Average Error: 10.6 → 10.6
Time: 26.3s
Precision: 64
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
\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 r62596 = 1.0;
        double r62597 = Om;
        double r62598 = Omc;
        double r62599 = r62597 / r62598;
        double r62600 = 2.0;
        double r62601 = pow(r62599, r62600);
        double r62602 = r62596 - r62601;
        double r62603 = t;
        double r62604 = l;
        double r62605 = r62603 / r62604;
        double r62606 = pow(r62605, r62600);
        double r62607 = r62600 * r62606;
        double r62608 = r62596 + r62607;
        double r62609 = r62602 / r62608;
        double r62610 = sqrt(r62609);
        double r62611 = asin(r62610);
        return r62611;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r62612 = 1.0;
        double r62613 = Om;
        double r62614 = Omc;
        double r62615 = r62613 / r62614;
        double r62616 = 2.0;
        double r62617 = pow(r62615, r62616);
        double r62618 = r62612 - r62617;
        double r62619 = t;
        double r62620 = l;
        double r62621 = r62619 / r62620;
        double r62622 = pow(r62621, r62616);
        double r62623 = r62616 * r62622;
        double r62624 = r62612 + r62623;
        double r62625 = r62618 / r62624;
        double r62626 = sqrt(r62625);
        double r62627 = asin(r62626);
        return r62627;
}

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 10.6

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

  2. Final simplification10.6

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

Reproduce

herbie shell --seed 2019305 
(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)))))))