Average Error: 13.2 → 0.2
Time: 10.2s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\frac{\tan y \cdot \tan y}{\tan y - \tan z} - \tan z \cdot \frac{\tan z}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\frac{\tan y \cdot \tan y}{\tan y - \tan z} - \tan z \cdot \frac{\tan z}{\tan y - \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r164799 = x;
        double r164800 = y;
        double r164801 = z;
        double r164802 = r164800 + r164801;
        double r164803 = tan(r164802);
        double r164804 = a;
        double r164805 = tan(r164804);
        double r164806 = r164803 - r164805;
        double r164807 = r164799 + r164806;
        return r164807;
}
↓
double f(double x, double y, double z, double a) {
        double r164808 = x;
        double r164809 = y;
        double r164810 = tan(r164809);
        double r164811 = r164810 * r164810;
        double r164812 = z;
        double r164813 = tan(r164812);
        double r164814 = r164810 - r164813;
        double r164815 = r164811 / r164814;
        double r164816 = r164813 / r164814;
        double r164817 = r164813 * r164816;
        double r164818 = r164815 - r164817;
        double r164819 = 1.0;
        double r164820 = r164810 * r164813;
        double r164821 = r164819 - r164820;
        double r164822 = r164818 / r164821;
        double r164823 = a;
        double r164824 = tan(r164823);
        double r164825 = r164822 - r164824;
        double r164826 = r164808 + r164825;
        return r164826;
}

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 13.2

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 flip-+0.2

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

  7. Applied div-sub0.2

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

  9. Applied *-un-lft-identity0.2

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

  10. Applied times-frac0.2

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

  11. Simplified0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020057 
(FPCore (x y z a)
  :name "(+ x (- (tan (+ y z)) (tan a)))"
  :precision binary64
  :pre (and (or (== x 0.0) (<= 0.5884142 x 505.5909)) (or (<= -1.796658e+308 y -9.425585e-310) (<= 1.284938e-309 y 1.7512240000000001e+308)) (or (<= -1.7767070000000002e+308 z -8.599796e-310) (<= 3.293145e-311 z 1.725154e+308)) (or (<= -1.796658e+308 a -9.425585e-310) (<= 1.284938e-309 a 1.7512240000000001e+308)))
  (+ x (- (tan (+ y z)) (tan a))))