Average Error: 0.1 → 0.1
Time: 17.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{\frac{\left(1 - m\right) \cdot m}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot \left(-m\right) + 1 \cdot \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{\frac{\left(1 - m\right) \cdot m}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot \left(-m\right) + 1 \cdot \left(\frac{\left(1 - m\right) \cdot m}{v} - 1\right)
double f(double m, double v) {
        double r1197582 = m;
        double r1197583 = 1.0;
        double r1197584 = r1197583 - r1197582;
        double r1197585 = r1197582 * r1197584;
        double r1197586 = v;
        double r1197587 = r1197585 / r1197586;
        double r1197588 = r1197587 - r1197583;
        double r1197589 = r1197588 * r1197584;
        return r1197589;
}
↓
double f(double m, double v) {
        double r1197590 = 1.0;
        double r1197591 = m;
        double r1197592 = r1197590 - r1197591;
        double r1197593 = r1197592 * r1197591;
        double r1197594 = v;
        double r1197595 = sqrt(r1197594);
        double r1197596 = r1197593 / r1197595;
        double r1197597 = r1197596 / r1197595;
        double r1197598 = r1197597 - r1197590;
        double r1197599 = -r1197591;
        double r1197600 = r1197598 * r1197599;
        double r1197601 = r1197593 / r1197594;
        double r1197602 = r1197601 - r1197590;
        double r1197603 = r1197590 * r1197602;
        double r1197604 = r1197600 + r1197603;
        return r1197604;
}

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-rgt-in0.1

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

  6. Applied add-sqr-sqrt0.1

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

  7. Applied associate-/r*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1.0 m)) v) 1.0) (- 1.0 m)))