(- (* (- Bx Ax) (- Y Ay)) (* (- By Ay) (- X Ax)))

Average Error: 8.1 → 8.1

Time: 2.3s

Precision: binary64

Math

\[\left(Bx - Ax\right) \cdot \left(Y - Ay\right) - \left(By - Ay\right) \cdot \left(X - Ax\right)\]

↓

\[\left(Bx - Ax\right) \cdot \left(Y - Ay\right) - \left(By - Ay\right) \cdot \left(X - Ax\right)\]

C

double code(double Bx, double Ax, double Y, double Ay, double By, double X) {
	return ((double) (((double) (((double) (Bx - Ax)) * ((double) (Y - Ay)))) - ((double) (((double) (By - Ay)) * ((double) (X - Ax))))));
}

↓

double code(double Bx, double Ax, double Y, double Ay, double By, double X) {
	return ((double) (((double) (((double) (Bx - Ax)) * ((double) (Y - Ay)))) - ((double) (((double) (By - Ay)) * ((double) (X - Ax))))));
}

Error

Bits error versus Bx

Bits error versus Ax

Bits error versus Y

Bits error versus Ay

Bits error versus By

Bits error versus X

Derivation

1. Initial program 8.1

   \[\left(Bx - Ax\right) \cdot \left(Y - Ay\right) - \left(By - Ay\right) \cdot \left(X - Ax\right)\]

2. Final simplification 8.1

   \[\leadsto \left(Bx - Ax\right) \cdot \left(Y - Ay\right) - \left(By - Ay\right) \cdot \left(X - Ax\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (Bx Ax Y Ay By X)
  :name "(- (* (- Bx Ax) (- Y Ay)) (* (- By Ay) (- X Ax)))"
  :precision binary64
  (- (* (- Bx Ax) (- Y Ay)) (* (- By Ay) (- X Ax))))