Average Error: 14.6 → 1.7
Time: 2.4s
Precision: 64
\[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \cdot y \le 2.02229087115117 \cdot 10^{-311} \lor \neg \left(x \cdot y \le 2.9801505688018316 \cdot 10^{156}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x \cdot y}{z}}{z}}{z + 1}\\ \end{array}\]
\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}
↓
\begin{array}{l}
\mathbf{if}\;x \cdot y \le 2.02229087115117 \cdot 10^{-311} \lor \neg \left(x \cdot y \le 2.9801505688018316 \cdot 10^{156}\right):\\
\;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z + 1}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{\frac{x \cdot y}{z}}{z}}{z + 1}\\

\end{array}
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) / ((double) (((double) (z * z)) * ((double) (z + 1.0))))));
}
↓
double code(double x, double y, double z) {
	double VAR;
	if (((((double) (x * y)) <= 2.0222908711512e-311) || !(((double) (x * y)) <= 2.9801505688018316e+156))) {
		VAR = ((double) (((double) (((double) (x / z)) * ((double) (y / z)))) / ((double) (z + 1.0))));
	} else {
		VAR = ((double) (((double) (((double) (((double) (x * y)) / z)) / z)) / ((double) (z + 1.0))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.6
Target4.0
Herbie1.7
\[\begin{array}{l} \mathbf{if}\;z \lt 249.618281453230708:\\ \;\;\;\;\frac{y \cdot \frac{x}{z}}{z + z \cdot z}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{y}{z}}{1 + z} \cdot x}{z}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (* x y) < 2.0222908711512e-311 or 2.9801505688018316e+156 < (* x y)

    1. Initial program 18.7

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
    2. Using strategy rm

    3. Applied associate-/r*16.6

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{z \cdot z}}{z + 1}}\]
    4. Using strategy rm

    5. Applied times-frac2.4

      \[\leadsto \frac{\color{blue}{\frac{x}{z} \cdot \frac{y}{z}}}{z + 1}\]

    if 2.0222908711512e-311 < (* x y) < 2.9801505688018316e+156

    1. Initial program 6.3

      \[\frac{x \cdot y}{\left(z \cdot z\right) \cdot \left(z + 1\right)}\]
    2. Using strategy rm

    3. Applied associate-/r*5.2

      \[\leadsto \color{blue}{\frac{\frac{x \cdot y}{z \cdot z}}{z + 1}}\]
    4. Using strategy rm

    5. Applied associate-/r*0.2

      \[\leadsto \frac{\color{blue}{\frac{\frac{x \cdot y}{z}}{z}}}{z + 1}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot y \le 2.02229087115117 \cdot 10^{-311} \lor \neg \left(x \cdot y \le 2.9801505688018316 \cdot 10^{156}\right):\\ \;\;\;\;\frac{\frac{x}{z} \cdot \frac{y}{z}}{z + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{\frac{x \cdot y}{z}}{z}}{z + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020129 
(FPCore (x y z)
  :name "Statistics.Distribution.Beta:$cvariance from math-functions-0.1.5.2"
  :precision binary64

  :herbie-target
  (if (< z 249.6182814532307) (/ (* y (/ x z)) (+ z (* z z))) (/ (* (/ (/ y z) (+ 1.0 z)) x) z))

  (/ (* x y) (* (* z z) (+ z 1.0))))