Average Error: 0.2 → 0.2
Time: 15.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r17159 = m;
        double r17160 = 1.0;
        double r17161 = r17160 - r17159;
        double r17162 = r17159 * r17161;
        double r17163 = v;
        double r17164 = r17162 / r17163;
        double r17165 = r17164 - r17160;
        double r17166 = r17165 * r17159;
        return r17166;
}
↓
double f(double m, double v) {
        double r17167 = m;
        double r17168 = 1.0;
        double r17169 = r17168 - r17167;
        double r17170 = v;
        double r17171 = r17169 / r17170;
        double r17172 = r17167 * r17171;
        double r17173 = r17172 - r17168;
        double r17174 = r17173 * r17167;
        return r17174;
}

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 add-sqr-sqrt0.3

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

  4. Applied associate-/r*0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied sqrt-prod0.3

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

  8. Applied *-un-lft-identity0.3

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

  9. Applied sqrt-prod0.3

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

  10. Applied times-frac0.4

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

  11. Applied times-frac0.4

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

  12. Simplified0.4

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019209 
(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))