Average Error: 12.7 → 12.7
Time: 2.8s
Precision: binary64
\[\cos^{-1} \left(\frac{z \cdot y}{\sqrt{x \cdot z} \cdot y}\right)\]
↓
\[\cos^{-1} \left(\frac{z \cdot y}{\sqrt{x \cdot z} \cdot y}\right)\]
\cos^{-1} \left(\frac{z \cdot y}{\sqrt{x \cdot z} \cdot y}\right)
↓
\cos^{-1} \left(\frac{z \cdot y}{\sqrt{x \cdot z} \cdot y}\right)
double code(double z, double y, double x) {
	return ((double) acos(((double) (((double) (z * y)) / ((double) (((double) sqrt(((double) (x * z)))) * y))))));
}
↓
double code(double z, double y, double x) {
	return ((double) acos(((double) (((double) (z * y)) / ((double) (((double) sqrt(((double) (x * z)))) * y))))));
}

Error

Bits error versus z

Bits error versus y

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.7

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

  2. Final simplification12.7

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

Reproduce

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