Average Error: 0.1 → 0.1
Time: 4.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{m \cdot m}{v}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r14476 = m;
        double r14477 = 1.0;
        double r14478 = r14477 - r14476;
        double r14479 = r14476 * r14478;
        double r14480 = v;
        double r14481 = r14479 / r14480;
        double r14482 = r14481 - r14477;
        double r14483 = r14482 * r14478;
        return r14483;
}
↓
double f(double m, double v) {
        double r14484 = 1.0;
        double r14485 = m;
        double r14486 = v;
        double r14487 = r14485 / r14486;
        double r14488 = r14484 * r14487;
        double r14489 = r14485 * r14485;
        double r14490 = r14489 / r14486;
        double r14491 = r14488 - r14490;
        double r14492 = r14491 - r14484;
        double r14493 = r14484 - r14485;
        double r14494 = r14492 * r14493;
        return r14494;
}

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

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  8. Applied distribute-lft-neg-out0.1

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

  9. Applied unsub-neg0.1

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

  10. Applied div-sub0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 +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)))