Average Error: 25.0 → 0.6
Time: 17.5s
Precision: 64
\[\frac{\sin \left(x + 1\right) + 1}{\frac{1}{2}}\]
\[\frac{1 + \left(\log \left(e^{\cos 1 \cdot \sin x}\right) + \cos x \cdot \sin 1\right)}{\frac{1}{2}}\]
\frac{\sin \left(x + 1\right) + 1}{\frac{1}{2}}
\frac{1 + \left(\log \left(e^{\cos 1 \cdot \sin x}\right) + \cos x \cdot \sin 1\right)}{\frac{1}{2}}
double f(double x) {
        double r34447959 = x;
        double r34447960 = 1.0;
        double r34447961 = r34447959 + r34447960;
        double r34447962 = sin(r34447961);
        double r34447963 = r34447962 + r34447960;
        double r34447964 = 2.0;
        double r34447965 = r34447960 / r34447964;
        double r34447966 = r34447963 / r34447965;
        return r34447966;
}

double f(double x) {
        double r34447967 = 1.0;
        double r34447968 = cos(r34447967);
        double r34447969 = x;
        double r34447970 = sin(r34447969);
        double r34447971 = r34447968 * r34447970;
        double r34447972 = exp(r34447971);
        double r34447973 = log(r34447972);
        double r34447974 = cos(r34447969);
        double r34447975 = sin(r34447967);
        double r34447976 = r34447974 * r34447975;
        double r34447977 = r34447973 + r34447976;
        double r34447978 = r34447967 + r34447977;
        double r34447979 = 2.0;
        double r34447980 = r34447967 / r34447979;
        double r34447981 = r34447978 / r34447980;
        return r34447981;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 25.0

    \[\frac{\sin \left(x + 1\right) + 1}{\frac{1}{2}}\]
  2. Using strategy rm
  3. Applied sin-sum0.5

    \[\leadsto \frac{\color{blue}{\left(\sin x \cdot \cos 1 + \cos x \cdot \sin 1\right)} + 1}{\frac{1}{2}}\]
  4. Using strategy rm
  5. Applied add-log-exp0.6

    \[\leadsto \frac{\left(\color{blue}{\log \left(e^{\sin x \cdot \cos 1}\right)} + \cos x \cdot \sin 1\right) + 1}{\frac{1}{2}}\]
  6. Final simplification0.6

    \[\leadsto \frac{1 + \left(\log \left(e^{\cos 1 \cdot \sin x}\right) + \cos x \cdot \sin 1\right)}{\frac{1}{2}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "(sin(x+1)+1)/(1/2)"
  (/ (+ (sin (+ x 1.0)) 1.0) (/ 1.0 2.0)))