Average Error: 10.1 → 10.1
Time: 31.4s
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 r64157 = 1.0;
        double r64158 = Om;
        double r64159 = Omc;
        double r64160 = r64158 / r64159;
        double r64161 = 2.0;
        double r64162 = pow(r64160, r64161);
        double r64163 = r64157 - r64162;
        double r64164 = t;
        double r64165 = l;
        double r64166 = r64164 / r64165;
        double r64167 = pow(r64166, r64161);
        double r64168 = r64161 * r64167;
        double r64169 = r64157 + r64168;
        double r64170 = r64163 / r64169;
        double r64171 = sqrt(r64170);
        double r64172 = asin(r64171);
        return r64172;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r64173 = 1.0;
        double r64174 = Om;
        double r64175 = Omc;
        double r64176 = r64174 / r64175;
        double r64177 = 2.0;
        double r64178 = pow(r64176, r64177);
        double r64179 = r64173 - r64178;
        double r64180 = t;
        double r64181 = l;
        double r64182 = r64180 / r64181;
        double r64183 = pow(r64182, r64177);
        double r64184 = r64177 * r64183;
        double r64185 = r64173 + r64184;
        double r64186 = r64179 / r64185;
        double r64187 = sqrt(r64186);
        double r64188 = asin(r64187);
        return r64188;
}

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 10.1

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

  2. Final simplification10.1

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

Reproduce

herbie shell --seed 2019323 
(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)))))))