Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot 1 + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)\]
\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 1 + \left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r16336 = m;
        double r16337 = 1.0;
        double r16338 = r16337 - r16336;
        double r16339 = r16336 * r16338;
        double r16340 = v;
        double r16341 = r16339 / r16340;
        double r16342 = r16341 - r16337;
        double r16343 = r16342 * r16338;
        return r16343;
}
↓
double f(double m, double v) {
        double r16344 = m;
        double r16345 = v;
        double r16346 = 1.0;
        double r16347 = r16346 - r16344;
        double r16348 = r16345 / r16347;
        double r16349 = r16344 / r16348;
        double r16350 = r16349 - r16346;
        double r16351 = r16350 * r16346;
        double r16352 = -r16344;
        double r16353 = r16350 * r16352;
        double r16354 = r16351 + r16353;
        return r16354;
}

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-lft-in0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 +o rules:numerics
(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)))