Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot \left(1 \cdot 1 - m \cdot m\right)}{v \cdot \left(1 + m\right)} - 1\right) \cdot \left(1 - m\right)\]
\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 r12472 = m;
        double r12473 = 1.0;
        double r12474 = r12473 - r12472;
        double r12475 = r12472 * r12474;
        double r12476 = v;
        double r12477 = r12475 / r12476;
        double r12478 = r12477 - r12473;
        double r12479 = r12478 * r12474;
        return r12479;
}
↓
double f(double m, double v) {
        double r12480 = m;
        double r12481 = 1.0;
        double r12482 = r12481 * r12481;
        double r12483 = r12480 * r12480;
        double r12484 = r12482 - r12483;
        double r12485 = r12480 * r12484;
        double r12486 = v;
        double r12487 = r12481 + r12480;
        double r12488 = r12486 * r12487;
        double r12489 = r12485 / r12488;
        double r12490 = r12489 - r12481;
        double r12491 = r12481 - r12480;
        double r12492 = r12490 * r12491;
        return r12492;
}

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 2019347 
(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)))