a parameter of renormalized beta distribution

Average Error: 0.2 → 0.2

Time: 19.9s

Precision: 64

\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]

Math

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

↓

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

C

double f(double m, double v) {
        double r24104 = m;
        double r24105 = 1.0;
        double r24106 = r24105 - r24104;
        double r24107 = r24104 * r24106;
        double r24108 = v;
        double r24109 = r24107 / r24108;
        double r24110 = r24109 - r24105;
        double r24111 = r24110 * r24104;
        return r24111;
}

↓

double f(double m, double v) {
        double r24112 = 1.0;
        double r24113 = m;
        double r24114 = r24112 - r24113;
        double r24115 = v;
        double r24116 = r24114 / r24115;
        double r24117 = r24116 * r24113;
        double r24118 = r24117 - r24112;
        double r24119 = r24118 * r24113;
        return r24119;
}

Error

Bits error versus m

Bits error versus v

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 *-un-lft-identity 0.2

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

4. Applied times-frac 0.2

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

5. Simplified 0.2

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

7. Applied add-sqr-sqrt 0.4

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

8. Applied associate-/r* 0.4

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

10. Applied *-un-lft-identity 0.4

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

11. Applied associate-*l* 0.4

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

12. Simplified 0.2

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

13. Final simplification 0.2

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

Reproduce

herbie shell --seed 2019303 
(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))