Average Error: 0.1 → 0.1
Time: 36.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r775095 = m;
        double r775096 = 1.0;
        double r775097 = r775096 - r775095;
        double r775098 = r775095 * r775097;
        double r775099 = v;
        double r775100 = r775098 / r775099;
        double r775101 = r775100 - r775096;
        double r775102 = r775101 * r775097;
        return r775102;
}
↓
double f(double m, double v) {
        double r775103 = m;
        double r775104 = v;
        double r775105 = 1.0;
        double r775106 = r775105 - r775103;
        double r775107 = r775104 / r775106;
        double r775108 = r775103 / r775107;
        double r775109 = r775108 - r775105;
        double r775110 = -r775103;
        double r775111 = r775109 * r775110;
        double r775112 = r775111 + r775109;
        return r775112;
}

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 0.1

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

  3. Applied associate-/l*0.1

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

  5. Applied sub-neg0.1

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

  6. Applied distribute-rgt-in0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019151 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))