Average Error: 0.2 → 0.2
Time: 19.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{m}{\sqrt{v}} \cdot \frac{m}{\sqrt{v}}\right) - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{m}{\sqrt{v}} \cdot \frac{m}{\sqrt{v}}\right) - 1\right) \cdot m
double f(double m, double v) {
        double r18889 = m;
        double r18890 = 1.0;
        double r18891 = r18890 - r18889;
        double r18892 = r18889 * r18891;
        double r18893 = v;
        double r18894 = r18892 / r18893;
        double r18895 = r18894 - r18890;
        double r18896 = r18895 * r18889;
        return r18896;
}
↓
double f(double m, double v) {
        double r18897 = 1.0;
        double r18898 = m;
        double r18899 = v;
        double r18900 = r18898 / r18899;
        double r18901 = r18897 * r18900;
        double r18902 = sqrt(r18899);
        double r18903 = r18898 / r18902;
        double r18904 = r18903 * r18903;
        double r18905 = r18901 - r18904;
        double r18906 = r18905 - r18897;
        double r18907 = r18906 * r18898;
        return r18907;
}

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. Taylor expanded around 0 0.2

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

  4. Applied add-sqr-sqrt0.2

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

  5. Applied add-sqr-sqrt0.3

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

  6. Applied unpow-prod-down0.3

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

  7. Applied times-frac0.3

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

  8. Simplified0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019305 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))