Average Error: 0.1 → 0.1
Time: 23.0s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{v} \cdot \frac{1 \cdot 1 - m \cdot m}{1 + m} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r23983 = m;
        double r23984 = 1.0;
        double r23985 = r23984 - r23983;
        double r23986 = r23983 * r23985;
        double r23987 = v;
        double r23988 = r23986 / r23987;
        double r23989 = r23988 - r23984;
        double r23990 = r23989 * r23985;
        return r23990;
}
↓
double f(double m, double v) {
        double r23991 = m;
        double r23992 = v;
        double r23993 = r23991 / r23992;
        double r23994 = 1.0;
        double r23995 = r23994 * r23994;
        double r23996 = r23991 * r23991;
        double r23997 = r23995 - r23996;
        double r23998 = r23994 + r23991;
        double r23999 = r23997 / r23998;
        double r24000 = r23993 * r23999;
        double r24001 = r24000 - r23994;
        double r24002 = r23994 - r23991;
        double r24003 = r24001 * r24002;
        return r24003;
}

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. Using strategy rm

  7. Applied times-frac0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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)))