Random Jason Timeout Test 012

Average Error: 60.4 → 59.5

Time: 1.3m

Precision: 64

• could not determine a ground truth for program body

  1. a = 5.03993005917793e+140

Math

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

↓

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

C

double f(double a) {
        double r1523943 = a;
        double r1523944 = cosh(r1523943);
        double r1523945 = r1523943 * r1523943;
        double r1523946 = fmod(r1523944, r1523945);
        double r1523947 = log1p(r1523943);
        double r1523948 = pow(r1523946, r1523947);
        double r1523949 = acos(r1523948);
        return r1523949;
}

↓

double f(double a) {
        double r1523950 = a;
        double r1523951 = cosh(r1523950);
        double r1523952 = r1523950 * r1523950;
        double r1523953 = fmod(r1523951, r1523952);
        double r1523954 = exp(r1523953);
        double r1523955 = log(r1523954);
        double r1523956 = log1p(r1523950);
        double r1523957 = pow(r1523955, r1523956);
        double r1523958 = acos(r1523957);
        double r1523959 = sqrt(r1523958);
        double r1523960 = r1523959 * r1523959;
        return r1523960;
}

Error

Bits error versus a

Derivation

1. Initial program 60.4

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

3. Applied add-log-exp 59.5

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

5. Applied add-sqr-sqrt 59.5

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

6. Final simplification 59.5

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

Reproduce

herbie shell --seed 2019151 +o rules:numerics
(FPCore (a)
  :name "Random Jason Timeout Test 012"
  (acos (pow (fmod (cosh a) (* a a)) (log1p a))))