(+ x (* (* (+ v v1) dt) 0.5))

Average Error: 0.1 → 0.1

Time: 1.0s

Precision: binary64

Math

\[x + \left(\left(v + v1\right) \cdot dt\right) \cdot 0.5\]

↓

\[x + \left(\left(v + v1\right) \cdot dt\right) \cdot 0.5\]

C

double code(double x, double v, double v1, double dt) {
	return ((double) (x + ((double) (((double) (((double) (v + v1)) * dt)) * 0.5))));
}

↓

double code(double x, double v, double v1, double dt) {
	return ((double) (x + ((double) (((double) (((double) (v + v1)) * dt)) * 0.5))));
}

Error

Bits error versus x

Bits error versus v

Bits error versus v1

Bits error versus dt

Derivation

1. Initial program 0.1

   \[x + \left(\left(v + v1\right) \cdot dt\right) \cdot 0.5\]

2. Final simplification 0.1

   \[\leadsto x + \left(\left(v + v1\right) \cdot dt\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x v v1 dt)
  :name "(+ x (* (* (+ v v1) dt) 0.5))"
  :precision binary64
  (+ x (* (* (+ v v1) dt) 0.5)))