Average Error: 61.2 → 60.2
Time: 26.4s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{{\left(\frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{\pi}{2}\right) + \frac{\pi}{2} \cdot \frac{\pi}{2}}\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\frac{{\left(\frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{\pi}{2}\right) + \frac{\pi}{2} \cdot \frac{\pi}{2}}
double f(double a) {
        double r4632 = a;
        double r4633 = cosh(r4632);
        double r4634 = r4632 * r4632;
        double r4635 = fmod(r4633, r4634);
        double r4636 = log1p(r4632);
        double r4637 = pow(r4635, r4636);
        double r4638 = acos(r4637);
        return r4638;
}
↓
double f(double a) {
        double r4639 = atan2(1.0, 0.0);
        double r4640 = 2.0;
        double r4641 = r4639 / r4640;
        double r4642 = 3.0;
        double r4643 = pow(r4641, r4642);
        double r4644 = a;
        double r4645 = cosh(r4644);
        double r4646 = r4644 * r4644;
        double r4647 = fmod(r4645, r4646);
        double r4648 = exp(r4647);
        double r4649 = log(r4648);
        double r4650 = log1p(r4644);
        double r4651 = pow(r4649, r4650);
        double r4652 = asin(r4651);
        double r4653 = pow(r4652, r4642);
        double r4654 = r4643 - r4653;
        double r4655 = r4652 + r4641;
        double r4656 = r4652 * r4655;
        double r4657 = r4641 * r4641;
        double r4658 = r4656 + r4657;
        double r4659 = r4654 / r4658;
        return r4659;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.2

    \[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  2. Using strategy rm

  3. Applied add-log-exp60.2

    \[\leadsto \cos^{-1} \left({\color{blue}{\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
  4. Using strategy rm

  5. Applied acos-asin60.2

    \[\leadsto \color{blue}{\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
  6. Using strategy rm

  7. Applied flip3--60.2

    \[\leadsto \color{blue}{\frac{{\left(\frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\frac{\pi}{2} \cdot \frac{\pi}{2} + \left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{\pi}{2} \cdot \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}}\]

  8. Simplified60.2

    \[\leadsto \frac{{\left(\frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\color{blue}{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{\pi}{2}\right) + \frac{\pi}{2} \cdot \frac{\pi}{2}}}\]

  9. Final simplification60.2

    \[\leadsto \frac{{\left(\frac{\pi}{2}\right)}^{3} - {\left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\right)}^{3}}{\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) \cdot \left(\sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right) + \frac{\pi}{2}\right) + \frac{\pi}{2} \cdot \frac{\pi}{2}}\]

Reproduce

herbie shell --seed 2019346 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))