Average Error: 10.4 → 10.4
Time: 9.5s
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 r58545 = 1.0;
        double r58546 = Om;
        double r58547 = Omc;
        double r58548 = r58546 / r58547;
        double r58549 = 2.0;
        double r58550 = pow(r58548, r58549);
        double r58551 = r58545 - r58550;
        double r58552 = t;
        double r58553 = l;
        double r58554 = r58552 / r58553;
        double r58555 = pow(r58554, r58549);
        double r58556 = r58549 * r58555;
        double r58557 = r58545 + r58556;
        double r58558 = r58551 / r58557;
        double r58559 = sqrt(r58558);
        double r58560 = asin(r58559);
        return r58560;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r58561 = 1.0;
        double r58562 = Om;
        double r58563 = Omc;
        double r58564 = r58562 / r58563;
        double r58565 = 2.0;
        double r58566 = pow(r58564, r58565);
        double r58567 = r58561 - r58566;
        double r58568 = t;
        double r58569 = l;
        double r58570 = r58568 / r58569;
        double r58571 = pow(r58570, r58565);
        double r58572 = r58565 * r58571;
        double r58573 = r58561 + r58572;
        double r58574 = r58567 / r58573;
        double r58575 = sqrt(r58574);
        double r58576 = asin(r58575);
        return r58576;
}

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 10.4

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

  2. Final simplification10.4

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

Reproduce

herbie shell --seed 2020021 
(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)))))))