Average Error: 0.1 → 0.1
Time: 5.1s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1\right) + \left(-{m}^{3}\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 \cdot 1\right) + \left(-{m}^{3}\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r17177 = m;
        double r17178 = 1.0;
        double r17179 = r17178 - r17177;
        double r17180 = r17177 * r17179;
        double r17181 = v;
        double r17182 = r17180 / r17181;
        double r17183 = r17182 - r17178;
        double r17184 = r17183 * r17179;
        return r17184;
}
↓
double f(double m, double v) {
        double r17185 = m;
        double r17186 = 1.0;
        double r17187 = r17186 * r17186;
        double r17188 = r17185 * r17187;
        double r17189 = 3.0;
        double r17190 = pow(r17185, r17189);
        double r17191 = -r17190;
        double r17192 = r17188 + r17191;
        double r17193 = v;
        double r17194 = r17186 + r17185;
        double r17195 = r17193 * r17194;
        double r17196 = r17192 / r17195;
        double r17197 = r17196 - r17186;
        double r17198 = r17186 - r17185;
        double r17199 = r17197 * r17198;
        return r17199;
}

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. Applied associate-/l/0.1

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

  7. Applied sub-neg0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Simplified0.1

    \[\leadsto \left(\frac{m \cdot \left(1 \cdot 1\right) + \color{blue}{\left(-{m}^{3}\right)}}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]

  10. Final simplification0.1

    \[\leadsto \left(\frac{m \cdot \left(1 \cdot 1\right) + \left(-{m}^{3}\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]

Reproduce

herbie shell --seed 2020049 +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)))