Average Error: 0.0 → 0.0
Time: 5.4s
Precision: binary64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \]
↓
\[2 \cdot \tan^{-1} \left({\left({\left(1 - x\right)}^{1.5} \cdot {\left(\frac{1}{1 + x}\right)}^{1.5}\right)}^{0.3333333333333333}\right) \]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left({\left({\left(1 - x\right)}^{1.5} \cdot {\left(\frac{1}{1 + x}\right)}^{1.5}\right)}^{0.3333333333333333}\right)

(FPCore (x) :precision binary64 (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))
↓
(FPCore (x)
 :precision binary64
 (*
  2.0
  (atan
   (pow
    (* (pow (- 1.0 x) 1.5) (pow (/ 1.0 (+ 1.0 x)) 1.5))
    0.3333333333333333))))
double code(double x) {
	return 2.0 * atan(sqrt(((1.0 - x) / (1.0 + x))));
}
↓
double code(double x) {
	return 2.0 * atan(pow((pow((1.0 - x), 1.5) * pow((1.0 / (1.0 + x)), 1.5)), 0.3333333333333333));
}

Error

Bits error versus x

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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. Applied egg-rr0.0

    \[\leadsto 2 \cdot \tan^{-1} \color{blue}{\left({\left({\left(\frac{1 - x}{1 + x}\right)}^{1.5}\right)}^{0.3333333333333333}\right)} \]

  3. Applied egg-rr0.0

    \[\leadsto 2 \cdot \tan^{-1} \left({\color{blue}{\left({\left(1 - x\right)}^{1.5} \cdot {\left(\frac{1}{1 + x}\right)}^{1.5}\right)}}^{0.3333333333333333}\right) \]

  4. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left({\left({\left(1 - x\right)}^{1.5} \cdot {\left(\frac{1}{1 + x}\right)}^{1.5}\right)}^{0.3333333333333333}\right) \]

Reproduce

herbie shell --seed 2022130 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2.0 (atan (sqrt (/ (- 1.0 x) (+ 1.0 x))))))