Average Error: 0.1 → 0.1
Time: 9.2s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m \cdot 1 + \left(-m\right) \cdot m}{v} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r12516 = m;
        double r12517 = 1.0;
        double r12518 = r12517 - r12516;
        double r12519 = r12516 * r12518;
        double r12520 = v;
        double r12521 = r12519 / r12520;
        double r12522 = r12521 - r12517;
        double r12523 = r12522 * r12518;
        return r12523;
}
↓
double f(double m, double v) {
        double r12524 = m;
        double r12525 = 1.0;
        double r12526 = r12524 * r12525;
        double r12527 = -r12524;
        double r12528 = r12527 * r12524;
        double r12529 = r12526 + r12528;
        double r12530 = v;
        double r12531 = r12529 / r12530;
        double r12532 = r12531 - r12525;
        double r12533 = r12525 - r12524;
        double r12534 = r12532 * r12533;
        return r12534;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))