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

Average Error: 8.7 → 8.7

Time: 2.2s

Precision: binary64

Math

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

↓

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

C

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

↓

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

Error

Bits error versus x2

Bits error versus x1

Bits error versus y3

Bits error versus y2

Bits error versus y1

Bits error versus x3

Derivation

1. Initial program 8.7

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

2. Final simplification 8.7

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

Reproduce

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