Average Error: 10.3 → 10.3
Time: 9.1s
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 r71392 = 1.0;
        double r71393 = Om;
        double r71394 = Omc;
        double r71395 = r71393 / r71394;
        double r71396 = 2.0;
        double r71397 = pow(r71395, r71396);
        double r71398 = r71392 - r71397;
        double r71399 = t;
        double r71400 = l;
        double r71401 = r71399 / r71400;
        double r71402 = pow(r71401, r71396);
        double r71403 = r71396 * r71402;
        double r71404 = r71392 + r71403;
        double r71405 = r71398 / r71404;
        double r71406 = sqrt(r71405);
        double r71407 = asin(r71406);
        return r71407;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r71408 = 1.0;
        double r71409 = Om;
        double r71410 = Omc;
        double r71411 = r71409 / r71410;
        double r71412 = 2.0;
        double r71413 = pow(r71411, r71412);
        double r71414 = r71408 - r71413;
        double r71415 = t;
        double r71416 = l;
        double r71417 = r71415 / r71416;
        double r71418 = pow(r71417, r71412);
        double r71419 = r71412 * r71418;
        double r71420 = r71408 + r71419;
        double r71421 = r71414 / r71420;
        double r71422 = sqrt(r71421);
        double r71423 = asin(r71422);
        return r71423;
}

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 10.3

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

  2. Final simplification10.3

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

Reproduce

herbie shell --seed 2020049 
(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)))))))