Average Error: 50.6 → 50.6
Time: 2.3s
Precision: binary64
\[\sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d\]
↓
\[\sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d\]
\sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d
↓
\sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d
double code(double x_element, double x, double dirX, double d, double y_element, double y, double dirZ, double dirY) {
	return ((double) (((double) sqrt(((double) (((double) (((double) (((double) (x_element - ((double) (x + ((double) (dirX * d)))))) * ((double) (x_element - ((double) (x + ((double) (dirX * d)))))))) + ((double) (((double) (y_element - ((double) (y + ((double) (dirZ * d)))))) * ((double) (y_element - ((double) (y + ((double) (dirZ * d)))))))))) + ((double) (((double) (dirY * d)) * ((double) (dirY * d)))))))) + d));
}
↓
double code(double x_element, double x, double dirX, double d, double y_element, double y, double dirZ, double dirY) {
	return ((double) (((double) sqrt(((double) (((double) (((double) (((double) (x_element - ((double) (x + ((double) (dirX * d)))))) * ((double) (x_element - ((double) (x + ((double) (dirX * d)))))))) + ((double) (((double) (y_element - ((double) (y + ((double) (dirZ * d)))))) * ((double) (y_element - ((double) (y + ((double) (dirZ * d)))))))))) + ((double) (((double) (dirY * d)) * ((double) (dirY * d)))))))) + d));
}

Error

Bits error versus x_element

Bits error versus x

Bits error versus dirX

Bits error versus d

Bits error versus y_element

Bits error versus y

Bits error versus dirZ

Bits error versus dirY

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 50.6

    \[\sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d\]

  2. Final simplification50.6

    \[\leadsto \sqrt{\left(\left(x_element - \left(x + dirX \cdot d\right)\right) \cdot \left(x_element - \left(x + dirX \cdot d\right)\right) + \left(y_element - \left(y + dirZ \cdot d\right)\right) \cdot \left(y_element - \left(y + dirZ \cdot d\right)\right)\right) + \left(dirY \cdot d\right) \cdot \left(dirY \cdot d\right)} + d\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x_element x dirX d y_element y dirZ dirY)
  :name "(+ (sqrt (+ (+ (* (- x_element (+ x (* dirX d))) (- x_element (+ x (* dirX d)))) (* (- y_element (+ y (* dirZ d))) (- y_element (+ y (* dirZ d))))) (* (* dirY d) (* dirY d)))) d)"
  :precision binary64
  (+ (sqrt (+ (+ (* (- x_element (+ x (* dirX d))) (- x_element (+ x (* dirX d)))) (* (- y_element (+ y (* dirZ d))) (- y_element (+ y (* dirZ d))))) (* (* dirY d) (* dirY d)))) d))