Average Error: 6.7 → 6.7
Time: 5.4s
Precision: binary64
\[\sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]
\sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)
↓
\sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)
double code(double x, double y, double z) {
	return ((double) asin(((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) asin(((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 6.7

    \[\sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]

  2. Final simplification6.7

    \[\leadsto \sin^{-1} \left(\sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z)
  :name "(asin (sqrt (+ (+ (* x x) (* y y)) (* z z))))"
  :precision binary64
  (asin (sqrt (+ (+ (* x x) (* y y)) (* z z)))))