Random Jason Timeout Test 012

Average Error: 61.2 → 60.3

Time: 36.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 3.3915171398033327e+295

Math

\[\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left(a \cdot a\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)\]

↓

\[\log \left(e^{\cos^{-1} \left({\left(\log \left(e^{\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)\]

C

double f(double a) {
        double r5928 = a;
        double r5929 = cosh(r5928);
        double r5930 = r5928 * r5928;
        double r5931 = fmod(r5929, r5930);
        double r5932 = log1p(r5928);
        double r5933 = pow(r5931, r5932);
        double r5934 = acos(r5933);
        return r5934;
}

↓

double f(double a) {
        double r5935 = a;
        double r5936 = cosh(r5935);
        double r5937 = 2.0;
        double r5938 = pow(r5935, r5937);
        double r5939 = fmod(r5936, r5938);
        double r5940 = exp(r5939);
        double r5941 = log(r5940);
        double r5942 = log1p(r5935);
        double r5943 = pow(r5941, r5942);
        double r5944 = acos(r5943);
        double r5945 = exp(r5944);
        double r5946 = log(r5945);
        return r5946;
}

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-exp 60.3

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

5. Applied add-log-exp 60.3

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

6. Simplified 61.2

   \[\leadsto \log \color{blue}{\left(e^{\cos^{-1} \left({\left(\left(\cosh a\right) \bmod \left({a}^{2}\right)\right)}^{\left(\mathsf{log1p}\left(a\right)\right)}\right)}\right)}\]
7. Using strategy rm

8. Applied add-log-exp 60.3

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

9. Final simplification 60.3

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

Reproduce

herbie shell --seed 2020047 
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  :precision binary64
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))