Average Error: 10.5 → 10.5
Time: 8.5s
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 r66449 = 1.0;
        double r66450 = Om;
        double r66451 = Omc;
        double r66452 = r66450 / r66451;
        double r66453 = 2.0;
        double r66454 = pow(r66452, r66453);
        double r66455 = r66449 - r66454;
        double r66456 = t;
        double r66457 = l;
        double r66458 = r66456 / r66457;
        double r66459 = pow(r66458, r66453);
        double r66460 = r66453 * r66459;
        double r66461 = r66449 + r66460;
        double r66462 = r66455 / r66461;
        double r66463 = sqrt(r66462);
        double r66464 = asin(r66463);
        return r66464;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r66465 = 1.0;
        double r66466 = Om;
        double r66467 = Omc;
        double r66468 = r66466 / r66467;
        double r66469 = 2.0;
        double r66470 = pow(r66468, r66469);
        double r66471 = r66465 - r66470;
        double r66472 = t;
        double r66473 = l;
        double r66474 = r66472 / r66473;
        double r66475 = pow(r66474, r66469);
        double r66476 = r66469 * r66475;
        double r66477 = r66465 + r66476;
        double r66478 = r66471 / r66477;
        double r66479 = sqrt(r66478);
        double r66480 = asin(r66479);
        return r66480;
}

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 10.5

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

  2. Final simplification10.5

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

Reproduce

herbie shell --seed 2020059 
(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)))))))