Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r15221 = m;
        double r15222 = 1.0;
        double r15223 = r15222 - r15221;
        double r15224 = r15221 * r15223;
        double r15225 = v;
        double r15226 = r15224 / r15225;
        double r15227 = r15226 - r15222;
        double r15228 = r15227 * r15223;
        return r15228;
}
↓
double f(double m, double v) {
        double r15229 = m;
        double r15230 = 1.0;
        double r15231 = r15229 * r15230;
        double r15232 = -r15229;
        double r15233 = r15232 * r15229;
        double r15234 = r15231 + r15233;
        double r15235 = v;
        double r15236 = r15234 / r15235;
        double r15237 = r15236 - r15230;
        double r15238 = r15230 - r15229;
        double r15239 = r15237 * r15238;
        return r15239;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 +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)))