(- (+ (- (+ (- (* x1 y2) (* y1 x2)) (* y1 x3)) (* x1 y3)) (* x2 y3)) (* x3 y2))

Average Error: 0.0 → 0.0

Time: 2.3s

Precision: binary64

Math

\[\left(\left(\left(\left(x1 \cdot y2 - y1 \cdot x2\right) + y1 \cdot x3\right) - x1 \cdot y3\right) + x2 \cdot y3\right) - x3 \cdot y2\]

↓

\[x2 \cdot \left(y3 - y1\right) + \left(x1 \cdot \left(y2 - y3\right) + x3 \cdot \left(y1 - y2\right)\right)\]

C

double code(double x1, double y2, double y1, double x2, double x3, double y3) {
	return ((double) (((double) (((double) (((double) (((double) (((double) (x1 * y2)) - ((double) (y1 * x2)))) + ((double) (y1 * x3)))) - ((double) (x1 * y3)))) + ((double) (x2 * y3)))) - ((double) (x3 * y2))));
}

↓

double code(double x1, double y2, double y1, double x2, double x3, double y3) {
	return ((double) (((double) (x2 * ((double) (y3 - y1)))) + ((double) (((double) (x1 * ((double) (y2 - y3)))) + ((double) (x3 * ((double) (y1 - y2))))))));
}

Error

Bits error versus x1

Bits error versus y2

Bits error versus y1

Bits error versus x2

Bits error versus x3

Bits error versus y3

Derivation

1. Initial program 0.0

   \[\left(\left(\left(\left(x1 \cdot y2 - y1 \cdot x2\right) + y1 \cdot x3\right) - x1 \cdot y3\right) + x2 \cdot y3\right) - x3 \cdot y2\]

2. Simplified 0.0

   \[\leadsto \color{blue}{x2 \cdot \left(y3 - y1\right) + \left(x1 \cdot \left(y2 - y3\right) + x3 \cdot \left(y1 - y2\right)\right)}\]

3. Final simplification 0.0

   \[\leadsto x2 \cdot \left(y3 - y1\right) + \left(x1 \cdot \left(y2 - y3\right) + x3 \cdot \left(y1 - y2\right)\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x1 y2 y1 x2 x3 y3)
  :name "(- (+ (- (+ (- (* x1 y2) (* y1 x2)) (* y1 x3)) (* x1 y3)) (* x2 y3)) (* x3 y2))"
  :precision binary64
  (- (+ (- (+ (- (* x1 y2) (* y1 x2)) (* y1 x3)) (* x1 y3)) (* x2 y3)) (* x3 y2)))