Average Error: 0.1 → 0.1
Time: 1.0s
Precision: binary64
\[dt \cdot a - \left(a \cdot dt\right) \cdot dt\]
↓
\[dt \cdot a - \left(a \cdot dt\right) \cdot dt\]
dt \cdot a - \left(a \cdot dt\right) \cdot dt
↓
dt \cdot a - \left(a \cdot dt\right) \cdot dt
double code(double dt, double a) {
	return ((double) (((double) (dt * a)) - ((double) (((double) (a * dt)) * dt))));
}
↓
double code(double dt, double a) {
	return ((double) (((double) (dt * a)) - ((double) (((double) (a * dt)) * dt))));
}

Error

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

    \[dt \cdot a - \left(a \cdot dt\right) \cdot dt\]

  2. Final simplification0.1

    \[\leadsto dt \cdot a - \left(a \cdot dt\right) \cdot dt\]

Reproduce

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