Average Error: 0.2 → 0.2
Time: 4.4s
Precision: 64
\[0.0 \lt m \land 0.0 \lt v \land v \lt 0.25\]
\[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
↓
\[\mathsf{fma}\left(\frac{m}{1}, \frac{1 - m}{v}, -1\right) \cdot m\]
\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m
↓
\mathsf{fma}\left(\frac{m}{1}, \frac{1 - m}{v}, -1\right) \cdot m
double code(double m, double v) {
	return ((((m * (1.0 - m)) / v) - 1.0) * m);
}
↓
double code(double m, double v) {
	return (fma((m / 1.0), ((1.0 - m) / v), -1.0) * m);
}

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 0.2

    \[\left(\frac{m \cdot \left(1 - m\right)}{v} - 1\right) \cdot m\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.2

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

  4. Applied times-frac0.2

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

  5. Applied fma-neg0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2020091 +o rules:numerics
(FPCore (m v)
  :name "a parameter of renormalized beta distribution"
  :precision binary64
  :pre (and (< 0.0 m) (< 0.0 v) (< v 0.25))
  (* (- (/ (* m (- 1 m)) v) 1) m))