Average Error: 0.2 → 0.3
Time: 7.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\left(\frac{\frac{m \cdot \left(1 - m\right)}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\left(\frac{\frac{m \cdot \left(1 - m\right)}{\sqrt{v}}}{\sqrt{v}} - 1\right) \cdot m
double f(double m, double v) {
        double r17283 = m;
        double r17284 = 1.0;
        double r17285 = r17284 - r17283;
        double r17286 = r17283 * r17285;
        double r17287 = v;
        double r17288 = r17286 / r17287;
        double r17289 = r17288 - r17284;
        double r17290 = r17289 * r17283;
        return r17290;
}
↓
double f(double m, double v) {
        double r17291 = m;
        double r17292 = 1.0;
        double r17293 = r17292 - r17291;
        double r17294 = r17291 * r17293;
        double r17295 = v;
        double r17296 = sqrt(r17295);
        double r17297 = r17294 / r17296;
        double r17298 = r17297 / r17296;
        double r17299 = r17298 - r17292;
        double r17300 = r17299 * r17291;
        return r17300;
}

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-sqrt0.4

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

  4. Applied associate-/r*0.3

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

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2020003 +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))