Average Error: 0.1 → 0.1
Time: 1.2s
Precision: binary64
\[\left(x + v \cdot dt\right) + \left(\left(a \cdot dt\right) \cdot dt\right) \cdot 0.5\]
↓
\[\left(x + v \cdot dt\right) + \left(\left(a \cdot dt\right) \cdot dt\right) \cdot 0.5\]
\left(x + v \cdot dt\right) + \left(\left(a \cdot dt\right) \cdot dt\right) \cdot 0.5
↓
\left(x + v \cdot dt\right) + \left(\left(a \cdot dt\right) \cdot dt\right) \cdot 0.5
double code(double x, double v, double dt, double a) {
	return ((double) (((double) (x + ((double) (v * dt)))) + ((double) (((double) (((double) (a * dt)) * dt)) * 0.5))));
}
↓
double code(double x, double v, double dt, double a) {
	return ((double) (((double) (x + ((double) (v * dt)))) + ((double) (((double) (((double) (a * dt)) * dt)) * 0.5))));
}

Error

Bits error versus x

Bits error versus v

Bits error versus dt

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

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