Average Error: 10.6 → 10.6
Time: 14.0s
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 r84557 = 1.0;
        double r84558 = Om;
        double r84559 = Omc;
        double r84560 = r84558 / r84559;
        double r84561 = 2.0;
        double r84562 = pow(r84560, r84561);
        double r84563 = r84557 - r84562;
        double r84564 = t;
        double r84565 = l;
        double r84566 = r84564 / r84565;
        double r84567 = pow(r84566, r84561);
        double r84568 = r84561 * r84567;
        double r84569 = r84557 + r84568;
        double r84570 = r84563 / r84569;
        double r84571 = sqrt(r84570);
        double r84572 = asin(r84571);
        return r84572;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r84573 = 1.0;
        double r84574 = Om;
        double r84575 = Omc;
        double r84576 = r84574 / r84575;
        double r84577 = 2.0;
        double r84578 = pow(r84576, r84577);
        double r84579 = r84573 - r84578;
        double r84580 = t;
        double r84581 = l;
        double r84582 = r84580 / r84581;
        double r84583 = pow(r84582, r84577);
        double r84584 = r84577 * r84583;
        double r84585 = r84573 + r84584;
        double r84586 = r84579 / r84585;
        double r84587 = sqrt(r84586);
        double r84588 = asin(r84587);
        return r84588;
}

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 2019322 
(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)))))))