Average Error: 13.5 → 0.2
Time: 16.3s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \left(\frac{\log \left(e^{\sin y \cdot \cos z}\right) + \cos y \cdot \sin z}{\left(1 - \frac{\tan y \cdot \sin z}{\cos z}\right) \cdot \left(\cos y \cdot \cos z\right)} - \tan a\right)\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \left(\frac{\log \left(e^{\sin y \cdot \cos z}\right) + \cos y \cdot \sin z}{\left(1 - \frac{\tan y \cdot \sin z}{\cos z}\right) \cdot \left(\cos y \cdot \cos z\right)} - \tan a\right)
double f(double x, double y, double z, double a) {
        double r194721 = x;
        double r194722 = y;
        double r194723 = z;
        double r194724 = r194722 + r194723;
        double r194725 = tan(r194724);
        double r194726 = a;
        double r194727 = tan(r194726);
        double r194728 = r194725 - r194727;
        double r194729 = r194721 + r194728;
        return r194729;
}
↓
double f(double x, double y, double z, double a) {
        double r194730 = x;
        double r194731 = y;
        double r194732 = sin(r194731);
        double r194733 = z;
        double r194734 = cos(r194733);
        double r194735 = r194732 * r194734;
        double r194736 = exp(r194735);
        double r194737 = log(r194736);
        double r194738 = cos(r194731);
        double r194739 = sin(r194733);
        double r194740 = r194738 * r194739;
        double r194741 = r194737 + r194740;
        double r194742 = 1.0;
        double r194743 = tan(r194731);
        double r194744 = r194743 * r194739;
        double r194745 = r194744 / r194734;
        double r194746 = r194742 - r194745;
        double r194747 = r194738 * r194734;
        double r194748 = r194746 * r194747;
        double r194749 = r194741 / r194748;
        double r194750 = a;
        double r194751 = tan(r194750);
        double r194752 = r194749 - r194751;
        double r194753 = r194730 + r194752;
        return r194753;
}

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 13.5

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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 tan-quot0.2

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

  6. Applied associate-*r/0.2

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

  8. Applied tan-quot0.2

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

  9. Applied tan-quot0.2

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

  10. Applied frac-add0.2

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

  11. Applied associate-/l/0.2

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

  13. Applied add-log-exp0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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))))