Average Error: 13.2 → 0.3
Time: 9.8s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \sqrt[3]{{\left(\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \frac{\tan y \cdot \sin z}{\cos z}\right) \cdot \cos a}\right)}^{3}}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \sqrt[3]{{\left(\frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \tan y \cdot \tan z\right) \cdot \sin a}{\left(1 - \frac{\tan y \cdot \sin z}{\cos z}\right) \cdot \cos a}\right)}^{3}}
double f(double x, double y, double z, double a) {
        double r129718 = x;
        double r129719 = y;
        double r129720 = z;
        double r129721 = r129719 + r129720;
        double r129722 = tan(r129721);
        double r129723 = a;
        double r129724 = tan(r129723);
        double r129725 = r129722 - r129724;
        double r129726 = r129718 + r129725;
        return r129726;
}
↓
double f(double x, double y, double z, double a) {
        double r129727 = x;
        double r129728 = y;
        double r129729 = tan(r129728);
        double r129730 = z;
        double r129731 = tan(r129730);
        double r129732 = r129729 + r129731;
        double r129733 = a;
        double r129734 = cos(r129733);
        double r129735 = r129732 * r129734;
        double r129736 = 1.0;
        double r129737 = r129729 * r129731;
        double r129738 = r129736 - r129737;
        double r129739 = sin(r129733);
        double r129740 = r129738 * r129739;
        double r129741 = r129735 - r129740;
        double r129742 = sin(r129730);
        double r129743 = r129729 * r129742;
        double r129744 = cos(r129730);
        double r129745 = r129743 / r129744;
        double r129746 = r129736 - r129745;
        double r129747 = r129746 * r129734;
        double r129748 = r129741 / r129747;
        double r129749 = 3.0;
        double r129750 = pow(r129748, r129749);
        double r129751 = cbrt(r129750);
        double r129752 = r129727 + r129751;
        return r129752;
}

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-quot13.3

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

  4. Applied tan-sum0.2

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

  5. Applied frac-sub0.2

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

  7. Applied tan-quot0.2

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

  8. Applied associate-*r/0.2

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

  10. Applied add-cbrt-cube0.3

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

  11. Applied add-cbrt-cube0.3

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

  12. Applied cbrt-unprod0.3

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

  13. Applied add-cbrt-cube0.3

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

  14. Applied cbrt-undiv0.3

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

  15. Simplified0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2020065 
(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))))