Average Error: 44.5 → 44.5
Time: 3.3s
Precision: binary64
\[\frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}\]
↓
\[\frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}\]
\frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}
↓
\frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}
double code(double x) {
	return ((double) (((double) (((double) sin(((double) (x + 0.001)))) + ((double) sin(((double) (x - 0.001)))))) / ((double) (2.0 * 0.001))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) sin(((double) (x + 0.001)))) + ((double) sin(((double) (x - 0.001)))))) / ((double) (2.0 * 0.001))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 44.5

    \[\frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}\]

  2. Final simplification44.5

    \[\leadsto \frac{\sin \left(x + 10^{-3}\right) + \sin \left(x - 10^{-3}\right)}{2 \cdot 10^{-3}}\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x)
  :name "(/ (+ (sin (+ x 0.001)) (sin (- x 0.001))) (* 2 0.001))"
  :precision binary64
  (/ (+ (sin (+ x 0.001)) (sin (- x 0.001))) (* 2.0 0.001)))