(+ (+ x (- x xp)) (* (* a dt) dt))

Average Error: 0.1 → 0.1

Time: 1.1s

Precision: binary64

Math

\[\left(x + \left(x - xp\right)\right) + \left(a \cdot dt\right) \cdot dt\]

↓

\[\left(x + \left(x - xp\right)\right) + \left(a \cdot dt\right) \cdot dt\]

C

double code(double x, double xp, double a, double dt) {
	return ((double) (((double) (x + ((double) (x - xp)))) + ((double) (((double) (a * dt)) * dt))));
}

↓

double code(double x, double xp, double a, double dt) {
	return ((double) (((double) (x + ((double) (x - xp)))) + ((double) (((double) (a * dt)) * dt))));
}

Error

Bits error versus x

Bits error versus xp

Bits error versus a

Bits error versus dt

Derivation

1. Initial program 0.1

   \[\left(x + \left(x - xp\right)\right) + \left(a \cdot dt\right) \cdot dt\]

2. Final simplification 0.1

   \[\leadsto \left(x + \left(x - xp\right)\right) + \left(a \cdot dt\right) \cdot dt\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x xp a dt)
  :name "(+ (+ x (- x xp)) (* (* a dt) dt))"
  :precision binary64
  (+ (+ x (- x xp)) (* (* a dt) dt)))