Average Error: 0.1 → 0.1
Time: 20.2s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(-m\right) \cdot \left(\frac{m}{\frac{v}{1 - m}} - 1\right) + \left(\frac{m}{\frac{v}{1 - m}} - 1\right)
double f(double m, double v) {
        double r478730 = m;
        double r478731 = 1.0;
        double r478732 = r478731 - r478730;
        double r478733 = r478730 * r478732;
        double r478734 = v;
        double r478735 = r478733 / r478734;
        double r478736 = r478735 - r478731;
        double r478737 = r478736 * r478732;
        return r478737;
}
↓
double f(double m, double v) {
        double r478738 = m;
        double r478739 = -r478738;
        double r478740 = v;
        double r478741 = 1.0;
        double r478742 = r478741 - r478738;
        double r478743 = r478740 / r478742;
        double r478744 = r478738 / r478743;
        double r478745 = r478744 - r478741;
        double r478746 = r478739 * r478745;
        double r478747 = r478746 + r478745;
        return r478747;
}

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. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019153 
(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)))