Average Error: 0.2 → 0.2
Time: 6.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{\left(1 + \left(-m\right)\right) \cdot \left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right)}{\sqrt{1} + \sqrt{m}}}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{\left(1 + \left(-m\right)\right) \cdot \left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right)}{\sqrt{1} + \sqrt{m}}}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r25046 = m;
        double r25047 = 1.0;
        double r25048 = r25047 - r25046;
        double r25049 = r25046 * r25048;
        double r25050 = v;
        double r25051 = r25049 / r25050;
        double r25052 = r25051 - r25047;
        double r25053 = r25052 * r25046;
        return r25053;
}
↓
double f(double m, double v) {
        double r25054 = 1.0;
        double r25055 = m;
        double r25056 = -r25055;
        double r25057 = r25054 + r25056;
        double r25058 = sqrt(r25054);
        double r25059 = sqrt(r25055);
        double r25060 = r25058 + r25059;
        double r25061 = r25055 * r25060;
        double r25062 = r25057 * r25061;
        double r25063 = r25062 / r25060;
        double r25064 = v;
        double r25065 = r25063 / r25064;
        double r25066 = r25065 - r25054;
        double r25067 = r25066 * r25055;
        return r25067;
}

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-sqrt0.2

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

  4. Applied add-sqr-sqrt0.2

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

  5. Applied difference-of-squares0.2

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

  6. Applied associate-*r*0.2

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

  8. Applied flip--0.2

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

  9. Applied associate-*r/0.2

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

  10. Simplified0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019346 
(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))