Average Error: 0.0 → 0.0
Time: 3.4s
Precision: binary64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{1 + x} - \frac{x}{1 + x}}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{1 + x} - \frac{x}{1 + x}}\right)
(FPCore (x) :precision binary64 (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
↓
(FPCore (x)
 :precision binary64
 (* 2.0 (atan (sqrt (- (/ 1.0 (+ 1.0 x)) (/ x (+ 1.0 x)))))))
double code(double x) {
	return ((double) (2.0 * ((double) atan(((double) sqrt((((double) (1.0 - x)) / ((double) (1.0 + x)))))))));
}
↓
double code(double x) {
	return ((double) (2.0 * ((double) atan(((double) sqrt(((double) ((1.0 / ((double) (1.0 + x))) - (x / ((double) (1.0 + x)))))))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
  2. Using strategy rm

  3. Applied div-sub0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\frac{1}{1 + x} - \frac{x}{1 + x}}}\right)\]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\frac{1}{1 + x} - \frac{x}{1 + x}}\right)\]

Reproduce

herbie shell --seed 2020198 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))