Average Error: 13.3 → 0.2
Time: 11.1s
Precision: 64
\[\left(x = 0.0 \lor 0.588414199999999998 \le x \le 505.590899999999976\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le y \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le y \le 1.7512240000000001 \cdot 10^{308}\right) \land \left(-1.7767070000000002 \cdot 10^{308} \le z \le -8.59979600000002 \cdot 10^{-310} \lor 3.29314499999998 \cdot 10^{-311} \le z \le 1.72515400000000009 \cdot 10^{308}\right) \land \left(-1.79665800000000009 \cdot 10^{308} \le a \le -9.425585000000013 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \le a \le 1.7512240000000001 \cdot 10^{308}\right)\]
\[x + \left(\tan \left(y + z\right) - \tan a\right)\]
↓
\[x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \frac{\sin y \cdot \sin z}{\cos z \cdot \cos y}\right) \cdot \sin a}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}\]
x + \left(\tan \left(y + z\right) - \tan a\right)
↓
x + \frac{\left(\tan y + \tan z\right) \cdot \cos a - \left(1 - \frac{\sin y \cdot \sin z}{\cos z \cdot \cos y}\right) \cdot \sin a}{\left(1 - \tan y \cdot \tan z\right) \cdot \cos a}
double f(double x, double y, double z, double a) {
        double r145100 = x;
        double r145101 = y;
        double r145102 = z;
        double r145103 = r145101 + r145102;
        double r145104 = tan(r145103);
        double r145105 = a;
        double r145106 = tan(r145105);
        double r145107 = r145104 - r145106;
        double r145108 = r145100 + r145107;
        return r145108;
}
↓
double f(double x, double y, double z, double a) {
        double r145109 = x;
        double r145110 = y;
        double r145111 = tan(r145110);
        double r145112 = z;
        double r145113 = tan(r145112);
        double r145114 = r145111 + r145113;
        double r145115 = a;
        double r145116 = cos(r145115);
        double r145117 = r145114 * r145116;
        double r145118 = 1.0;
        double r145119 = sin(r145110);
        double r145120 = sin(r145112);
        double r145121 = r145119 * r145120;
        double r145122 = cos(r145112);
        double r145123 = cos(r145110);
        double r145124 = r145122 * r145123;
        double r145125 = r145121 / r145124;
        double r145126 = r145118 - r145125;
        double r145127 = sin(r145115);
        double r145128 = r145126 * r145127;
        double r145129 = r145117 - r145128;
        double r145130 = r145111 * r145113;
        double r145131 = r145118 - r145130;
        double r145132 = r145131 * r145116;
        double r145133 = r145129 / r145132;
        double r145134 = r145109 + r145133;
        return r145134;
}

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 13.3

    \[x + \left(\tan \left(y + z\right) - \tan a\right)\]
  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. Taylor expanded around inf 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020024 
(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))))