Average Error: 10.3 → 10.3
Time: 28.3s
Precision: 64
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\frac{1 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{1 + \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right) \cdot 2}}\right)\]
\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 - \frac{Om}{Omc} \cdot \frac{Om}{Omc}}{1 + \left(\frac{t}{\ell} \cdot \frac{t}{\ell}\right) \cdot 2}}\right)
double f(double t, double l, double Om, double Omc) {
        double r1382955 = 1.0;
        double r1382956 = Om;
        double r1382957 = Omc;
        double r1382958 = r1382956 / r1382957;
        double r1382959 = 2.0;
        double r1382960 = pow(r1382958, r1382959);
        double r1382961 = r1382955 - r1382960;
        double r1382962 = t;
        double r1382963 = l;
        double r1382964 = r1382962 / r1382963;
        double r1382965 = pow(r1382964, r1382959);
        double r1382966 = r1382959 * r1382965;
        double r1382967 = r1382955 + r1382966;
        double r1382968 = r1382961 / r1382967;
        double r1382969 = sqrt(r1382968);
        double r1382970 = asin(r1382969);
        return r1382970;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r1382971 = 1.0;
        double r1382972 = Om;
        double r1382973 = Omc;
        double r1382974 = r1382972 / r1382973;
        double r1382975 = r1382974 * r1382974;
        double r1382976 = r1382971 - r1382975;
        double r1382977 = t;
        double r1382978 = l;
        double r1382979 = r1382977 / r1382978;
        double r1382980 = r1382979 * r1382979;
        double r1382981 = 2.0;
        double r1382982 = r1382980 * r1382981;
        double r1382983 = r1382971 + r1382982;
        double r1382984 = r1382976 / r1382983;
        double r1382985 = sqrt(r1382984);
        double r1382986 = asin(r1382985);
        return r1382986;
}

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. Simplified10.3

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

  3. Final simplification10.3

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

Reproduce

herbie shell --seed 2019144 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  (asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))))