Average Error: 0.0 → 0.0
Time: 19.2s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
\tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right) \cdot 2
double f(double x) {
        double r182191 = 2.0;
        double r182192 = 1.0;
        double r182193 = x;
        double r182194 = r182192 - r182193;
        double r182195 = r182192 + r182193;
        double r182196 = r182194 / r182195;
        double r182197 = sqrt(r182196);
        double r182198 = atan(r182197);
        double r182199 = r182191 * r182198;
        return r182199;
}
↓
double f(double x) {
        double r182200 = 1.0;
        double r182201 = x;
        double r182202 = r182200 - r182201;
        double r182203 = r182200 + r182201;
        double r182204 = r182202 / r182203;
        double r182205 = sqrt(r182204);
        double r182206 = atan(r182205);
        double r182207 = 2.0;
        double r182208 = r182206 * r182207;
        return r182208;
}

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. Final simplification0.0

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

Reproduce

herbie shell --seed 2019142 +o rules:numerics
(FPCore (x)
  :name "arccos"
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))