Average Error: 0.1 → 0.1
Time: 19.9s
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 r26399 = m;
        double r26400 = 1.0;
        double r26401 = r26400 - r26399;
        double r26402 = r26399 * r26401;
        double r26403 = v;
        double r26404 = r26402 / r26403;
        double r26405 = r26404 - r26400;
        double r26406 = r26405 * r26401;
        return r26406;
}
↓
double f(double m, double v) {
        double r26407 = m;
        double r26408 = 1.0;
        double r26409 = r26408 * r26408;
        double r26410 = r26407 * r26407;
        double r26411 = r26409 - r26410;
        double r26412 = r26407 * r26411;
        double r26413 = v;
        double r26414 = r26408 + r26407;
        double r26415 = r26413 * r26414;
        double r26416 = r26412 / r26415;
        double r26417 = r26416 - r26408;
        double r26418 = r26408 - r26407;
        double r26419 = r26417 * r26418;
        return r26419;
}

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)))