Average Error: 0.1 → 0.1
Time: 3.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{1}{\frac{v}{m \cdot m}}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r8710 = m;
        double r8711 = 1.0;
        double r8712 = r8711 - r8710;
        double r8713 = r8710 * r8712;
        double r8714 = v;
        double r8715 = r8713 / r8714;
        double r8716 = r8715 - r8711;
        double r8717 = r8716 * r8712;
        return r8717;
}
↓
double f(double m, double v) {
        double r8718 = 1.0;
        double r8719 = m;
        double r8720 = v;
        double r8721 = r8719 / r8720;
        double r8722 = r8718 * r8721;
        double r8723 = 1.0;
        double r8724 = r8719 * r8719;
        double r8725 = r8720 / r8724;
        double r8726 = r8723 / r8725;
        double r8727 = r8722 - r8726;
        double r8728 = r8727 - r8718;
        double r8729 = r8718 - r8719;
        double r8730 = r8728 * r8729;
        return r8730;
}

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. Using strategy rm

  13. Applied clear-num0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))