4952964 = g;
        double r4952965 = r4952963 * r4952964;
        double r4952966 = r4952965 * r4952962;
        double r4952967 = cbrt(r4952966);
        double r4952968 = r4952960 * r4952967;
        return r4952968;
}

Error

Bits error versus g

Bits error versus a

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.4

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied div-inv15.4

    \[\leadsto \sqrt[3]{\color{blue}{g \cdot \frac{1}{2 \cdot a}}}\]

  4. Applied cbrt-prod0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \sqrt[3]{\frac{1}{2 \cdot a}}}\]

  5. Simplified0.8

    \[\leadsto \sqrt[3]{g} \cdot \color{blue}{\sqrt[3]{\frac{\frac{1}{2}}{a}}}\]
  6. Using strategy rm

  7. Applied div-inv0.8

    \[\leadsto \sqrt[3]{g} \cdot \sqrt[3]{\color{blue}{\frac{1}{2} \cdot \frac{1}{a}}}\]

  8. Applied cbrt-prod0.8

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

  9. Applied associate-*r*0.8

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

  11. Applied add-cbrt-cube1.0

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

  12. Simplified0.9

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

  13. Final simplification0.9

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

Reproduce

herbie shell --seed 2019130 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))