Average Error: 0.2 → 0.2
Time: 6.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{\left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(1 + \left(-m\right)\right)}{\sqrt{1} + \sqrt{m}}}{v} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{\left(m \cdot \left(\sqrt{1} + \sqrt{m}\right)\right) \cdot \left(1 + \left(-m\right)\right)}{\sqrt{1} + \sqrt{m}}}{v} - 1\right) \cdot m
double f(double m, double v) {
        double r25990 = m;
        double r25991 = 1.0;
        double r25992 = r25991 - r25990;
        double r25993 = r25990 * r25992;
        double r25994 = v;
        double r25995 = r25993 / r25994;
        double r25996 = r25995 - r25991;
        double r25997 = r25996 * r25990;
        return r25997;
}
↓
double f(double m, double v) {
        double r25998 = m;
        double r25999 = 1.0;
        double r26000 = sqrt(r25999);
        double r26001 = sqrt(r25998);
        double r26002 = r26000 + r26001;
        double r26003 = r25998 * r26002;
        double r26004 = -r25998;
        double r26005 = r25999 + r26004;
        double r26006 = r26003 * r26005;
        double r26007 = r26006 / r26002;
        double r26008 = v;
        double r26009 = r26007 / r26008;
        double r26010 = r26009 - r25999;
        double r26011 = r26010 * r25998;
        return r26011;
}

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

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019346 +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))