Average Error: 13.0 → 13.0
Time: 5.8s
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) (((double) sqrt(((double) (0.5 * ((double) (((double) pow(1.0, 3.0)) + ((double) pow(((double) (x / ((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))))), 3.0)))))))) / ((double) sqrt(((double) (((double) (1.0 * 1.0)) + ((double) (x * ((double) (((double) (x / ((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))) - ((double) (1.0 / ((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
Original13.0
Target13.0
Herbie13.0
\[\]
Derivation
  1. Initial program 13.0
    \[\]
  2. Using strategy rm
  3. Applied flip3-+13.0
    \[\leadsto \]
  4. Applied associate-*r/13.0
    \[\leadsto \]
  5. Applied sqrt-div13.0
    \[\leadsto \]
  6. Simplified13.0
    \[\leadsto \]
  7. Simplified13.0
    \[\leadsto \]
  8. Final simplification13.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(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))))))))