Average Error: 0.1 → 0.1
Time: 18.8s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{m} + 1\right)\right) \cdot \left(1 - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(\sqrt{m} + 1\right)\right) \cdot \left(1 - \sqrt{m}\right)
double f(double m, double v) {
        double r1300485 = m;
        double r1300486 = 1.0;
        double r1300487 = r1300486 - r1300485;
        double r1300488 = r1300485 * r1300487;
        double r1300489 = v;
        double r1300490 = r1300488 / r1300489;
        double r1300491 = r1300490 - r1300486;
        double r1300492 = r1300491 * r1300487;
        return r1300492;
}
↓
double f(double m, double v) {
        double r1300493 = m;
        double r1300494 = 1.0;
        double r1300495 = r1300494 - r1300493;
        double r1300496 = r1300493 * r1300495;
        double r1300497 = v;
        double r1300498 = r1300496 / r1300497;
        double r1300499 = r1300498 - r1300494;
        double r1300500 = sqrt(r1300493);
        double r1300501 = r1300500 + r1300494;
        double r1300502 = r1300499 * r1300501;
        double r1300503 = r1300494 - r1300500;
        double r1300504 = r1300502 * r1300503;
        return r1300504;
}

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 add-sqr-sqrt0.1

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

  4. Applied *-un-lft-identity0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 
(FPCore (m v)
  :name "b parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) (- 1 m)))