Average Error: 10.0 → 10.0
Time: 21.5s
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 r51034 = 1.0;
        double r51035 = Om;
        double r51036 = Omc;
        double r51037 = r51035 / r51036;
        double r51038 = 2.0;
        double r51039 = pow(r51037, r51038);
        double r51040 = r51034 - r51039;
        double r51041 = t;
        double r51042 = l;
        double r51043 = r51041 / r51042;
        double r51044 = pow(r51043, r51038);
        double r51045 = r51038 * r51044;
        double r51046 = r51034 + r51045;
        double r51047 = r51040 / r51046;
        double r51048 = sqrt(r51047);
        double r51049 = asin(r51048);
        return r51049;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r51050 = 1.0;
        double r51051 = Om;
        double r51052 = Omc;
        double r51053 = r51051 / r51052;
        double r51054 = 2.0;
        double r51055 = pow(r51053, r51054);
        double r51056 = r51050 - r51055;
        double r51057 = t;
        double r51058 = l;
        double r51059 = r51057 / r51058;
        double r51060 = pow(r51059, r51054);
        double r51061 = r51054 * r51060;
        double r51062 = r51050 + r51061;
        double r51063 = r51056 / r51062;
        double r51064 = sqrt(r51063);
        double r51065 = asin(r51064);
        return r51065;
}

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 10.0

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

  2. Final simplification10.0

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

Reproduce

herbie shell --seed 2019212 
(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)))))))