Average Error: 0.2 → 0.2
Time: 4.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m
double f(double m, double v) {
        double r14252 = m;
        double r14253 = 1.0;
        double r14254 = r14253 - r14252;
        double r14255 = r14252 * r14254;
        double r14256 = v;
        double r14257 = r14255 / r14256;
        double r14258 = r14257 - r14253;
        double r14259 = r14258 * r14252;
        return r14259;
}
↓
double f(double m, double v) {
        double r14260 = m;
        double r14261 = v;
        double r14262 = 1.0;
        double r14263 = 3.0;
        double r14264 = pow(r14262, r14263);
        double r14265 = pow(r14260, r14263);
        double r14266 = r14264 - r14265;
        double r14267 = r14261 / r14266;
        double r14268 = r14262 * r14262;
        double r14269 = -r14260;
        double r14270 = r14269 * r14269;
        double r14271 = r14262 * r14269;
        double r14272 = r14270 - r14271;
        double r14273 = r14268 + r14272;
        double r14274 = r14267 * r14273;
        double r14275 = r14260 / r14274;
        double r14276 = r14275 - r14262;
        double r14277 = r14276 * r14260;
        return r14277;
}

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 sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.2

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

  6. Simplified0.2

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

  8. Applied distribute-rgt-out0.2

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

  9. Applied associate-/l*0.2

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

  11. Applied flip3-+0.2

    \[\leadsto \left(\frac{m}{\frac{v}{\color{blue}{\frac{{1}^{3} + {\left(-m\right)}^{3}}{1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)}}}} - 1\right) \cdot m\]

  12. Applied associate-/r/0.2

    \[\leadsto \left(\frac{m}{\color{blue}{\frac{v}{{1}^{3} + {\left(-m\right)}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)}} - 1\right) \cdot m\]

  13. Simplified0.2

    \[\leadsto \left(\frac{m}{\color{blue}{\frac{v}{{1}^{3} - {m}^{3}}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]

  14. Final simplification0.2

    \[\leadsto \left(\frac{m}{\frac{v}{{1}^{3} - {m}^{3}} \cdot \left(1 \cdot 1 + \left(\left(-m\right) \cdot \left(-m\right) - 1 \cdot \left(-m\right)\right)\right)} - 1\right) \cdot m\]

Reproduce

herbie shell --seed 2020056 
(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))