Average Error: 31.5 → 0.3
Time: 7.1s
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 <= -0.036336696848678435)) {
		VAR = ((double) (((double) (((double) exp(((double) log(((double) sqrt(((double) (((double) (((double) pow(1.0, 3.0)) - ((double) pow(((double) cos(x)), 3.0)))) / ((double) (((double) (1.0 * 1.0)) + ((double) (((double) cos(x)) * ((double) (1.0 + ((double) cos(x)))))))))))))))) / x)) * ((double) (((double) sqrt(((double) log(((double) exp(((double) (1.0 - ((double) cos(x)))))))))) / x))));
	} else {
		double VAR_1;
		if ((x <= 0.03595994027748503)) {
			VAR_1 = ((double) (0.5 + ((double) (((double) (((double) pow(x, 4.0)) * 0.001388888888888889)) + ((double) (x * ((double) (x * -0.041666666666666664))))))));
		} else {
			VAR_1 = ((double) (((double) (((double) sqrt(((double) log(((double) exp(((double) (1.0 - ((double) cos(x)))))))))) / x)) * ((double) (((double) sqrt(((double) (((double) log(((double) exp(((double) (((double) pow(1.0, 3.0)) - ((double) pow(((double) cos(x)), 3.0)))))))) / ((double) (((double) (1.0 * 1.0)) + ((double) (((double) cos(x)) * ((double) (1.0 + ((double) cos(x)))))))))))) / 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  < -0.036336696848678435
    1. Initial program 1.0
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.1
      \[\leadsto \]
    4. Applied times-frac0.6
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-log-exp0.6
      \[\leadsto \]
    7. Applied add-log-exp0.6
      \[\leadsto \]
    8. Applied diff-log0.6
      \[\leadsto \]
    9. Simplified0.6
      \[\leadsto \]
    10. Using strategy rm
    11. Applied flip3--0.6
      \[\leadsto \]
    12. Simplified0.6
      \[\leadsto \]
    13. Using strategy rm
    14. Applied add-exp-log0.6
      \[\leadsto \]
    if -0.036336696848678435 <  x  < 0.035959940277485031
    1. Initial program 62.3
      \[\]
    2. Taylor expanded around 0 0.0
      \[\leadsto \]
    3. Simplified0.0
      \[\leadsto \]
    if 0.035959940277485031 <  x 
    1. Initial program 1.3
      \[\]
    2. Using strategy rm
    3. Applied add-sqr-sqrt1.4
      \[\leadsto \]
    4. Applied times-frac0.6
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-log-exp0.6
      \[\leadsto \]
    7. Applied add-log-exp0.6
      \[\leadsto \]
    8. Applied diff-log0.6
      \[\leadsto \]
    9. Simplified0.6
      \[\leadsto \]
    10. Using strategy rm
    11. Applied flip3--0.6
      \[\leadsto \]
    12. Simplified0.6
      \[\leadsto \]
    13. Using strategy rm
    14. Applied add-log-exp0.6
      \[\leadsto \]
    15. Applied add-log-exp0.6
      \[\leadsto \]
    16. Applied diff-log0.6
      \[\leadsto \]
    17. Simplified0.6
      \[\leadsto \]
  3. Recombined 3 regimes into one program.
  4. Final simplification0.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x)
  :name "cos2 (problem 3.4.1)"
  :precision binary64
  (/ (- 1.0 (cos x)) (* x x)))