Average Error: 0.1 → 0.1
Time: 20.7s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\frac{\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)}{\sqrt{1} - \sqrt{m}} \cdot \left(\sqrt{1} - \sqrt{m}\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\frac{\left(1 - m\right) \cdot \left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right)}{\sqrt{1} - \sqrt{m}} \cdot \left(\sqrt{1} - \sqrt{m}\right)
double f(double m, double v) {
        double r26060 = m;
        double r26061 = 1.0;
        double r26062 = r26061 - r26060;
        double r26063 = r26060 * r26062;
        double r26064 = v;
        double r26065 = r26063 / r26064;
        double r26066 = r26065 - r26061;
        double r26067 = r26066 * r26062;
        return r26067;
}
↓
double f(double m, double v) {
        double r26068 = 1.0;
        double r26069 = m;
        double r26070 = r26068 - r26069;
        double r26071 = r26069 * r26070;
        double r26072 = v;
        double r26073 = r26071 / r26072;
        double r26074 = r26073 - r26068;
        double r26075 = r26070 * r26074;
        double r26076 = sqrt(r26068);
        double r26077 = sqrt(r26069);
        double r26078 = r26076 - r26077;
        double r26079 = r26075 / r26078;
        double r26080 = r26079 * r26078;
        return r26080;
}

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 add-sqr-sqrt0.1

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

  4. Applied add-sqr-sqrt0.1

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

  5. Applied difference-of-squares0.1

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

  6. Applied associate-*r*0.1

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

  8. Applied flip-+0.1

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

  9. Applied associate-*r/0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 +o rules:numerics
(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)))