(if (>= (- (* x x) x) 0.0) (/ x 10) (+ (* x x) 2))

Average Error: 0 → 0

Time: 572.0ms

Precision: binary64

Math

\[\begin{array}{l} \mathbf{if}\;x \cdot x - x \ge 0.0:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + 2\\ \end{array}\]

↓

\[\begin{array}{l} \mathbf{if}\;x \cdot x - x \ge 0.0:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + 2\\ \end{array}\]

C

double code(double x) {
	double VAR;
	if ((((double) (((double) (x * x)) - x)) >= 0.0)) {
		VAR = ((double) (x / 10.0));
	} else {
		VAR = ((double) (((double) (x * x)) + 2.0));
	}
	return VAR;
}

↓

double code(double x) {
	double VAR;
	if ((((double) (((double) (x * x)) - x)) >= 0.0)) {
		VAR = ((double) (x / 10.0));
	} else {
		VAR = ((double) (((double) (x * x)) + 2.0));
	}
	return VAR;
}

Error

Bits error versus x

Derivation

1. Initial program 0

   \[\begin{array}{l} \mathbf{if}\;x \cdot x - x \ge 0.0:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + 2\\ \end{array}\]

2. Final simplification 0

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \cdot x - x \ge 0.0:\\ \;\;\;\;\frac{x}{10}\\ \mathbf{else}:\\ \;\;\;\;x \cdot x + 2\\ \end{array}\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(if (>= (- (* x x) x) 0.0) (/ x 10) (+ (* x x) 2))"
  :precision binary64
  (if (>= (- (* x x) x) 0.0) (/ x 10.0) (+ (* x x) 2.0)))