Average Error: 0.2 → 0.2
Time: 23.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - {m}^{3} \cdot \frac{1}{v}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - {m}^{3} \cdot \frac{1}{v}
double f(double m, double v) {
        double r38008 = m;
        double r38009 = 1.0;
        double r38010 = r38009 - r38008;
        double r38011 = r38008 * r38010;
        double r38012 = v;
        double r38013 = r38011 / r38012;
        double r38014 = r38013 - r38009;
        double r38015 = r38014 * r38008;
        return r38015;
}
↓
double f(double m, double v) {
        double r38016 = m;
        double r38017 = v;
        double r38018 = r38017 / r38016;
        double r38019 = r38016 / r38018;
        double r38020 = r38019 - r38016;
        double r38021 = 1.0;
        double r38022 = r38020 * r38021;
        double r38023 = 3.0;
        double r38024 = pow(r38016, r38023);
        double r38025 = 1.0;
        double r38026 = r38025 / r38017;
        double r38027 = r38024 * r38026;
        double r38028 = r38022 - r38027;
        return r38028;
}

Error

Bits error versus m

Bits error versus v

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied associate-/l*0.2

    \[\leadsto \left(\color{blue}{\frac{m}{\frac{v}{1 - m}}} - 1\right) \cdot m\]

  4. Taylor expanded around 0 6.8

    \[\leadsto \color{blue}{1 \cdot \frac{{m}^{2}}{v} - \left(1 \cdot m + \frac{{m}^{3}}{v}\right)}\]

  5. Simplified0.2

    \[\leadsto \color{blue}{1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{3}}{v}}\]
  6. Using strategy rm

  7. Applied *-un-lft-identity0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{\color{blue}{\left(1 \cdot m\right)}}^{3}}{v}\]

  8. Applied unpow-prod-down0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{\color{blue}{{1}^{3} \cdot {m}^{3}}}{v}\]

  9. Applied associate-/l*0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \color{blue}{\frac{{1}^{3}}{\frac{v}{{m}^{3}}}}\]
  10. Using strategy rm

  11. Applied div-inv0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{1}^{3}}{\color{blue}{v \cdot \frac{1}{{m}^{3}}}}\]

  12. Applied add-cube-cbrt0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{\color{blue}{\left(\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{1}^{3}}\right) \cdot \sqrt[3]{{1}^{3}}}}{v \cdot \frac{1}{{m}^{3}}}\]

  13. Applied times-frac0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \color{blue}{\frac{\sqrt[3]{{1}^{3}} \cdot \sqrt[3]{{1}^{3}}}{v} \cdot \frac{\sqrt[3]{{1}^{3}}}{\frac{1}{{m}^{3}}}}\]

  14. Simplified0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \color{blue}{\frac{1 \cdot 1}{v}} \cdot \frac{\sqrt[3]{{1}^{3}}}{\frac{1}{{m}^{3}}}\]

  15. Simplified0.2

    \[\leadsto 1 \cdot \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{1 \cdot 1}{v} \cdot \color{blue}{{m}^{3}}\]

  16. Final simplification0.2

    \[\leadsto \left(\frac{m}{\frac{v}{m}} - m\right) \cdot 1 - {m}^{3} \cdot \frac{1}{v}\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) m))