Average Error: 0.1 → 0
Time: 1.9s
Precision: binary64
\[\frac{1}{\sin x \cdot \sin x + \cos x \cdot \cos x}\]
↓
\[1\]
\frac{1}{\sin x \cdot \sin x + \cos x \cdot \cos x}
↓
1
double code(double x) {
	return ((double) (1.0 / ((double) (((double) (((double) sin(x)) * ((double) sin(x)))) + ((double) (((double) cos(x)) * ((double) cos(x))))))));
}
↓
double code(double x) {
	return 1.0;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\frac{1}{\sin x \cdot \sin x + \cos x \cdot \cos x}\]

  2. Simplified0

    \[\leadsto \color{blue}{1}\]

  3. Final simplification0

    \[\leadsto 1\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x)
  :name "(/ 1 (+ (* (sin x) (sin x)) (* (cos x) (cos x))))"
  :precision binary64
  (/ 1.0 (+ (* (sin x) (sin x)) (* (cos x) (cos x)))))