Average Error: 0.2 → 0.2
Time: 16.3s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{v} - m \cdot \frac{m}{v}\right) \cdot m - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{v} - m \cdot \frac{m}{v}\right) \cdot m - m
double f(double m, double v) {
        double r1193552 = m;
        double r1193553 = 1.0;
        double r1193554 = r1193553 - r1193552;
        double r1193555 = r1193552 * r1193554;
        double r1193556 = v;
        double r1193557 = r1193555 / r1193556;
        double r1193558 = r1193557 - r1193553;
        double r1193559 = r1193558 * r1193552;
        return r1193559;
}
↓
double f(double m, double v) {
        double r1193560 = m;
        double r1193561 = v;
        double r1193562 = r1193560 / r1193561;
        double r1193563 = r1193560 * r1193562;
        double r1193564 = r1193562 - r1193563;
        double r1193565 = r1193564 * r1193560;
        double r1193566 = r1193565 - r1193560;
        return r1193566;
}

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 0.2

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

  2. Simplified0.2

    \[\leadsto \color{blue}{\frac{m - m \cdot m}{\frac{v}{m}} - m}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.2

    \[\leadsto \frac{m - m \cdot m}{\frac{v}{\color{blue}{1 \cdot m}}} - m\]

  5. Applied *-un-lft-identity0.2

    \[\leadsto \frac{m - m \cdot m}{\frac{\color{blue}{1 \cdot v}}{1 \cdot m}} - m\]

  6. Applied times-frac0.2

    \[\leadsto \frac{m - m \cdot m}{\color{blue}{\frac{1}{1} \cdot \frac{v}{m}}} - m\]

  7. Applied *-un-lft-identity0.2

    \[\leadsto \frac{\color{blue}{1 \cdot m} - m \cdot m}{\frac{1}{1} \cdot \frac{v}{m}} - m\]

  8. Applied distribute-rgt-out--0.2

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

  9. Applied times-frac0.2

    \[\leadsto \color{blue}{\frac{m}{\frac{1}{1}} \cdot \frac{1 - m}{\frac{v}{m}}} - m\]

  10. Simplified0.2

    \[\leadsto \color{blue}{m} \cdot \frac{1 - m}{\frac{v}{m}} - m\]

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))