Average Error: 0.1 → 0.1
Time: 5.6s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r17198 = m;
        double r17199 = 1.0;
        double r17200 = r17199 - r17198;
        double r17201 = r17198 * r17200;
        double r17202 = v;
        double r17203 = r17201 / r17202;
        double r17204 = r17203 - r17199;
        double r17205 = r17204 * r17200;
        return r17205;
}
↓
double f(double m, double v) {
        double r17206 = 1.0;
        double r17207 = m;
        double r17208 = v;
        double r17209 = r17207 / r17208;
        double r17210 = r17206 * r17209;
        double r17211 = 2.0;
        double r17212 = pow(r17207, r17211);
        double r17213 = r17212 / r17208;
        double r17214 = r17210 - r17213;
        double r17215 = r17214 - r17206;
        double r17216 = r17206 - r17207;
        double r17217 = r17215 * r17216;
        return r17217;
}

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 flip--0.1

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

  4. Applied associate-*r/0.1

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

  5. Taylor expanded around inf 0.1

    \[\leadsto \left(\color{blue}{\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right)} - 1\right) \cdot \left(1 - m\right)\]

  6. Final simplification0.1

    \[\leadsto \left(\left(1 \cdot \frac{m}{v} - \frac{{m}^{2}}{v}\right) - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2020081 +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)))