Average Error: 31.2 → 0.3
Time: 4.1s
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 <= -0.03662840477444983) || !(x <= 0.03564219456903279))) {
		VAR = ((double) (((double) (((double) log(((double) exp(((double) (1.0 - ((double) cos(x)))))))) / x)) / x));
	} else {
		VAR = ((double) (((double) (((double) pow(x, 4.0)) * 0.001388888888888889)) + ((double) (0.5 - ((double) (x * ((double) (x * 0.041666666666666664))))))));
	}
	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 2 regimes
  2. if  x  < -0.036628404774449827 or 0.0356421945690327882 <  x 
    1. Initial program 1.1
      \[\]
    2. Using strategy rm
    3. Applied associate-/r*0.5
      \[\leadsto \]
    4. Using strategy rm
    5. Applied add-log-exp0.6
      \[\leadsto \]
    6. Applied add-log-exp0.6
      \[\leadsto \]
    7. Applied diff-log0.7
      \[\leadsto \]
    8. Simplified0.6
      \[\leadsto \]
    if -0.036628404774449827 <  x  < 0.0356421945690327882
    1. Initial program 62.4
      \[\]
    2. Taylor expanded around 0 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (x)
  :name "cos2 (problem 3.4.1)"
  :precision binary64
  (/ (- 1.0 (cos x)) (* x x)))