Average Error: 13.4 → 14.0
Time: 6.3s
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) (1.0 + ((double) (((double) (((double) cbrt(x)) * ((double) (((double) cbrt(x)) / ((double) (((double) cbrt(((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))))) * ((double) cbrt(((double) sqrt(((double) (((double) (4.0 * ((double) (p * p)))) + ((double) (x * x)))))))))))))) * ((double) (((double) cbrt(x)) / ((double) cbrt(((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
Original13.4
Target13.4
Herbie14.0
\[\]
Derivation
  1. Initial program 13.4
    \[\]
  2. Using strategy rm
  3. Applied add-cube-cbrt15.3
    \[\leadsto \]
  4. Applied add-cube-cbrt13.4
    \[\leadsto \]
  5. Applied times-frac13.4
    \[\leadsto \]
  6. Simplified14.0
    \[\leadsto \]
  7. Simplified14.0
    \[\leadsto \]
  8. Final simplification14.0
    \[\leadsto \]
Reproduce
herbie shell --seed 2020192 
(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))))))))