Average Error: 61.2 → 60.3
Time: 26.3s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\pi}{2} - \sin^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)
↓
\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)
double f(double a) {
        double r3168 = a;
        double r3169 = cosh(r3168);
        double r3170 = r3168 * r3168;
        double r3171 = fmod(r3169, r3170);
        double r3172 = log1p(r3168);
        double r3173 = pow(r3171, r3172);
        double r3174 = acos(r3173);
        return r3174;
}
↓
double f(double a) {
        double r3175 = atan2(1.0, 0.0);
        double r3176 = 2.0;
        double r3177 = r3175 / r3176;
        double r3178 = a;
        double r3179 = cosh(r3178);
        double r3180 = r3178 * r3178;
        double r3181 = fmod(r3179, r3180);
        double r3182 = exp(r3181);
        double r3183 = log(r3182);
        double r3184 = log1p(r3178);
        double r3185 = pow(r3183, r3184);
        double r3186 = asin(r3185);
        double r3187 = r3177 - r3186;
        return r3187;
}

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-exp60.3

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

  5. Applied acos-asin60.3

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

  6. Final simplification60.3

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

Reproduce

herbie shell --seed 2020025 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))