Average Error: 12.9 → 13.3
Time: 6.0s
Precision: binary64
\[\]
\[\]
↓
\[\]
↓
double code(double p, double x) {
	return ((double) sqrt(((double) (0.5 * ((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (((double) (4.0 * p)) * p)) + ((double) (x * x))))))))))))));
}

↓
double code(double p, double x) {
	return ((double) sqrt(((double) (0.5 * ((double) exp(((double) (((double) cbrt(((double) log(((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))))))))))) * ((double) (((double) cbrt(((double) log(((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))))))))))) * ((double) cbrt(((double) log(((double) (1.0 + ((double) (x / ((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x))))))))))))))))))))))));
}

Error
Bits error versus p
Bits error versus x
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original12.9
Target12.9
Herbie13.3
\[\]
Derivation
  1. Initial program 12.9
    \[\]
  2. Using strategy rm
  3. Applied add-exp-log12.9
    \[\leadsto \]
  4. Simplified12.9
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-cube-cbrt13.3
    \[\leadsto \]
  7. Final simplification13.3
    \[\leadsto \]
Reproduce
herbie shell --seed 2020181 
(FPCore (p x)
  :name "Given's Rotation SVD example"
  :precision binary64
  :pre (< 1e-150 (fabs x) 1e+150)

  :herbie-target
  (sqrt (+ 0.5 (/ (copysign 0.5 x) (hypot 1.0 (/ (* 2.0 p) x)))))

  (sqrt (* 0.5 (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))))