Average Error: 0.1 → 0.1
Time: 40.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \frac{1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \frac{1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r22330 = m;
        double r22331 = 1.0;
        double r22332 = r22331 - r22330;
        double r22333 = r22330 * r22332;
        double r22334 = v;
        double r22335 = r22333 / r22334;
        double r22336 = r22335 - r22331;
        double r22337 = r22336 * r22332;
        return r22337;
}
↓
double f(double m, double v) {
        double r22338 = m;
        double r22339 = v;
        double r22340 = r22338 / r22339;
        double r22341 = 1.0;
        double r22342 = r22338 * r22338;
        double r22343 = r22341 - r22342;
        double r22344 = r22341 + r22338;
        double r22345 = r22343 / r22344;
        double r22346 = r22340 * r22345;
        double r22347 = r22346 - r22341;
        double r22348 = r22341 - r22338;
        double r22349 = r22347 * r22348;
        return r22349;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Applied associate-/l/0.1

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

  6. Taylor expanded around 0 0.1

    \[\leadsto \left(\frac{\color{blue}{1 \cdot m - {m}^{3}}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
  7. Using strategy rm

  8. Applied unpow30.1

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

  9. Applied distribute-rgt-out--0.1

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

  10. Applied times-frac0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 
(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)))