Average Error: 10.0 → 10.0
Time: 20.1s
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 r57664 = 1.0;
        double r57665 = Om;
        double r57666 = Omc;
        double r57667 = r57665 / r57666;
        double r57668 = 2.0;
        double r57669 = pow(r57667, r57668);
        double r57670 = r57664 - r57669;
        double r57671 = t;
        double r57672 = l;
        double r57673 = r57671 / r57672;
        double r57674 = pow(r57673, r57668);
        double r57675 = r57668 * r57674;
        double r57676 = r57664 + r57675;
        double r57677 = r57670 / r57676;
        double r57678 = sqrt(r57677);
        double r57679 = asin(r57678);
        return r57679;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r57680 = 1.0;
        double r57681 = Om;
        double r57682 = Omc;
        double r57683 = r57681 / r57682;
        double r57684 = 2.0;
        double r57685 = pow(r57683, r57684);
        double r57686 = r57680 - r57685;
        double r57687 = t;
        double r57688 = l;
        double r57689 = r57687 / r57688;
        double r57690 = pow(r57689, r57684);
        double r57691 = r57684 * r57690;
        double r57692 = r57680 + r57691;
        double r57693 = r57686 / r57692;
        double r57694 = sqrt(r57693);
        double r57695 = asin(r57694);
        return r57695;
}

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 10.0

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

  2. Final simplification10.0

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

Reproduce

herbie shell --seed 2019297 
(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)))))))