Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(-m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot 1 + \left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(-m\right)
double f(double m, double v) {
        double r14405 = m;
        double r14406 = 1.0;
        double r14407 = r14406 - r14405;
        double r14408 = r14405 * r14407;
        double r14409 = v;
        double r14410 = r14408 / r14409;
        double r14411 = r14410 - r14406;
        double r14412 = r14411 * r14407;
        return r14412;
}
↓
double f(double m, double v) {
        double r14413 = m;
        double r14414 = 1.0;
        double r14415 = r14414 - r14413;
        double r14416 = r14413 * r14415;
        double r14417 = v;
        double r14418 = r14416 / r14417;
        double r14419 = r14418 - r14414;
        double r14420 = r14419 * r14414;
        double r14421 = r14414 * r14414;
        double r14422 = r14413 * r14413;
        double r14423 = r14421 - r14422;
        double r14424 = r14413 * r14423;
        double r14425 = r14414 + r14413;
        double r14426 = r14417 * r14425;
        double r14427 = r14424 / r14426;
        double r14428 = r14427 - r14414;
        double r14429 = -r14413;
        double r14430 = r14428 * r14429;
        double r14431 = r14420 + r14430;
        return r14431;
}

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

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

  4. Applied distribute-lft-in0.1

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

  6. Applied flip--0.1

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

  7. Applied associate-*r/0.1

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

  8. Applied associate-/l/0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 +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)))