Average Error: 0.1 → 0.1
Time: 4.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{m}{v} \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{m}{v} \cdot \left(1 \cdot 1 - m \cdot m\right)}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r9537 = m;
        double r9538 = 1.0;
        double r9539 = r9538 - r9537;
        double r9540 = r9537 * r9539;
        double r9541 = v;
        double r9542 = r9540 / r9541;
        double r9543 = r9542 - r9538;
        double r9544 = r9543 * r9539;
        return r9544;
}
↓
double f(double m, double v) {
        double r9545 = m;
        double r9546 = v;
        double r9547 = r9545 / r9546;
        double r9548 = 1.0;
        double r9549 = r9548 * r9548;
        double r9550 = r9545 * r9545;
        double r9551 = r9549 - r9550;
        double r9552 = r9547 * r9551;
        double r9553 = r9548 + r9545;
        double r9554 = r9552 / r9553;
        double r9555 = r9554 - r9548;
        double r9556 = r9548 - r9545;
        double r9557 = r9555 * r9556;
        return r9557;
}

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 associate-/r/0.1

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

  7. Applied flip--0.1

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

  8. Applied associate-*r/0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 +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)))