Average Error: 10.3 → 10.3
Time: 9.5s
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 r67938 = 1.0;
        double r67939 = Om;
        double r67940 = Omc;
        double r67941 = r67939 / r67940;
        double r67942 = 2.0;
        double r67943 = pow(r67941, r67942);
        double r67944 = r67938 - r67943;
        double r67945 = t;
        double r67946 = l;
        double r67947 = r67945 / r67946;
        double r67948 = pow(r67947, r67942);
        double r67949 = r67942 * r67948;
        double r67950 = r67938 + r67949;
        double r67951 = r67944 / r67950;
        double r67952 = sqrt(r67951);
        double r67953 = asin(r67952);
        return r67953;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r67954 = 1.0;
        double r67955 = Om;
        double r67956 = Omc;
        double r67957 = r67955 / r67956;
        double r67958 = 2.0;
        double r67959 = pow(r67957, r67958);
        double r67960 = r67954 - r67959;
        double r67961 = t;
        double r67962 = l;
        double r67963 = r67961 / r67962;
        double r67964 = pow(r67963, r67958);
        double r67965 = r67958 * r67964;
        double r67966 = r67954 + r67965;
        double r67967 = r67960 / r67966;
        double r67968 = sqrt(r67967);
        double r67969 = asin(r67968);
        return r67969;
}

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 2019353 
(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)))))))