Average Error: 10.1 → 10.1
Time: 23.0s
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 r43457 = 1.0;
        double r43458 = Om;
        double r43459 = Omc;
        double r43460 = r43458 / r43459;
        double r43461 = 2.0;
        double r43462 = pow(r43460, r43461);
        double r43463 = r43457 - r43462;
        double r43464 = t;
        double r43465 = l;
        double r43466 = r43464 / r43465;
        double r43467 = pow(r43466, r43461);
        double r43468 = r43461 * r43467;
        double r43469 = r43457 + r43468;
        double r43470 = r43463 / r43469;
        double r43471 = sqrt(r43470);
        double r43472 = asin(r43471);
        return r43472;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r43473 = 1.0;
        double r43474 = Om;
        double r43475 = Omc;
        double r43476 = r43474 / r43475;
        double r43477 = 2.0;
        double r43478 = pow(r43476, r43477);
        double r43479 = r43473 - r43478;
        double r43480 = t;
        double r43481 = l;
        double r43482 = r43480 / r43481;
        double r43483 = pow(r43482, r43477);
        double r43484 = r43477 * r43483;
        double r43485 = r43473 + r43484;
        double r43486 = r43479 / r43485;
        double r43487 = sqrt(r43486);
        double r43488 = asin(r43487);
        return r43488;
}

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 10.1

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

  2. Final simplification10.1

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

Reproduce

herbie shell --seed 2019195 
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  (asin (sqrt (/ (- 1.0 (pow (/ Om Omc) 2.0)) (+ 1.0 (* 2.0 (pow (/ t l) 2.0)))))))