Average Error: 0.2 → 0.2
Time: 3.3s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{m}{1}}{\frac{v}{1 - m}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{m}{1}}{\frac{v}{1 - m}} - 1\right) \cdot m
double f(double m, double v) {
        double r10732 = m;
        double r10733 = 1.0;
        double r10734 = r10733 - r10732;
        double r10735 = r10732 * r10734;
        double r10736 = v;
        double r10737 = r10735 / r10736;
        double r10738 = r10737 - r10733;
        double r10739 = r10738 * r10732;
        return r10739;
}
↓
double f(double m, double v) {
        double r10740 = m;
        double r10741 = 1.0;
        double r10742 = r10740 / r10741;
        double r10743 = v;
        double r10744 = 1.0;
        double r10745 = r10744 - r10740;
        double r10746 = r10743 / r10745;
        double r10747 = r10742 / r10746;
        double r10748 = r10747 - r10744;
        double r10749 = r10748 * r10740;
        return r10749;
}

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-sqrt0.4

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

  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

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

  7. Applied times-frac0.4

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

  8. Applied associate-/l*0.4

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2020064 
(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))