Average Error: 0.1 → 0.1
Time: 4.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r9000 = m;
        double r9001 = 1.0;
        double r9002 = r9001 - r9000;
        double r9003 = r9000 * r9002;
        double r9004 = v;
        double r9005 = r9003 / r9004;
        double r9006 = r9005 - r9001;
        double r9007 = r9006 * r9002;
        return r9007;
}
↓
double f(double m, double v) {
        double r9008 = 1.0;
        double r9009 = m;
        double r9010 = v;
        double r9011 = r9009 / r9010;
        double r9012 = r9008 * r9011;
        double r9013 = 2.0;
        double r9014 = pow(r9009, r9013);
        double r9015 = r9014 / r9010;
        double r9016 = r9012 - r9015;
        double r9017 = r9016 - r9008;
        double r9018 = r9008 - r9009;
        double r9019 = r9017 * r9018;
        return r9019;
}

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. Taylor expanded around 0 0.1

    \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]

  5. Final simplification0.1

    \[\leadsto \left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2020100 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))