Average Error: 9.9 → 9.9
Time: 11.6s
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 r72323 = 1.0;
        double r72324 = Om;
        double r72325 = Omc;
        double r72326 = r72324 / r72325;
        double r72327 = 2.0;
        double r72328 = pow(r72326, r72327);
        double r72329 = r72323 - r72328;
        double r72330 = t;
        double r72331 = l;
        double r72332 = r72330 / r72331;
        double r72333 = pow(r72332, r72327);
        double r72334 = r72327 * r72333;
        double r72335 = r72323 + r72334;
        double r72336 = r72329 / r72335;
        double r72337 = sqrt(r72336);
        double r72338 = asin(r72337);
        return r72338;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r72339 = 1.0;
        double r72340 = Om;
        double r72341 = Omc;
        double r72342 = r72340 / r72341;
        double r72343 = 2.0;
        double r72344 = pow(r72342, r72343);
        double r72345 = r72339 - r72344;
        double r72346 = t;
        double r72347 = l;
        double r72348 = r72346 / r72347;
        double r72349 = pow(r72348, r72343);
        double r72350 = r72343 * r72349;
        double r72351 = r72339 + r72350;
        double r72352 = r72345 / r72351;
        double r72353 = sqrt(r72352);
        double r72354 = asin(r72353);
        return r72354;
}

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 9.9

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

  2. Final simplification9.9

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

Reproduce

herbie shell --seed 2019354 
(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)))))))