Average Error: 0.1 → 0.1
Time: 17.5s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \left(1 - m\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r18592 = m;
        double r18593 = 1.0;
        double r18594 = r18593 - r18592;
        double r18595 = r18592 * r18594;
        double r18596 = v;
        double r18597 = r18595 / r18596;
        double r18598 = r18597 - r18593;
        double r18599 = r18598 * r18594;
        return r18599;
}
↓
double f(double m, double v) {
        double r18600 = m;
        double r18601 = v;
        double r18602 = r18600 / r18601;
        double r18603 = 1.0;
        double r18604 = r18603 - r18600;
        double r18605 = r18602 * r18604;
        double r18606 = r18605 - r18603;
        double r18607 = r18606 * r18604;
        return r18607;
}

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. Using strategy rm

  7. Applied flip-+0.1

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

  8. Applied associate-*r/0.1

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

  9. Applied associate-/r/0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +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)))