Average Error: 10.1 → 10.1
Time: 50.9s
Precision: 64
Internal Precision: 384
\[\sin^{-1} \left(\sqrt{\frac{1 - {\left(\frac{Om}{Omc}\right)}^{2}}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]
↓
\[\sin^{-1} \left(\sqrt{\frac{1 - \log \left(e^{{\left(\frac{Om}{Omc}\right)}^{2}}\right)}{1 + 2 \cdot {\left(\frac{t}{\ell}\right)}^{2}}}\right)\]

Error

Bits error versus t

Bits error versus l

Bits error versus Om

Bits error versus Omc

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. Using strategy rm

  3. Applied add-log-exp10.1

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

Runtime

Time bar (total: 50.9s)Debug logProfile

herbie shell --seed '#(1070227846 1561819246 480764335 4016816270 2602869839 2117310382)' +o rules:numerics
(FPCore (t l Om Omc)
  :name "Toniolo and Linder, Equation (2)"
  (asin (sqrt (/ (- 1 (pow (/ Om Omc) 2)) (+ 1 (* 2 (pow (/ t l) 2)))))))