Average Error: 0.2 → 0.2
Time: 2.4s
Precision: binary64
\[\left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}\]
↓
\[\left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}\]
\left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}
↓
\left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}
double code(double x, double v, double dt, double a, double a_prev) {
	return ((double) (((double) (x + ((double) (v * dt)))) + ((double) (((double) (((double) (((double) (((double) (a * 4.0)) - a_prev)) * dt)) * dt)) * ((double) (1.0 / 6.0))))));
}
↓
double code(double x, double v, double dt, double a, double a_prev) {
	return ((double) (((double) (x + ((double) (v * dt)))) + ((double) (((double) (((double) (((double) (((double) (a * 4.0)) - a_prev)) * dt)) * dt)) * ((double) (1.0 / 6.0))))));
}

Error

Bits error versus x

Bits error versus v

Bits error versus dt

Bits error versus a

Bits error versus a_prev

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}\]

  2. Final simplification0.2

    \[\leadsto \left(x + v \cdot dt\right) + \left(\left(\left(a \cdot 4 - a_prev\right) \cdot dt\right) \cdot dt\right) \cdot \frac{1}{6}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x v dt a a_prev)
  :name "(+ (+ x (* v dt)) (* (* (* (- (* a 4) a_prev) dt) dt) (/ 1 6)))"
  :precision binary64
  (+ (+ x (* v dt)) (* (* (* (- (* a 4.0) a_prev) dt) dt) (/ 1.0 6.0))))