Average Error: 61.1 → 59.3
Time: 39.8s
Precision: 64
\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]
↓
\[\frac{\pi}{2} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\]
\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} - \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)} \cdot \sqrt{\sin^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}
double f(double a) {
        double r7536 = a;
        double r7537 = cosh(r7536);
        double r7538 = r7536 * r7536;
        double r7539 = fmod(r7537, r7538);
        double r7540 = log1p(r7536);
        double r7541 = pow(r7539, r7540);
        double r7542 = acos(r7541);
        return r7542;
}
↓
double f(double a) {
        double r7543 = atan2(1.0, 0.0);
        double r7544 = 2.0;
        double r7545 = r7543 / r7544;
        double r7546 = a;
        double r7547 = cosh(r7546);
        double r7548 = r7546 * r7546;
        double r7549 = fmod(r7547, r7548);
        double r7550 = log1p(r7546);
        double r7551 = pow(r7549, r7550);
        double r7552 = asin(r7551);
        double r7553 = sqrt(r7552);
        double r7554 = r7553 * r7553;
        double r7555 = r7545 - r7554;
        return r7555;
}

Error

Bits error versus a

Derivation

  1. Initial program 61.1

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

  3. Applied acos-asin61.1

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

  5. Applied add-sqr-sqrt59.3

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

  6. Final simplification59.3

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

Reproduce

herbie shell --seed 2020044 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))