Average Error: 14.9 → 0.8
Time: 26.1s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\frac{\sqrt[3]{g}}{\sqrt[3]{a \cdot 2}}
double f(double g, double a) {
        double r19835959 = g;
        double r19835960 = 2.0;
        double r19835961 = a;
        double r19835962 = r19835960 * r19835961;
        double r19835963 = r19835959 / r19835962;
        double r19835964 = cbrt(r19835963);
        return r19835964;
}
↓
double f(double g, double a) {
        double r19835965 = g;
        double r19835966 = cbrt(r19835965);
        double r19835967 = a;
        double r19835968 = 2.0;
        double r19835969 = r19835967 * r19835968;
        double r19835970 = cbrt(r19835969);
        double r19835971 = r19835966 / r19835970;
        return r19835971;
}

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 14.9

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

  3. Applied cbrt-div0.8

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

  5. Applied *-un-lft-identity0.8

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

  6. Applied associate-/l*0.9

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

  8. Applied *-un-lft-identity0.9

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

  9. Applied cbrt-prod0.9

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

  10. Applied *-un-lft-identity0.9

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

  11. Applied times-frac0.9

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

  12. Applied *-un-lft-identity0.9

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

  13. Applied times-frac0.9

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

  14. Simplified0.9

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

  15. Simplified0.8

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

  16. Final simplification0.8

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

Reproduce

herbie shell --seed 2019124 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))