Average Error: 10.3 → 10.3
Time: 26.5s
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 r58232 = 1.0;
        double r58233 = Om;
        double r58234 = Omc;
        double r58235 = r58233 / r58234;
        double r58236 = 2.0;
        double r58237 = pow(r58235, r58236);
        double r58238 = r58232 - r58237;
        double r58239 = t;
        double r58240 = l;
        double r58241 = r58239 / r58240;
        double r58242 = pow(r58241, r58236);
        double r58243 = r58236 * r58242;
        double r58244 = r58232 + r58243;
        double r58245 = r58238 / r58244;
        double r58246 = sqrt(r58245);
        double r58247 = asin(r58246);
        return r58247;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r58248 = 1.0;
        double r58249 = Om;
        double r58250 = Omc;
        double r58251 = r58249 / r58250;
        double r58252 = 2.0;
        double r58253 = pow(r58251, r58252);
        double r58254 = r58248 - r58253;
        double r58255 = t;
        double r58256 = l;
        double r58257 = r58255 / r58256;
        double r58258 = pow(r58257, r58252);
        double r58259 = r58252 * r58258;
        double r58260 = r58248 + r58259;
        double r58261 = r58254 / r58260;
        double r58262 = sqrt(r58261);
        double r58263 = asin(r58262);
        return r58263;
}

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 10.3

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

  2. Final simplification10.3

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

Reproduce

herbie shell --seed 2019304 
(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)))))))