Average Error: 10.5 → 10.5
Time: 12.0s
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 r78153 = 1.0;
        double r78154 = Om;
        double r78155 = Omc;
        double r78156 = r78154 / r78155;
        double r78157 = 2.0;
        double r78158 = pow(r78156, r78157);
        double r78159 = r78153 - r78158;
        double r78160 = t;
        double r78161 = l;
        double r78162 = r78160 / r78161;
        double r78163 = pow(r78162, r78157);
        double r78164 = r78157 * r78163;
        double r78165 = r78153 + r78164;
        double r78166 = r78159 / r78165;
        double r78167 = sqrt(r78166);
        double r78168 = asin(r78167);
        return r78168;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r78169 = 1.0;
        double r78170 = Om;
        double r78171 = Omc;
        double r78172 = r78170 / r78171;
        double r78173 = 2.0;
        double r78174 = pow(r78172, r78173);
        double r78175 = r78169 - r78174;
        double r78176 = t;
        double r78177 = l;
        double r78178 = r78176 / r78177;
        double r78179 = pow(r78178, r78173);
        double r78180 = r78173 * r78179;
        double r78181 = r78169 + r78180;
        double r78182 = r78175 / r78181;
        double r78183 = sqrt(r78182);
        double r78184 = asin(r78183);
        return r78184;
}

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 2020001 
(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)))))))