Average Error: 30.2 → 15.2
Time: 4.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x) {
	return ((double) sqrt(((double) (((double) pow(x, 2.0)) + ((double) pow(x, 2.0))))));
}

↓
double code(double x) {
	double VAR;
	if ((x <= 1.91106969199616e-310)) {
		VAR = ((double) sqrt(((double) (((double) pow(x, 2.0)) * 2.0))));
	} else {
		VAR = ((double) (((double) (((double) cbrt(((double) sqrt(2.0)))) * ((double) cbrt(((double) sqrt(2.0)))))) * ((double) (((double) cbrt(((double) sqrt(2.0)))) * ((double) pow(x, 1.0))))));
	}
	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  < 1.911069691996156e-310
    1. Initial program 29.7
      \[\]
    2. Simplified29.7
      \[\leadsto \]
    if 1.911069691996156e-310 <  x 
    1. Initial program 30.8
      \[\]
    2. Simplified30.8
      \[\leadsto \]
    3. Taylor expanded around 0 5.7
      \[\leadsto \]
    4. Simplified0.4
      \[\leadsto \]
    5. Using strategy rm
    6. Applied add-cube-cbrt0.4
      \[\leadsto \]
    7. Applied associate-*l*0.4
      \[\leadsto \]
    8. Simplified0.4
      \[\leadsto \]
  3. Recombined 2 regimes into one program.
  4. Final simplification15.2
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x)
  :name "sqrt E"
  :precision binary64
  (sqrt (+ (pow x 2.0) (pow x 2.0))))