Average Error: 0.2 → 0.4
Time: 13.7s
Precision: 64
\[\frac{a}{-\cos^{-1} a}\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\cos^{-1} a \cdot \frac{-1}{a}}\right)\right)\]
\frac{a}{-\cos^{-1} a}
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\cos^{-1} a \cdot \frac{-1}{a}}\right)\right)
double f(double a) {
        double r92784 = a;
        double r92785 = acos(r92784);
        double r92786 = -r92785;
        double r92787 = r92784 / r92786;
        return r92787;
}
↓
double f(double a) {
        double r92788 = 1.0;
        double r92789 = a;
        double r92790 = acos(r92789);
        double r92791 = -1.0;
        double r92792 = r92791 / r92789;
        double r92793 = r92790 * r92792;
        double r92794 = r92788 / r92793;
        double r92795 = expm1(r92794);
        double r92796 = log1p(r92795);
        return r92796;
}

Error

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\frac{a}{-\cos^{-1} a}\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.2

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\frac{a}{-\cos^{-1} a}\right)\right)}\]
  4. Using strategy rm

  5. Applied clear-num0.3

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\color{blue}{\frac{1}{\frac{-\cos^{-1} a}{a}}}\right)\right)\]

  6. Simplified0.3

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\color{blue}{-\frac{\cos^{-1} a}{a}}}\right)\right)\]
  7. Using strategy rm

  8. Applied div-inv0.4

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{-\color{blue}{\cos^{-1} a \cdot \frac{1}{a}}}\right)\right)\]

  9. Final simplification0.4

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\frac{1}{\cos^{-1} a \cdot \frac{-1}{a}}\right)\right)\]

Reproduce

herbie shell --seed 2019194 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 001"
  (/ a (- (acos a))))