(+ v (* (* (+ a a1) dt) 0.5))

Average Error: 0.1 → 0.1

Time: 1.1s

Precision: binary64

Math

\[v + \left(\left(a + a1\right) \cdot dt\right) \cdot 0.5\]

↓

\[v + \left(\left(a + a1\right) \cdot dt\right) \cdot 0.5\]

C

double code(double v, double a, double a1, double dt) {
	return ((double) (v + ((double) (((double) (((double) (a + a1)) * dt)) * 0.5))));
}

↓

double code(double v, double a, double a1, double dt) {
	return ((double) (v + ((double) (((double) (((double) (a + a1)) * dt)) * 0.5))));
}

Error

Bits error versus v

Bits error versus a

Bits error versus a1

Bits error versus dt

Derivation

1. Initial program 0.1

   \[v + \left(\left(a + a1\right) \cdot dt\right) \cdot 0.5\]

2. Final simplification 0.1

   \[\leadsto v + \left(\left(a + a1\right) \cdot dt\right) \cdot 0.5\]

Reproduce

herbie shell --seed 2020152 
(FPCore (v a a1 dt)
  :name "(+ v (* (* (+ a a1) dt) 0.5))"
  :precision binary64
  (+ v (* (* (+ a a1) dt) 0.5)))