Average Error: 10.3 → 10.3
Time: 13.4s
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 r62255 = 1.0;
        double r62256 = Om;
        double r62257 = Omc;
        double r62258 = r62256 / r62257;
        double r62259 = 2.0;
        double r62260 = pow(r62258, r62259);
        double r62261 = r62255 - r62260;
        double r62262 = t;
        double r62263 = l;
        double r62264 = r62262 / r62263;
        double r62265 = pow(r62264, r62259);
        double r62266 = r62259 * r62265;
        double r62267 = r62255 + r62266;
        double r62268 = r62261 / r62267;
        double r62269 = sqrt(r62268);
        double r62270 = asin(r62269);
        return r62270;
}
↓
double f(double t, double l, double Om, double Omc) {
        double r62271 = 1.0;
        double r62272 = Om;
        double r62273 = Omc;
        double r62274 = r62272 / r62273;
        double r62275 = 2.0;
        double r62276 = pow(r62274, r62275);
        double r62277 = r62271 - r62276;
        double r62278 = t;
        double r62279 = l;
        double r62280 = r62278 / r62279;
        double r62281 = pow(r62280, r62275);
        double r62282 = r62275 * r62281;
        double r62283 = r62271 + r62282;
        double r62284 = r62277 / r62283;
        double r62285 = sqrt(r62284);
        double r62286 = asin(r62285);
        return r62286;
}

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 2019304 
(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)))))))