Average Error: 5.7 → 5.7
Time: 1.1s
Precision: binary64
\[\left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)\]
↓
\[\left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)\]
\left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)
↓
\left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)
double code(double x, double x_prev, double a, double dt) {
	return ((double) (((double) (((double) (2.0 * x)) - x_prev)) + ((double) (a * ((double) (dt * dt))))));
}
↓
double code(double x, double x_prev, double a, double dt) {
	return ((double) (((double) (((double) (2.0 * x)) - x_prev)) + ((double) (a * ((double) (dt * dt))))));
}

Error

Bits error versus x

Bits error versus x_prev

Bits error versus a

Bits error versus dt

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 5.7

    \[\left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)\]

  2. Final simplification5.7

    \[\leadsto \left(2 \cdot x - x_prev\right) + a \cdot \left(dt \cdot dt\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x x_prev a dt)
  :name "(+ (- (* 2 x) x_prev) (* a (* dt dt)))"
  :precision binary64
  (+ (- (* 2.0 x) x_prev) (* a (* dt dt))))