(- (+ (- (+ (* (* (* 2 x1) x2) x3) (* (* 3 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3 x3) x3)) x2)

Average Error: 5.9 → 0.2

Time: 2.1s

Precision: binary64

Math

\[\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2 \le -1.08432228300016621 \cdot 10^{98} \lor \neg \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2 \le 6.57015712383150898 \cdot 10^{297}\right):\\ \;\;\;\;\left(3 \cdot x3\right) \cdot \left(x3 + x3\right) + \left(\left(x1 \cdot \left(x2 \cdot x3\right)\right) \cdot \left(2 - x2\right) - x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\\ \end{array}\]

C

double code(double x1, double x2, double x3) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * x2)) * x3)) + ((double) (((double) (3.0 * x3)) * x3)))) - ((double) (((double) (((double) (x2 * x1)) * x2)) * x3)))) + ((double) (((double) (3.0 * x3)) * x3)))) - x2));
}

↓

double code(double x1, double x2, double x3) {
	double VAR;
	if (((((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * x2)) * x3)) + ((double) (((double) (3.0 * x3)) * x3)))) - ((double) (((double) (((double) (x2 * x1)) * x2)) * x3)))) + ((double) (((double) (3.0 * x3)) * x3)))) - x2)) <= -1.0843222830001662e+98) || !(((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * x2)) * x3)) + ((double) (((double) (3.0 * x3)) * x3)))) - ((double) (((double) (((double) (x2 * x1)) * x2)) * x3)))) + ((double) (((double) (3.0 * x3)) * x3)))) - x2)) <= 6.570157123831509e+297))) {
		VAR = ((double) (((double) (((double) (3.0 * x3)) * ((double) (x3 + x3)))) + ((double) (((double) (((double) (x1 * ((double) (x2 * x3)))) * ((double) (2.0 - x2)))) - x2))));
	} else {
		VAR = ((double) (((double) (((double) (((double) (((double) (((double) (((double) (2.0 * x1)) * x2)) * x3)) + ((double) (((double) (3.0 * x3)) * x3)))) - ((double) (((double) (((double) (x2 * x1)) * x2)) * x3)))) + ((double) (((double) (3.0 * x3)) * x3)))) - x2));
	}
	return VAR;
}

Error

Bits error versus x1

Bits error versus x2

Bits error versus x3

Derivation

1. Split input into 2 regimes

2. if (- (+ (- (+ (* (* (* 2.0 x1) x2) x3) (* (* 3.0 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3.0 x3) x3)) x2) < -1.08432228300016621e98 or 6.57015712383150898e297 < (- (+ (- (+ (* (* (* 2.0 x1) x2) x3) (* (* 3.0 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3.0 x3) x3)) x2)

   1. Initial program 29.9

      \[\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\]

   2. Simplified 0.3

      \[\leadsto \color{blue}{\left(3 \cdot x3\right) \cdot \left(x3 + x3\right) + \left(\left(x1 \cdot \left(x2 \cdot x3\right)\right) \cdot \left(2 - x2\right) - x2\right)}\]

   if -1.08432228300016621e98 < (- (+ (- (+ (* (* (* 2.0 x1) x2) x3) (* (* 3.0 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3.0 x3) x3)) x2) < 6.57015712383150898e297

   1. Initial program 0.1

      \[\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2 \le -1.08432228300016621 \cdot 10^{98} \lor \neg \left(\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2 \le 6.57015712383150898 \cdot 10^{297}\right):\\ \;\;\;\;\left(3 \cdot x3\right) \cdot \left(x3 + x3\right) + \left(\left(x1 \cdot \left(x2 \cdot x3\right)\right) \cdot \left(2 - x2\right) - x2\right)\\ \mathbf{else}:\\ \;\;\;\;\left(\left(\left(\left(\left(2 \cdot x1\right) \cdot x2\right) \cdot x3 + \left(3 \cdot x3\right) \cdot x3\right) - \left(\left(x2 \cdot x1\right) \cdot x2\right) \cdot x3\right) + \left(3 \cdot x3\right) \cdot x3\right) - x2\\ \end{array}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x1 x2 x3)
  :name "(- (+ (- (+ (* (* (* 2 x1) x2) x3) (* (* 3 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3 x3) x3)) x2)"
  :precision binary64
  (- (+ (- (+ (* (* (* 2.0 x1) x2) x3) (* (* 3.0 x3) x3)) (* (* (* x2 x1) x2) x3)) (* (* 3.0 x3) x3)) x2))