Average Error: 54.6 → 54.6
Time: 3.6s
Precision: binary64
\[\sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]
↓
\[\sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]
\sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)
↓
\sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)
double code(double x, double y, double z) {
	return ((double) sin(((double) (((double) (((double) (2.0 * ((double) M_PI))) / 6.5e-07)) * ((double) sqrt(((double) (((double) (((double) (x * x)) + ((double) (y * y)))) + ((double) (z * z))))))))));
}
↓
double code(double x, double y, double z) {
	return ((double) sin(((double) (((double) (((double) (2.0 * ((double) M_PI))) / 6.5e-07)) * ((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 54.6

    \[\sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]

  2. Final simplification54.6

    \[\leadsto \sin \left(\frac{2 \cdot \pi}{6.50000000000000024 \cdot 10^{-7}} \cdot \sqrt{\left(x \cdot x + y \cdot y\right) + z \cdot z}\right)\]

Reproduce

herbie shell --seed 2020152 
(FPCore (x y z)
  :name "(sin (* (/ (* 2 PI) 6.5e-07) (sqrt (+ (+ (* x x) (* y y)) (* z z)))))"
  :precision binary64
  (sin (* (/ (* 2.0 PI) 6.5e-07) (sqrt (+ (+ (* x x) (* y y)) (* z z))))))