Average Error: 32.1 → 0.4
Time: 4.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) (((double) (1.0 - ((double) cos(x)))) / ((double) (x * x))));
}

↓
double code(double x) {
	double VAR;
	if ((x <= -0.0302754788051601)) {
		VAR = ((double) (((double) (((double) (1.0 - ((double) cos(x)))) / x)) / x));
	} else {
		double VAR_1;
		if ((x <= 0.03110119868356473)) {
			VAR_1 = ((double) (((double) (((double) pow(x, 4.0)) * 0.001388888888888889)) + ((double) (0.5 + ((double) (x * ((double) (x * -0.041666666666666664))))))));
		} else {
			VAR_1 = ((double) (1.0 / ((double) (x * ((double) (x / ((double) (1.0 - ((double) cos(x))))))))));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Split input into 3 regimes
  2. if  x  < -0.0302754788051601
    1. Initial program 1.0
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*0.5
      \[\leadsto \]
    if -0.0302754788051601 <  x  < 0.031101198683564729
    1. Initial program 62.4
      \[\]
    2. Taylor expanded around 0 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if 0.031101198683564729 <  x 
    1. Initial program 1.1
      \[\]
    2. Using strategy rm
    3. Applied clear-num1.1
      \[\leadsto \]
    4. Simplified1.1
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.4
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(FPCore (x)
  :name "cos2 (problem 3.4.1)"
  :precision binary64
  (/ (- 1.0 (cos x)) (* x x)))