Average Error: 13.1 → 0.3
Time: 45.7s
Precision: 64
\[\left(x = 0 \lor 0.5884142 \le x \le 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \le y \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.751224 \cdot 10^{+308}\right) \land \left(-1.776707 \cdot 10^{+308} \le z \le -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \le z \le 1.725154 \cdot 10^{+308}\right) \land \left(-1.796658 \cdot 10^{+308} \le a \le -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.751224 \cdot 10^{+308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[\sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \frac{\sin y \cdot \tan z}{\cos y}} - \tan a\right)} + x\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
\sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \frac{\sin y \cdot \tan z}{\cos y}} - \tan a\right)} + x
double f(double x, double y, double z, double a) {
        double r2585849 = x;
        double r2585850 = y;
        double r2585851 = z;
        double r2585852 = r2585850 + r2585851;
        double r2585853 = tan(r2585852);
        double r2585854 = a;
        double r2585855 = tan(r2585854);
        double r2585856 = r2585853 - r2585855;
        double r2585857 = r2585849 + r2585856;
        return r2585857;
}
↓
double f(double x, double y, double z, double a) {
        double r2585858 = y;
        double r2585859 = tan(r2585858);
        double r2585860 = z;
        double r2585861 = tan(r2585860);
        double r2585862 = r2585859 + r2585861;
        double r2585863 = 1.0;
        double r2585864 = r2585861 * r2585859;
        double r2585865 = r2585863 - r2585864;
        double r2585866 = r2585862 / r2585865;
        double r2585867 = a;
        double r2585868 = tan(r2585867);
        double r2585869 = r2585866 - r2585868;
        double r2585870 = r2585869 * r2585869;
        double r2585871 = sin(r2585858);
        double r2585872 = r2585871 * r2585861;
        double r2585873 = cos(r2585858);
        double r2585874 = r2585872 / r2585873;
        double r2585875 = r2585863 - r2585874;
        double r2585876 = r2585862 / r2585875;
        double r2585877 = r2585876 - r2585868;
        double r2585878 = r2585870 * r2585877;
        double r2585879 = cbrt(r2585878);
        double r2585880 = x;
        double r2585881 = r2585879 + r2585880;
        return r2585881;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 13.1

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  2. Using strategy rm

  3. Applied tan-sum0.2

    \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right)\]
  4. Using strategy rm

  5. Applied add-log-exp0.2

    \[\leadsto x + \left(\frac{\tan y + \tan z}{1 - \color{blue}{\log \left(e^{\tan y \cdot \tan z}\right)}} - \tan a\right)\]
  6. Using strategy rm

  7. Applied add-cbrt-cube0.3

    \[\leadsto x + \color{blue}{\sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \log \left(e^{\tan y \cdot \tan z}\right)} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \log \left(e^{\tan y \cdot \tan z}\right)} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \log \left(e^{\tan y \cdot \tan z}\right)} - \tan a\right)}}\]

  8. Simplified0.3

    \[\leadsto x + \sqrt[3]{\color{blue}{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)}}\]
  9. Using strategy rm

  10. Applied tan-quot0.3

    \[\leadsto x + \sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \color{blue}{\frac{\sin y}{\cos y}}} - \tan a\right)}\]

  11. Applied associate-*r/0.3

    \[\leadsto x + \sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \color{blue}{\frac{\tan z \cdot \sin y}{\cos y}}} - \tan a\right)}\]

  12. Final simplification0.3

    \[\leadsto \sqrt[3]{\left(\left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right) \cdot \left(\frac{\tan y + \tan z}{1 - \tan z \cdot \tan y} - \tan a\right)\right) \cdot \left(\frac{\tan y + \tan z}{1 - \frac{\sin y \cdot \tan z}{\cos y}} - \tan a\right)} + x\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :pre (and (or (== x 0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.751224e+308)) (or (<= -1.776707e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.751224e+308)))
  (+ x (- (tan (+ y z)) (tan a))))