Average Error: 0.1 → 0.1
Time: 2.5s
Precision: binary64
\[\left(x + v \cdot dt\right) + \left(\left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) \cdot dt\]
↓
\[dt \cdot \left(v + \left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) + x\]
\left(x + v \cdot dt\right) + \left(\left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) \cdot dt
↓
dt \cdot \left(v + \left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) + x
double code(double x, double v, double dt, double a, double aprev) {
	return ((double) (((double) (x + ((double) (v * dt)))) + ((double) (((double) (((double) (((double) (a * ((double) (2.0 / 3.0)))) - ((double) (aprev * ((double) (1.0 / 6.0)))))) * dt)) * dt))));
}
↓
double code(double x, double v, double dt, double a, double aprev) {
	return ((double) (((double) (dt * ((double) (v + ((double) (((double) (((double) (a * ((double) (2.0 / 3.0)))) - ((double) (aprev * ((double) (1.0 / 6.0)))))) * dt)))))) + x));
}

Error

Bits error versus x

Bits error versus v

Bits error versus dt

Bits error versus a

Bits error versus aprev

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x + v \cdot dt\right) + \left(\left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) \cdot dt\]

  2. Simplified0.1

    \[\leadsto \color{blue}{dt \cdot \left(v + \left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) + x}\]

  3. Final simplification0.1

    \[\leadsto dt \cdot \left(v + \left(a \cdot \frac{2}{3} - aprev \cdot \frac{1}{6}\right) \cdot dt\right) + x\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x v dt a aprev)
  :name "(+ (+ x (* v dt)) (* (* (- (* a (/ 2 3)) (* aprev (/ 1 6))) dt) dt))"
  :precision binary64
  (+ (+ x (* v dt)) (* (* (- (* a (/ 2.0 3.0)) (* aprev (/ 1.0 6.0))) dt) dt)))