Average Error: 17.3 → 17.3
Time: 1.7s
Precision: binary64
\[\frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}\]
↓
\[\frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}\]
\frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}
↓
\frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}
double code(double k, double l0, double ndir, double dir, double n, double dt) {
	return ((double) (((double) (((double) (((double) (((double) (k * ((double) (((double) (l0 * ndir)) - dir)))) / ((double) (n + 1.0)))) * dt)) * dt)) / ((double) (n + 2.0))));
}
↓
double code(double k, double l0, double ndir, double dir, double n, double dt) {
	return ((double) (((double) (((double) (((double) (((double) (k * ((double) (((double) (l0 * ndir)) - dir)))) / ((double) (n + 1.0)))) * dt)) * dt)) / ((double) (n + 2.0))));
}

Error

Bits error versus k

Bits error versus l0

Bits error versus ndir

Bits error versus dir

Bits error versus n

Bits error versus dt

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 17.3

    \[\frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}\]

  2. Final simplification17.3

    \[\leadsto \frac{\left(\frac{k \cdot \left(l0 \cdot ndir - dir\right)}{n + 1} \cdot dt\right) \cdot dt}{n + 2}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (k l0 ndir dir n dt)
  :name "(/ (* (* (/ (* k (- (* l0 ndir) dir)) (+ n 1)) dt) dt) (+ n 2))"
  :precision binary64
  (/ (* (* (/ (* k (- (* l0 ndir) dir)) (+ n 1.0)) dt) dt) (+ n 2.0)))