Average Error: 0.2 → 0.2
Time: 15.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(m \cdot \frac{1 - m}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r17517 = m;
        double r17518 = 1.0;
        double r17519 = r17518 - r17517;
        double r17520 = r17517 * r17519;
        double r17521 = v;
        double r17522 = r17520 / r17521;
        double r17523 = r17522 - r17518;
        double r17524 = r17523 * r17517;
        return r17524;
}
↓
double f(double m, double v) {
        double r17525 = m;
        double r17526 = 1.0;
        double r17527 = r17526 - r17525;
        double r17528 = v;
        double r17529 = r17527 / r17528;
        double r17530 = r17525 * r17529;
        double r17531 = r17530 - r17526;
        double r17532 = r17531 * r17525;
        return r17532;
}

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 add-sqr-sqrt0.3

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

  4. Applied associate-/r*0.3

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

  6. Applied *-un-lft-identity0.3

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

  7. Applied sqrt-prod0.3

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

  8. Applied *-un-lft-identity0.3

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

  9. Applied sqrt-prod0.3

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

  10. Applied times-frac0.4

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

  11. Applied times-frac0.4

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

  12. Simplified0.4

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019209 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))