Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)\]
↓
\[\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot \left(1 - m\right)
↓
\left(\frac{m}{\frac{v}{1 - m}} - 1\right) \cdot \left(1 - m\right)
double f(double m, double v) {
        double r20959 = m;
        double r20960 = 1.0;
        double r20961 = r20960 - r20959;
        double r20962 = r20959 * r20961;
        double r20963 = v;
        double r20964 = r20962 / r20963;
        double r20965 = r20964 - r20960;
        double r20966 = r20965 * r20961;
        return r20966;
}
↓
double f(double m, double v) {
        double r20967 = m;
        double r20968 = v;
        double r20969 = 1.0;
        double r20970 = r20969 - r20967;
        double r20971 = r20968 / r20970;
        double r20972 = r20967 / r20971;
        double r20973 = r20972 - r20969;
        double r20974 = r20973 * r20970;
        return r20974;
}

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 associate-/l*0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 +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)))