Average Error: 0.1 → 0.1
Time: 19.8s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r26410 = m;
        double r26411 = 1.0;
        double r26412 = r26411 - r26410;
        double r26413 = r26410 * r26412;
        double r26414 = v;
        double r26415 = r26413 / r26414;
        double r26416 = r26415 - r26411;
        double r26417 = r26416 * r26412;
        return r26417;
}
↓
double f(double m, double v) {
        double r26418 = m;
        double r26419 = 1.0;
        double r26420 = r26419 * r26419;
        double r26421 = r26418 * r26418;
        double r26422 = r26420 - r26421;
        double r26423 = r26418 * r26422;
        double r26424 = v;
        double r26425 = r26419 + r26418;
        double r26426 = r26424 * r26425;
        double r26427 = r26423 / r26426;
        double r26428 = r26427 - r26419;
        double r26429 = r26419 - r26418;
        double r26430 = r26428 * r26429;
        return r26430;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 
(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)))