Average Error: 0.2 → 0.2
Time: 28.0s
Precision: 64
\[0 \lt m \land 0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m}{\frac{v}{m \cdot m}}\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{m}{\frac{v}{m}} - m\right) - \frac{m}{\frac{v}{m \cdot m}}
double f(double m, double v) {
        double r1134807 = m;
        double r1134808 = 1.0;
        double r1134809 = r1134808 - r1134807;
        double r1134810 = r1134807 * r1134809;
        double r1134811 = v;
        double r1134812 = r1134810 / r1134811;
        double r1134813 = r1134812 - r1134808;
        double r1134814 = r1134813 * r1134807;
        return r1134814;
}
↓
double f(double m, double v) {
        double r1134815 = m;
        double r1134816 = v;
        double r1134817 = r1134816 / r1134815;
        double r1134818 = r1134815 / r1134817;
        double r1134819 = r1134818 - r1134815;
        double r1134820 = r1134815 * r1134815;
        double r1134821 = r1134816 / r1134820;
        double r1134822 = r1134815 / r1134821;
        double r1134823 = r1134819 - r1134822;
        return r1134823;
}

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. Taylor expanded around 0 6.7

    \[\leadsto \color{blue}{\frac{{m}^{2}}{v} - \left(m + \frac{{m}^{3}}{v}\right)}\]

  3. Simplified0.2

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

  5. Applied pow10.2

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

  6. Applied pow10.2

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

  7. Applied pow10.2

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

  8. Applied pow-prod-up0.2

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

  9. Applied pow-prod-up0.2

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

  10. Simplified0.2

    \[\leadsto \left(\frac{m}{\frac{v}{m}} - m\right) - \frac{{m}^{\color{blue}{3}}}{v}\]
  11. Using strategy rm

  12. Applied cube-mult0.2

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

  13. Applied associate-/l*0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :pre (and (< 0 m) (< 0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))