Average Error: 10.5 → 10.5
Time: 11.9s
Precision: 64
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)
↓
\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)
double f(double t, double l, double Om, double Omc) {
        double r78165 = 1.0;
        double r78166 = Om;
        double r78167 = Omc;
        double r78168 = r78166 / r78167;
        double r78169 = 2.0;
        double r78170 = pow(r78168, r78169);
        double r78171 = r78165 - r78170;
        double r78172 = t;
        double r78173 = l;
        double r78174 = r78172 / r78173;
        double r78175 = pow(r78174, r78169);
        double r78176 = r78169 * r78175;
        double r78177 = r78165 + r78176;
        double r78178 = r78171 / r78177;
        double r78179 = sqrt(r78178);
        double r78180 = asin(r78179);
        return r78180;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r78181 = 1.0;
        double r78182 = Om;
        double r78183 = Omc;
        double r78184 = r78182 / r78183;
        double r78185 = 2.0;
        double r78186 = pow(r78184, r78185);
        double r78187 = r78181 - r78186;
        double r78188 = t;
        double r78189 = l;
        double r78190 = r78188 / r78189;
        double r78191 = pow(r78190, r78185);
        double r78192 = r78185 * r78191;
        double r78193 = r78181 + r78192;
        double r78194 = r78187 / r78193;
        double r78195 = sqrt(r78194);
        double r78196 = asin(r78195);
        return r78196;
}

Error

Bits error versus t

Bits error versus l

Bits error versus Om

Bits error versus Omc

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 10.5

    \[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

  2. Final simplification10.5

    \[\leadsto \sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

Reproduce

herbie shell --seed 2020001 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  :precision binary64
  (asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))))