Average Error: 0.0 → 0.0
Time: 8.6s
Precision: 64
\[2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)\]
↓
\[2 \cdot \tan^{-1} \left(\sqrt{\left(\frac{1}{{1}^{3} + {x}^{3}} - \frac{x}{{1}^{3} + {x}^{3}}\right) \cdot \left(1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)\right)}\right)\]
2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{1 + x}}\right)
↓
2 \cdot \tan^{-1} \left(\sqrt{\left(\frac{1}{{1}^{3} + {x}^{3}} - \frac{x}{{1}^{3} + {x}^{3}}\right) \cdot \left(1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)\right)}\right)
double f(double x) {
        double r22158 = 2.0;
        double r22159 = 1.0;
        double r22160 = x;
        double r22161 = r22159 - r22160;
        double r22162 = r22159 + r22160;
        double r22163 = r22161 / r22162;
        double r22164 = sqrt(r22163);
        double r22165 = atan(r22164);
        double r22166 = r22158 * r22165;
        return r22166;
}
↓
double f(double x) {
        double r22167 = 2.0;
        double r22168 = 1.0;
        double r22169 = 3.0;
        double r22170 = pow(r22168, r22169);
        double r22171 = x;
        double r22172 = pow(r22171, r22169);
        double r22173 = r22170 + r22172;
        double r22174 = r22168 / r22173;
        double r22175 = r22171 / r22173;
        double r22176 = r22174 - r22175;
        double r22177 = r22168 * r22168;
        double r22178 = r22171 * r22171;
        double r22179 = r22168 * r22171;
        double r22180 = r22178 - r22179;
        double r22181 = r22177 + r22180;
        double r22182 = r22176 * r22181;
        double r22183 = sqrt(r22182);
        double r22184 = atan(r22183);
        double r22185 = r22167 * r22184;
        return r22185;
}

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 flip3-+0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\frac{1 - x}{\color{blue}{\frac{{1}^{3} + {x}^{3}}{1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)}}}}\right)\]

  4. Applied associate-/r/0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\frac{1 - x}{{1}^{3} + {x}^{3}} \cdot \left(1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)\right)}}\right)\]
  5. Using strategy rm

  6. Applied div-sub0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\color{blue}{\left(\frac{1}{{1}^{3} + {x}^{3}} - \frac{x}{{1}^{3} + {x}^{3}}\right)} \cdot \left(1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)\right)}\right)\]

  7. Final simplification0.0

    \[\leadsto 2 \cdot \tan^{-1} \left(\sqrt{\left(\frac{1}{{1}^{3} + {x}^{3}} - \frac{x}{{1}^{3} + {x}^{3}}\right) \cdot \left(1 \cdot 1 + \left(x \cdot x - 1 \cdot x\right)\right)}\right)\]

Reproduce

herbie shell --seed 2019308 
(FPCore (x)
  :name "arccos"
  :precision binary64
  (* 2 (atan (sqrt (/ (- 1 x) (+ 1 x))))))