Average Error: 0.2 → 0.2
Time: 21.9s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{m}{v} - \frac{m}{\frac{v}{m}} \cdot m\right) - m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{m}{v} - \frac{m}{\frac{v}{m}} \cdot m\right) - m
double f(double m, double v) {
        double r641551 = m;
        double r641552 = 1.0;
        double r641553 = r641552 - r641551;
        double r641554 = r641551 * r641553;
        double r641555 = v;
        double r641556 = r641554 / r641555;
        double r641557 = r641556 - r641552;
        double r641558 = r641557 * r641551;
        return r641558;
}
↓
double f(double m, double v) {
        double r641559 = m;
        double r641560 = v;
        double r641561 = r641559 / r641560;
        double r641562 = r641559 * r641561;
        double r641563 = r641560 / r641559;
        double r641564 = r641559 / r641563;
        double r641565 = r641564 * r641559;
        double r641566 = r641562 - r641565;
        double r641567 = r641566 - r641559;
        return r641567;
}

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. Using strategy rm

  3. Applied *-commutative0.2

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

  4. Taylor expanded around inf 6.7

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  5. Simplified0.2

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

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

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

  8. Applied times-frac0.2

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

  9. Simplified0.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019132 +o rules:numerics
(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))