Average Error: 15.0 → 0.2
Time: 3.0s
Precision: 64
\[\frac{\left(x \cdot 2\right) \cdot y}{x - y}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -5.11464869607731017 \cdot 10^{53} \lor \neg \left(y \le 2.4256422012160796 \cdot 10^{27}\right):\\ \;\;\;\;\frac{x \cdot 1}{\frac{x - y}{2 \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array}\]
\frac{\left(x \cdot 2\right) \cdot y}{x - y}
↓
\begin{array}{l}
\mathbf{if}\;y \le -5.11464869607731017 \cdot 10^{53} \lor \neg \left(y \le 2.4256422012160796 \cdot 10^{27}\right):\\
\;\;\;\;\frac{x \cdot 1}{\frac{x - y}{2 \cdot y}}\\

\mathbf{else}:\\
\;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\

\end{array}
double code(double x, double y) {
	return ((double) (((double) (((double) (x * 2.0)) * y)) / ((double) (x - y))));
}
↓
double code(double x, double y) {
	double VAR;
	if (((y <= -5.11464869607731e+53) || !(y <= 2.4256422012160796e+27))) {
		VAR = ((double) (((double) (x * 1.0)) / ((double) (((double) (x - y)) / ((double) (2.0 * y))))));
	} else {
		VAR = ((double) (y / ((double) (((double) (x - y)) / ((double) (x * 2.0))))));
	}
	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

Original15.0
Target0.4
Herbie0.2
\[\begin{array}{l} \mathbf{if}\;x \lt -1.7210442634149447 \cdot 10^{81}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \mathbf{elif}\;x \lt 83645045635564432:\\ \;\;\;\;\frac{x \cdot 2}{\frac{x - y}{y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{2 \cdot x}{x - y} \cdot y\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if y < -5.11464869607731e+53 or 2.4256422012160796e+27 < y

    1. Initial program 18.0

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

    3. Applied *-un-lft-identity18.0

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

    4. Applied associate-*r*18.0

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

    5. Applied associate-*l*18.0

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

    6. Applied associate-/l*0.1

      \[\leadsto \color{blue}{\frac{x \cdot 1}{\frac{x - y}{2 \cdot y}}}\]

    if -5.11464869607731e+53 < y < 2.4256422012160796e+27

    1. Initial program 12.8

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

    3. Applied *-commutative12.8

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

    4. Applied associate-/l*0.4

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

  4. Final simplification0.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -5.11464869607731017 \cdot 10^{53} \lor \neg \left(y \le 2.4256422012160796 \cdot 10^{27}\right):\\ \;\;\;\;\frac{x \cdot 1}{\frac{x - y}{2 \cdot y}}\\ \mathbf{else}:\\ \;\;\;\;\frac{y}{\frac{x - y}{x \cdot 2}}\\ \end{array}\]

Reproduce

herbie shell --seed 2020113 +o rules:numerics
(FPCore (x y)
  :name "Linear.Projection:perspective from linear-1.19.1.3, B"
  :precision binary64

  :herbie-target
  (if (< x -1.7210442634149447e+81) (* (/ (* 2 x) (- x y)) y) (if (< x 83645045635564432) (/ (* x 2) (/ (- x y) y)) (* (/ (* 2 x) (- x y)) y)))

  (/ (* (* x 2) y) (- x y)))