Average Error: 0.1 → 0.1
Time: 9.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\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 r15088 = m;
        double r15089 = 1.0;
        double r15090 = r15089 - r15088;
        double r15091 = r15088 * r15090;
        double r15092 = v;
        double r15093 = r15091 / r15092;
        double r15094 = r15093 - r15089;
        double r15095 = r15094 * r15090;
        return r15095;
}
↓
double f(double m, double v) {
        double r15096 = m;
        double r15097 = 1.0;
        double r15098 = r15096 * r15097;
        double r15099 = -r15096;
        double r15100 = r15099 * r15096;
        double r15101 = r15098 + r15100;
        double r15102 = v;
        double r15103 = r15101 / r15102;
        double r15104 = r15103 - r15097;
        double r15105 = r15097 - r15096;
        double r15106 = r15104 * r15105;
        return r15106;
}

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)))