Average Error: 0.0 → 0.0
Time: 3.0s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\log \left(e^{\frac{\sqrt{1 - x}}{\sqrt{1 + x}}}\right)\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\log \left(e^{\frac{\sqrt{1 - x}}{\sqrt{1 + x}}}\right)\right)
double code(double x) {
	return (2.0 * atan(sqrt(((1.0 - x) / (1.0 + x)))));
}
↓
double code(double x) {
	return (2.0 * atan(log(exp((sqrt((1.0 - x)) / sqrt((1.0 + x)))))));
}

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. Using strategy rm

  3. Applied sqrt-div0.0

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

  5. Applied add-log-exp0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2020066 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))