Average Error: 7.8 → 0.0
Time: 1.9s
Precision: binary64
\[\frac{x \cdot y}{y + 1}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -3269494741.838665 \lor \neg \left(y \le 238450.39056172513\right):\\ \;\;\;\;x + 1 \cdot \left(\frac{x}{{y}^{2}} - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \end{array}\]
\frac{x \cdot y}{y + 1}
↓
\begin{array}{l}
\mathbf{if}\;y \le -3269494741.838665 \lor \neg \left(y \le 238450.39056172513\right):\\
\;\;\;\;x + 1 \cdot \left(\frac{x}{{y}^{2}} - \frac{x}{y}\right)\\

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

\end{array}
double code(double x, double y) {
	return ((double) (((double) (x * y)) / ((double) (y + 1.0))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -3269494741.838665) || !(y <= 238450.39056172513))) {
		VAR = ((double) (x + ((double) (1.0 * ((double) (((double) (x / ((double) pow(y, 2.0)))) - ((double) (x / y))))))));
	} else {
		VAR = ((double) (((double) (x * y)) / ((double) (y + 1.0))));
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original7.8
Target0.0
Herbie0.0
\[\begin{array}{l} \mathbf{if}\;y \lt -3693.84827882972468:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \mathbf{elif}\;y \lt 6799310503.41891003:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y \cdot y} - \left(\frac{x}{y} - x\right)\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -3269494741.838665 or 238450.39056172513 < y

    1. Initial program 16.0

      \[\frac{x \cdot y}{y + 1}\]

    2. Taylor expanded around inf 0.0

      \[\leadsto \color{blue}{\left(x + 1 \cdot \frac{x}{{y}^{2}}\right) - 1 \cdot \frac{x}{y}}\]

    3. Simplified0.0

      \[\leadsto \color{blue}{x + 1 \cdot \left(\frac{x}{{y}^{2}} - \frac{x}{y}\right)}\]

    if -3269494741.838665 < y < 238450.39056172513

    1. Initial program 0.0

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

  4. Final simplification0.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -3269494741.838665 \lor \neg \left(y \le 238450.39056172513\right):\\ \;\;\;\;x + 1 \cdot \left(\frac{x}{{y}^{2}} - \frac{x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x \cdot y}{y + 1}\\ \end{array}\]

Reproduce

herbie shell --seed 2020162 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, B"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ x (* y y)) (- (/ x y) x)) (if (< y 6799310503.41891) (/ (* x y) (+ y 1.0)) (- (/ x (* y y)) (- (/ x y) x))))

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